OptiStruct Verification Problems - Altair University...This manual presents solved verification...
Transcript of OptiStruct Verification Problems - Altair University...This manual presents solved verification...
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ContentsIntellectual Property Rights Notice.............................................................................iiiTechnical Support............................................................................................................vii
Verification Problems...................................................................................................... 9
Accessing the Model Files.................................................................................................10NAFEMS Linear Elastic......................................................................................................11
OS-V: 0010 Elliptic Membrane.................................................................................. 11OS-V: 0020 Cylinder Shell Patch............................................................................... 14OS-V: 0030 Radial Point Load on a Hemisphere.......................................................... 16OS-V: 0040 Z-Section Cantilever...............................................................................18OS-V: 0050 Skew Plate Normal Pressure....................................................................20OS-V: 0060 Thick Plate Pressure...............................................................................22OS-V: 0070 Solid Cylinder/Taper/Sphere - Temperature............................................... 24OS-V: 0080 Buckling of Shells and Composites with Offset........................................... 26OS-V: 0085 Plane Strain: Analysis of Pressure Vessel.................................................. 31
NAFEMS Thermo-elastic....................................................................................................34OS-V: 0100 Membrane with Hot-Spot........................................................................ 34
NAFEMS Heat Transfer..................................................................................................... 36OS-V: 0110 One Dimensional Transient Heat Transfer.................................................. 36OS-V: 0120 Two-Dimensional Heat Transfer with Convection.........................................38
NAFEMS Nonlinear Quasi-static Analysis............................................................................. 40OS-V: 0200 Simply-Supported Thin Square Plate........................................................ 40OS-V: 0210 Simply-Supported Thick Square Plate....................................................... 43OS-V: 0220 3D Punch (Rounded Edges).....................................................................46OS-V: 0230 3D Loaded Pin.......................................................................................51OS-V: 0240 3D Steel Roller on Rubber...................................................................... 54OS-V: 0250 3D Sheet Metal Forming.........................................................................57OS-V: 0260 Shell Bending under a Tip Load...............................................................59
NAFEMS Frequency Response Analysis............................................................................... 61OS-V: 0300 Deep Simply-Supported Beam Harmonic Forced Vibration Response.............. 61OS-V: 0310 Deep Simply-Supported Beam Periodic Forced Vibration Response................ 63OS-V: 0320 Deep Simply-Supported Beam Random Forced Vibration Response................65OS-V: 0330 Deep Simply-Supported Beam Transient Forced Vibration Response...............67OS-V: 0340 Simply-Supported Thin Square Plate Harmonic ForcedVibration Response.................................................................................................. 69OS-V: 0350 Simply-Supported Thin Square Plate Periodic Forced Vibration Response........ 71OS-V: 0360 Simply-Supported Thin Square Plate Harmonic ForcedVibration Response.................................................................................................. 73OS-V: 0365 Simply-Supported Thin Square Plate Transient ForcedVibration Response.................................................................................................. 75OS-V: 0370 Simply-Supported Thick Square Plate Harmonic ForcedVibration Response.................................................................................................. 77
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OS-V: 0375 Simply-Supported Thick Square Plate Periodic Forced Vibration Response.......79OS-V: 0380 Simply-Supported Thick Square Plate Random ForcedVibration Response.................................................................................................. 81OS-V: 0385 Simply-Supported Thick Square Plate Transient ForcedVibration Response.................................................................................................. 83
NAFEMS Normal Modes Analysis........................................................................................85OS-V: 0400 Pin-ended Double Cross..........................................................................85OS-V: 0410 Cantilever with Off-Center Point Masses....................................................88OS-V: 0415 Deep Simply-Supported Beam................................................................. 90OS-V: 0420 Free Thin Square Plate...........................................................................92OS-V: 0425 Clamped Thin Rhombic Plate...................................................................94OS-V: 0430 Cantilevered Thin Square Plate................................................................96OS-V: 0435 Clamped Thick Rhombic Plate................................................................100OS-V: 0440 Cantilevered Tapered Membrane............................................................ 102OS-V: 0450 Free Cylinder: Axi-symmetric Vibration................................................... 104OS-V: 0455 Simply-Supported Solid Square Plate......................................................107OS-V: 0460 Dynamic Behavior of a Fluid-containing Structure using MFLUID................. 110
NAFEMS Composites.......................................................................................................116OS-V: 0500 Laminated Strip................................................................................... 116OS-V: 0510 Wrapped Thick Cylinder........................................................................ 118OS-V: 0520 Sandwich Shell.................................................................................... 121OS-V: 0530 Composite Shell Bending...................................................................... 123
Response Spectrum Analysis........................................................................................... 128OS-V: 0600 Simply Support Beam...........................................................................128
Elements.......................................................................................................................130OS-V: 0700 Twisted Cantilever Beam.......................................................................130OS-V: 0710 Curved Cantilever Beam....................................................................... 132OS-V: 0720 Straight Cantilever Beam...................................................................... 134OS-V: 0730 Scordelis-Lo Roof................................................................................. 137OS-V: 0750 Radial Stretching of a Cylinder.............................................................. 139
Materials....................................................................................................................... 142OS-V: 0800 Hyperelastic Material Verification............................................................142OS-V: 0810 Hyperelastic Large Displacement Nonlinear Analysis with aPressurized Rubber Disk......................................................................................... 149
Index.................................................................................................................................152
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Intellectual Property Rights NoticeCopyrights, Trademarks, Trade Secrets, Patents & Third Party Software Licenses
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OptiStruct Verification ProblemsIntellectual Property Rights Notice p.iv
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OptiStruct Verification ProblemsIntellectual Property Rights Notice p.vi
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OptiStruct Verification ProblemsTechnical Support p.viii
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Verification Problems 1
Verification Problems
This manual presents solved verification models including NAFEMS problems.
This chapter covers the following:
• Accessing the Model Files (p. 10)
• NAFEMS Linear Elastic (p. 11)
• NAFEMS Thermo-elastic (p. 34)
• NAFEMS Heat Transfer (p. 36)
• NAFEMS Nonlinear Quasi-static Analysis (p. 40)
• NAFEMS Frequency Response Analysis (p. 61)
• NAFEMS Normal Modes Analysis (p. 85)
• NAFEMS Composites (p. 116)
• Response Spectrum Analysis (p. 128)
• Elements (p. 130)
• Materials (p. 142)
The verification problems use model files that are located in the demos directory of the softwareinstallation. In the verification problems, file paths are referenced as /../.
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OptiStruct Verification ProblemsVerification Problems p.10
Accessing the Model FilesRequired model files for the models you build.
1. The OptiStruct verification problem model files are located on /demos/hwsolvers/optistruct/verification.
Note: The files may require unzipping before proceeding with the verificationproblem. When extracting zipped files, preserve any directory structure included in thefile package.
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OptiStruct Verification ProblemsVerification Problems p.11
NAFEMS Linear Elastic
OS-V: 0010 Elliptic MembraneTest No. LE1The model is a thin plate of thickness 0.1m subjected to a uniform pressure for linear static analysis.OptiStruct examines the direct stress at the point on inside the ellipse on the x-axis.
Figure 1:
Benchmark ModelSecond order Hexahedral, Penta, Tetra, Quad and Tria elements are used to create the coarse and finemesh. A uniform outward pressure of 10 MPa is applied on the outer face. The pressure is converted toforce and is applied to the nodes for Quad8 and Tria6 elements.
The material properties are:
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Linear Static Analysis ResultsAll results are normalized with the target value (92.7 MPa).
Direct Stress at Point D(MPa)
Normalized with the TargetValue
Solid Hexahedral
Hex8 coarse 63.15 1.467933492
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OptiStruct Verification ProblemsVerification Problems p.12
Direct Stress at Point D(MPa)
Normalized with the TargetValue
Hex20 coarse 87.46 1.059913103
Hex8 fine 79.8 1.161654135
Hex20 fine 91.01 1.018569388
Solid Wedges:
Penta6 coarse 48.68 1.904272802
Penta15 coarse 95.21 0.973637223
Penta6 fine 67.3 1.377414562
Penta15 fine 94.28 0.983241409
Solid Tetrahedral:
Tetra4 coarse 53.34 1.737907762
Tetra10 coarse 95.96 0.966027511
Tetra4 fine 66.56 1.392728365
Tetra10 fine 95.28 0.972921914
Quad Shells:
Quad4 coarse 61.83 1.499272198
Quad8 coarse 86.67 1.069574247
Quad4 fine 79.7 1.163111669
Quad8 fine 91.48 1.013336248
Triangular Shells:
Tria3 coarse 54.06 1.714761376
Tria6 coarse 97.07 0.954980942
Tria3 fine 74.21 1.249157795
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OptiStruct Verification ProblemsVerification Problems p.13
Direct Stress at Point D(MPa)
Normalized with the TargetValue
Tria6 fine 96.64 0.959230132
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/LE1Hex8C.fem
/LE1Hex20C.fem
/LE1Hex8F.fem
/LE1Hex20F.fem
/LE1Pen6C.fem
/LE1Pen15C.fem
/LE1Pen6F.fem
/LE1Pen15F.fem
/LE1Tet4C.fem
/LE1Tet10C.fem
/LE1Tet4F.fem
/LE1Tet10F.fem
/LE1Quad4C.fem
/LE1Quad8C.fem
/LE1Quad4F.fem
/LE1Quad8F.fem
/LE1Tria3C.fem
/LE1Tria6C.fem
/LE1Tria3F.fem
/LE1Tria6F.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.14
OS-V: 0020 Cylinder Shell PatchTest No. LE2OptiStruct examines the outer surface tangential stress at point E for linear static analysis.
Figure 2:
Benchmark ModelQuad8 elements are used to create a mesh on the cylindrical patch with 4 elements for the loadcase 1 and Quad4 elements are used to create a mesh with 16 elements for the load case 2. Allthe translations and rotations are constrained at edge AB, z-translation and normal rotations areconstrained at the edges AD and BC. For Load case 1 a uniform normal edge moment of 1.0 kNm/m isapplied on the edge DC and for the Load case 2, uniform outward normal pressure of 0.6 MPa is appliedon the mid surface ABCD and a tangential outward normal pressure of 60.0 MPa is applied on edge DC.
The material properties are:
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Linear Static Analysis ResultsAll results are normalized with the target value (60.0 MPa).
Surface Tangential Stress at Point E (MPa)
Normalized with the TargetValue
Load Case 1: Quad8 58.03 1.033947958
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OptiStruct Verification ProblemsVerification Problems p.15
Surface Tangential Stress at Point E (MPa)
Normalized with the TargetValue
Load Case 2: Quad4 58.92 1.018329939
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
le2quad8lc1.fem
le2quad4lc2.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.16
OS-V: 0030 Radial Point Load on a HemisphereTest No. LE3The model is a hemispherical shell subjected to concentrated radial loads at its free edges. It examinesthe performance of the three-dimensional shell to model local bending behavior under conditions wherethe deformations are primarily due to bending.
Figure 3:
Benchmark Model4-node, first order CQUAD4 elements are benchmarked in LE3. The hemisphere is 10m in radius and0.04m in radial thickness. Two pairs of identical loads, 4000N, are applied at the free edge of thehemisphere, and are at right angles to each other. One pair of the loads is directed inwards (towardthe center) of the hemisphere, while the second pair is directed outward from the center, producingdeformation of compression in one direction and elongation in another. Since both the geometry andloads are symmetrical, only a quarter of the hemisphere is modeled. Symmetric boundary constraintsare applied on edges AE and CE. The z-translation at point E is fixed, and all displacements on edge ACare free. The test also requires the mesh of the hemisphere to have equally spaced nodes on edges AC,CE, EA, BG, DG, and FG. The target is x-translation at point A, with a target value of 0.185m.
The material properties for the hemisphere are:
E68.25 GPa
0.3
Linear Static Analysis ResultsAll results are normalized with the target values of x translation at point A.
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OptiStruct Verification ProblemsVerification Problems p.17
ElementType
Mesh Configuration nacx nce x nea
CQUAD4 4 x 4 x 4 8 x 8 x 816 x
16 x 1632 x
32 x 3264 x
64 x 64
0.9865 1.0200 1.0076 1.0032 1.0016
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/LE3.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.18
OS-V: 0040 Z-Section CantileverTest No. LE5OptiStruct examines the axial (x-x) stress (compression) at mid-surface, point A for linear staticanalysis.
Figure 4:
Benchmark ModelQuad4 and Quad8 elements are used to create a uniform mesh of 8 elements along the length with oneelement across width of flange. All the displacements at one end are maintained zero, at the other endtwo uniformly distributed force of 0.6MN each are applied.
The material properties are:
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Linear Static Analysis ResultsAll results are normalized with the target value (-108 MPa Compression).
Quadrilateral Shells Axial Stress (x-x) at Mid-surface Point A (MPa)
Normalized with the TargetValue
Quad4 -112.2 0.962566845
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OptiStruct Verification ProblemsVerification Problems p.19
Quadrilateral Shells Axial Stress (x-x) at Mid-surface Point A (MPa)
Normalized with the TargetValue
Quad8 -110.9 0.973850316
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/LE5Quad4.fem
/LE5Quad8.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.20
OS-V: 0050 Skew Plate Normal PressureTest No. LE6OptiStruct examines the maximum principal stress on the lower surface at the plate center point E forlinear static analysis.
Figure 5:
Benchmark ModelQuad4 and Quad8 elements are used to create a uniform mesh on the skew plate with 4 elementsas coarse mesh and 16 elements as fine mesh. The plate is simply supported at all the four edges. ANormal pressure of -0.7 KPa is applied on the face of the plate in the vertical z-direction.
The material properties are:
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Linear Static Analysis ResultsAll results are normalized with the target value (0.802 MPa).
Quadrilateral Shell Maximum principal stress onthe lower surface at the platecenter point E (MPa)
Normalized with the TargetValue
Quad8 coarse 0.8294 0.96696407
Quad8 fine 0.7869 1.019189224
Model FilesThe model files used in this example include:
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OptiStruct Verification ProblemsVerification Problems p.21
/demos/hwsolvers/optistruct/verification
/le6quad8c.fem
/le6quad8f.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.22
OS-V: 0060 Thick Plate PressureTest No. LE10The model is a thick plate subjected to uniform normal pressure of 1MPa on the upper surface of theplate. OptiStruct examines the direct stress at the point D for linear static analysis.
Figure 6:
Benchmark ModelSecond order Hexahedral, Penta and Tetra elements are used to create the coarse and fine mesh. Auniform pressure of 1 MPa is applied on the upper surface of the plate.
The material properties are:
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Linear Static Analysis ResultsAll results are normalized with the target value (5.38 MPa).
Direct Stress at Point D(MPa)
Normalized with the TargetValue
Solid Hexahedral:
Hex20 coarse 5.32 1.011278195
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OptiStruct Verification ProblemsVerification Problems p.23
Direct Stress at Point D(MPa)
Normalized with the TargetValue
Hex20 fine 5.58 0.964157706
Solid Wedges:
Penta15 coarse 4.91 1.095723014
Penta15 fine 5.94 0.905723906
Solid Tetrahedral:
Tetra10 coarse 5.741 0.937118969
Tetra10 fine 5.029 1.069795188
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/LE10Hex20C.fem
/LE10Hex20F.fem
/LE10Pyr15C.fem
/LE10Pyr15F.fem
/LE10Tet10C.fem
/LE10Tet10F.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.24
OS-V: 0070 Solid Cylinder/Taper/Sphere - TemperatureTest No. LE11The model is a thick solid cylinder subjected to linear temperature gradient in the radial and axialdirection. OptiStruct examines the direct stress at the point A inside the cylinder on the y axis forlinear static analysis.
Figure 7:
Benchmark ModelSecond order Hexahedral, Penta and Tetra elements are used to create the coarse and fine mesh. ALinear temperature gradient of T°C = (x2 + y2)1/2 + z is applied in the radial and axial direction fromthe center of the cylinder. Only one quarter of the cylinder is considered.
The material properties are:
MAT1 Isotropic
Young's Modulus210 x 103 MPa
Poisson's Ratio0.3
Coefficient of Thermal Expansion2.3 x 10-4/°C
Linear Static Analysis ResultsAll results are normalized with the target value (-105 MPa).
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OptiStruct Verification ProblemsVerification Problems p.25
Direct Stress at Point A(MPa)
Normalized with the TargetValue
Solid Hexahedral:
Hex20 coarse -93.21 1.126488574
Hex20 fine -99.12 1.059322034
Solid Wedges:
Penta15 coarse -100.3 1.046859422
Penta15 fine -103.7 1.012536162
Solid Tetrahedral:
Tetra10 coarse -91.97 1.141676634
Tetra10 fine -98.68 1.064045399
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/LE11Hex20C.fem
/LE11Hex20F.fem
/LE11Pyr15C.fem
/LE11Pyr15F.fem
/LE11Tet10C.fem
/LE11Tet10F.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.26
OS-V: 0080 Buckling of Shells and Composites with OffsetA test of influence of offset on buckling solution for shells, including composite with offset Z0 andelement offset ZOFFS.
Figure 8: FE-Model of the Beam with Boundary Conditions and Loadcases
Benchmark ModelHere, you solve several problems to calculate the critical load on different conditions. The model is asimply supported beam of height 1mm, breadth 2mm and length 100mm with one end constrained inall DOFs and an axial load applied on the other end.
The material properties for the beam are:
MAT1
Young's Modulus1 x 106 N/mm2
Poisson Ratio0.0
Density2 kg/mm3
Thermal Expansion Coefficient1 x 10-4 ºC-1
Reference Temperature for Thermal Loading300ºC
The different case description of the problem are:
1. Buckling without offset.2. Buckling with moment equivalent to offset.3. Buckling with offset created by a frame.4. Buckling with offset applied through ZOFFS.5. Buckling of composite with non-symmetrical layup.6. Buckling of composite with offset.
The theoretical critical buckling load is calculated using the Euler Buckling equation:
(1)
Where,
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OptiStruct Verification ProblemsVerification Problems p.27
Maximum or critical force
Modulus of Elasticity
Area moment of Inertia (second moment of area)
Unsupported length of the beam
Column effective length factor (for one end fixed and the other end free, =2)
Results
Figure 9: First Four Buckling Eigenvalues for Non-offset (z0 = -0.5)
Quantity Theoretical No-offset Normalized
cr(1) 4.1123 4.1208 0.997937
cr(2) 16.449 16.513 0.996124
cr(3) 37.011 37.701 0.981698
cr(4) 102.81 108.19 0.950273
Figure 10: First Four Buckling Eigenvalues for Non-offset + Moment(the effect of offset is simulated by adding a moment at the end of the beam)
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OptiStruct Verification ProblemsVerification Problems p.28
Quantity TheoreticalNo-offset +Moment
Normalized
cr(1) 4.1123 4.1208 0.997937
cr(2) 16.449 16.513 0.996124
cr(3) 37.011 37.701 0.981698
cr(4) 102.81 108.19 0.950273
Figure 11: First Four Buckling Eigenvalues for C-Frame(the effect of offset is simulated by creating a C-shaped frame)
Quantity Theoretical C-Frame Normalized
cr(1) 4.1123 4.1208 0.997937
cr(2) 16.449 16.513 0.996124
cr (3) 37.011 37.700 0.981724
cr(4) 102.81 108.19 0.950273
Figure 12: First Four Buckling Eigenvalues for z-offset (Zoffs = -0.5)
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OptiStruct Verification ProblemsVerification Problems p.29
Quantity Theoretical ZOFFS Normalized
cr(1) 4.1123 4.1208 0.997937
cr(2) 16.449 16.513 0.996124
cr(3) 37.011 37.700 0.981724
cr(4) 102.81 108.19 0.950273
Figure 13: First Four Buckling Eigenvalues for Non-symmetric Layup(since the top layer is very weak, the load is applied to the “strong” layer with an offset of 0.5)
Quantity TheoreticalNon-symmetricLayup
Normalized
cr(1) 4.1123 4.1203 0.998058
cr(2) 16.449 16.510 0.996305
cr(3) 37.011 37.663 0.982689
cr(4) 102.81 107.89 0.952915
Figure 14: First Four Buckling Eigenvalues for Composites with Offset (z0 = -1)
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OptiStruct Verification ProblemsVerification Problems p.30
Quantity TheoreticalOffsetComposite
Normalized
cr(1) 4.1123 4.1203 0.998058
cr(2) 16.449 16.510 0.996305
cr(3) 37.011 37.663 0.982689
cr(4) 102.81 107.89 0.952915
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/s100_buckl.zip
s100comp_buckl.fem
s100compmom_buckl.fem
s100comp_frame_buckl.fem
s100comp_buckl_zoffs.fem
s100comp2ply_buckl.fem
s100compoffs_buckl.fem
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OptiStruct Verification ProblemsVerification Problems p.31
OS-V: 0085 Plane Strain: Analysis of Pressure VesselThis problem examines the expansion of a pressure vessel due to an internal pressure. OptiStructexamines the principal stresses in the pressure vessel, due to the applied loading and boundaryconditions. Two-dimensional plane strain element will be used for this analysis.
Figure 15:
Benchmark ModelQuad4 Plane Strain elements are used to model the quarter symmetric slice of the pressure vessel ofradius 0.1m and thickness 0.020m. Internal pressure of 10,000 Pa which is converted to force andapplied on the nodes of the inner surface of the pressure vessel. A Linear Static analysis is performedon this model.
The material properties are:
Young's Modulus207 x 109 Pa
Poisson's Ratio0.27
Linear Static Analysis Results
ModelHoop Stress
(Pa)
Radial Stress
(Pa)
Theoretical 55455 -10000
OptiStruct 54710 -9205.6
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OptiStruct Verification ProblemsVerification Problems p.32
ModelHoop Stress
(Pa)
Radial Stress
(Pa)
Normalized 1.013 1.086
Figure 16: First Principle Stress (Hoop Stress)
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OptiStruct Verification ProblemsVerification Problems p.33
Figure 17: Third Principle Stress (Radial Stress)
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/Pressure_Vessel_LS.fem
ReferenceMacDonald, Bryan J., "Practical Stress Analysis with Finite Elements" (2nd Ed), page 327-329
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OptiStruct Verification ProblemsVerification Problems p.34
NAFEMS Thermo-elastic
OS-V: 0100 Membrane with Hot-SpotTest No. T1OptiStruct examines the direct stress in y direction at a point D outside the hot-spot for linear thermoselastic analysis.
Figure 18:
Benchmark ModelQuarter model is considered and Quad4 elements with the specific mesh specifications are used formodel building. The hotspot area is maintained at a temperature 100°C.
The material properties are:
Hot-spot Area
Young's Modulus100 x 103 MPa
Poisson's Ratio0.3
Coefficient of thermal expansion1 x 10-5/°C
Remaining Area
Young's modulus100 x 103 MPa
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OptiStruct Verification ProblemsVerification Problems p.35
Poisson's ratio0.3
Coefficient of thermal expansion0.0
Linear Static Analysis ResultsAll results are normalized with the target value (50 MPa).
Quadrilateral ShellsDirect Stress in y Direction at aPoint D, Outside Hot-spot (MPa)
Normalized withthe Target Value
Quad4 45.51 1.098659635
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/T1Quad4.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.36
NAFEMS Heat Transfer
OS-V: 0110 One Dimensional Transient Heat TransferTest No. T3OptiStruct examines the material temperature at point C, 0.08m from point A and the total simulationtime is 32 seconds for transient heat transfer analysis.
Figure 19:
Benchmark ModelThe 2-noded beam elements, Quad4 elements and Quad8 elements are used to build the modelwith 5 elements each for the coarse mesh and 10 elements each for the fine mesh. At time t=0, alltemperature = zero and at time t>0, at one end temperature is zero and at the other end temperatureis 100 sin(πt/40) °C. There is no heat flux perpendicular to the length of the beam.
The material properties are:
Conductivity35.0 W/m°C
Specific Heat440.5 J/kg°C
Density7200 kg/m3
Linear Static Analysis ResultsAll results are normalized with the target value (36.60°C).
Material temperatureat point C, x=0.08m,
time t=32sec (°C)
Normalized withthe Target Value
Beam Elements:
CBEAM coarse 33.6 1.089285714
CBEAM fine 34.58 1.058415269
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OptiStruct Verification ProblemsVerification Problems p.37
Material temperatureat point C, x=0.08m,
time t=32sec (°C)
Normalized withthe Target Value
Quadrilateral Element:
Quad4 coarse 33.6 1.089285714
Quad8 coarse 35.1 1.042735043
Quad4 fine 34.58 1.058415269
Quad8 fine 35.19 1.040068201
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/T3CbeamC.fem
/T3CbeamF.fem
/T3Quad4C.fem
/T3Quad8C.fem
/T3Quad4F.fem
/T3Quad8F.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.38
OS-V: 0120 Two-Dimensional Heat Transfer withConvectionTest No. T4The model is having zero internal heat generation and OptiStruct examines the temperature at point Efor steady state heat transfer analysis.
Figure 20:
Benchmark ModelA 10x6 mesh configuration is created with QUAD4, QUAD8, TRIA3 and TRIA6 elements. One edge ofthe plate is having a prescribed temperature of 100°C, one end insulated and convection to the ambienttemperature at the other two edges.
The material properties are:
Conductivity52.0 W/m°C
Surface Convective Heat Transfer Coefficient750.0 W/m2 °C
Linear Static Analysis ResultsAll results are normalized with the target value (18.30°C).
Shell ElementMaterial Temperature at Point C,x=0.08m, time t=32sec (°C)
Normalized with the Target Value
Quad4 17.77 1.029825549
Quad8 17.1 1.070175439
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OptiStruct Verification ProblemsVerification Problems p.39
Shell ElementMaterial Temperature at Point C,x=0.08m, time t=32sec (°C)
Normalized with the Target Value
Tria3 17.29 1.058415269
Tria6 16.83 1.087344029
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/T4Quad4.fem
/T4Quad8.fem
/T4Tria3.fem
/T4Tria6.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.40
NAFEMS Nonlinear Quasi-static Analysis
OS-V: 0200 Simply-Supported Thin Square PlateTest No. 13OptiStruct is used to investigate the repeated eigenvalues.
Figure 21:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.
The material properties are:
Young’s Modulus200 x 109 N/m2
Poisson’s Ratio0.3
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OptiStruct Verification ProblemsVerification Problems p.41
Density8000 kg/m3
Modal Analysis ResultsThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Mode 1 Mode 2 and 3 Mode 4
f* 2.377 Hz f* 5.942 Hz f* 9.507 Hz
HOE 1.021926053 HOE 1.066977913 HOE 1.076061121
LOE 1.013646055 LOE 1.015552897 LOE 1.053290494
Mode 5 and 6 Mode 7 and 8
f* 11.884 Hz f* 15.449 Hz
HOE 1.176750173 HOE 1.175007606
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OptiStruct Verification ProblemsVerification Problems p.42
Mode 5 and 6 Mode 7 and 8
LOE 1.002869198 LOE 1.065889334
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
Test13HOE.fem
Test13LOE.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.43
OS-V: 0210 Simply-Supported Thick Square PlateTest 21OptiStruct is used to investigate the repeated eigenvalues and the effect of ‘secondary’ restrains.
Figure 22:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Modal Analysis ResultsThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
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OptiStruct Verification ProblemsVerification Problems p.44
Mode 1 Modes 2 and 3 Mode 4
f* 45.897 Hz f* 109.44 Hz f* 167.89 Hz
HOE 1.013827837 HOE 1.044863043 HOE 1.046793653
LOE 1.005851414 LOE 1.002363027 LOE 1.034589005
Modes 5 and 6 Modes 7 and 8
f* 204.51 Hz f* 256.50 Hz
HOE 1.125821617 HOE 1.094829757
LOE 0.993823531 LOE 1.051061511
Model FilesThe model files used in this example include:
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OptiStruct Verification ProblemsVerification Problems p.45
/demos/hwsolvers/optistruct/verification
/Test21HOE.fem
/Test21LOE.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.46
OS-V: 0220 3D Punch (Rounded Edges)Contacts Benchmark 2For Quasi-static analysis using Linear elastic material, geometric non-linearity and nonlinear boundaryconditions.
OptiStruct FE results examine the plot of contact pressure, tangential stress against radial distance fromthe center of contact and relative tangential slip against distance from the center of contact. OptiStructalso examines the 3D contact, stick/slip behavior along the contact plane, compares the linear andquadratic elements and the plasticity.
Figure 23:
Benchmark ModelHexa8 and Hexa20 elements are used to create one quarter model with punch diameter 100mm, punchheight 100mm, foundation diameter 200mm, foundation height 200mm and fillet radius at the edgeof the punch contact is 10mm. A uniform pressure of 100N/mm2 is applied at the top surface of thepunch. The bottom surface of the foundation is fixed. Two different contact properties are used, onewith coefficient of friction 0.0 and the second with coefficient of friction 0.1. The straight edge of thefoundation is considered as the master surface and the nodes on the bottom edge of the punch areselected as the slave surface.
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OptiStruct Verification ProblemsVerification Problems p.47
The material properties are:
Epunch210 kN/mm2
Vpunch0.3
Efoundation70 kN/mm2
Nfoundation0.3
Nonlinear Quasi-static Analysis Results
Figure 24: Axial displacement as a function of the radial coordinate (friction coefficient 0.0 and 0.1) obtained withlinear elastic elements
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OptiStruct Verification ProblemsVerification Problems p.48
Figure 25: Radial displacement as function of the radial coordinate (friction coefficient 0.0 and 0.1) obtained withlinear elastic elements
Figure 26: Axial displacement along top surface of foundation (with friction)
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OptiStruct Verification ProblemsVerification Problems p.49
Figure 27: Radial displacement along top surface of foundation (with friction)
Figure 28: Effect of different friction coefficient and method of fiction handling on the radial displacement of thefoundation edge (Linear Elements)
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/contb2H8.fem
/contb2H8f.fem
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OptiStruct Verification ProblemsVerification Problems p.50
/contb2H20.fem
/contb2H20f.fem
/contb2H8L.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.51
OS-V: 0230 3D Loaded PinContacts Benchmark 4For Quasi-static analysis using Linear elastic material, geometric non-linearity and nonlinear boundaryconditions. OptiStruct FE results examine the plot of contact pressure, tangential stress and relativetangential slip against angle .
Figure 29:
Benchmark ModelHexa8 and Hexa20 elements are used to create one quarter model. The length of the sheet from leftside to the center is 200mm, the inner radius of the sheet is 50mm, the outer radius of the sheet is100mm, height of the sheet is 200mm, length of the pin is 20mm and the thickness of the sheet is10mm. The outer surface of the pin and the inner surface of the sheet are in contact. Two equal pointforces, resulting in a total force on the pin of 100kN is acting on both sides of the pin. The left side ofthe sheet is fixed. A frictional coefficient of 0.1 is acting between the contacts. The nodes along the pinboundary are selected as slave nodes, while the nodes along the strip are specified to be the masternodes.
The material properties for the loaded pin are:
Epin210 kN/mm2
Vpin0.3
Esheet70 kN/mm2
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OptiStruct Verification ProblemsVerification Problems p.52
Vsheet0.3
Nonlinear Quasi-Static Analysis Results
Figure 30: Displacement as a function of the angles obtained with first order elements for the nodes of the sheetcontact surface
Figure 31: Displacement as a function of the angles obtained with second order elements for the nodes of the sheetcontact surface
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OptiStruct Verification ProblemsVerification Problems p.53
Figure 32: Displacement in x-direction for nodes along the pin as a function of the angle
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/contb4H8.fem
/contb4H20.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.54
OS-V: 0240 3D Steel Roller on RubberContacts Benchmark 3For Quasi-static analysis using Linear elastic material, geometric non-linearity and nonlinear boundaryconditions.
OptiStruct FE results examine the horizontal displacement of the point A after 360 degrees’ motion.OptiStruct also examines the 3D deformable-deformable contact, Rolling contact and Incompressiblematerial feature.
Figure 33:
Benchmark ModelHexa8 elements are used to create one half of the model. The Steel is of 20mm width and 30mmradius, the rubber mat is 22mm wide, 20mm in high and 360mm long. The steel roller starts rollingfrom a point 60mm from the left-hand side of the rubber mat. The center of the roller is fixed inhorizontal and vertical direction, for a time period of 0-1 second the bottom surface of the rubber isdisplaced 3mm in the negative y direction, the sheet x-displacement is fixed and there is no rollerrotation. For the time period of 1-2 second the bottom surface of the rubber sheet is held at 3mm y-displacement and rotation of 360 degrees is prescribed to the steel roller where the sheet is free tomove in horizontal direction. There is no force applied on the system and the coefficient of frictionbetween the two surface is 0.3. The nodes on the outer surface of the roll are selected as master nodes,while the nodes on the top surface of the mat are specified as the slave nodes.
The material properties are:
Esteel210 kN/mm2
Nsteel0.3
C10, rubber10 N/mm2 (Neo Hookean material description)
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OptiStruct Verification ProblemsVerification Problems p.55
D1rubber0.0001
Nonlinear Quasi-static Analysis Results
Horizontal Displacement (mm) NAFEMS OptiStruct Normalized
3D first order elements 182.9 182.06 1.00461386
Figure 34: Vertical Forces on the Roller versus Time
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OptiStruct Verification ProblemsVerification Problems p.56
Figure 35: 3D Analysis – Undeformed and Contour Plots of Contact Pressure on Deformed Structure
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/contb5H8.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.57
OS-V: 0250 3D Sheet Metal FormingContacts Benchmark 3For Quasi-static analysis using Elastic plastic material, geometric non-linearity and nonlinear boundaryconditions.
OptiStruct FE results examine the forming angle and angle after the punch is released. OptiStruct alsoexamines the contact features of the rigid and deformable bodies and sliding contact around the circularsurfaces.
Figure 36:
Benchmark ModelHexa8 elements are used to create the half model of the sheet and Quad4 elements are used to modelthe punch and the die. The punch radius is 23.5mm, the die radius is 25mm, the die shoulder radiusis 4mm, width of the tool is 50mm, length of sheet is 120mm, sheet thickness is 1mm and the widthof the sheet is 30mm. The punch stroke is 28.5mm. The bottom surface is fixed. Two different contactproperties are used, one with coefficient of friction 0.0 and the second with coefficient of friction0.1342. For the contacts between the punch and the sheet, punch is considered as master surface andthe sheet as slave and for the contacts between the die and the sheet die is considered as master andsheet as slave.
The material properties are:
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OptiStruct Verification ProblemsVerification Problems p.58
E70.5 kN/mm2
0.342
0 (Initial yield stress)194 N/mm2
Hollomon hardening=K x n
K = 550.4 N/mm2
n = 0.223
Nonlinear Quasi Static Analysis ResultsCharacteristic angles during process.
Frictional Coefficient=0 NAFEMSOptiStruct
ResultsNormalized
Forming angle 21.88 20.50 1.067317
Angle after release 48.38 45.53 1.062596
Frictional Coefficient=0.1348 NAFEMSOptiStruct
ResultsNormalized
Forming angle 21.84 22.437 0.973392
Angle after release 54.45 43.22 1.259833
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/contb3f0.fem
/contb3fc.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.59
OS-V: 0260 Shell Bending under a Tip LoadA beam is analyzed for bending due to tip load. OptiStruct investigates the vertical steady-statedisplacement at the tip of the beam.
Figure 37:
Benchmark ModelTwo Beams are analyzed, Beam1 without follower load and Beam 2 with follower load. Shell elementsare used to model the beams which is 400mm long consists of 40 elements and a cross section of20mm. All the nodes are constrained for the 3,4 and 5 degrees of freedom and the ends of the beamsare constrained in all degrees of freedom. Both the beams are loaded at the edge by a point force of125N on each node in the negative y direction. The load on the Beam1 is not having a follower forcewhereas the load on the Beam2 is a follower force. Nonlinear Quasi-static analysis is performed withLarge displacement.
The material properties are:
Young's Modulus1000 MPa
Poisson's Ratio0.0
Density10000 kg/m3
Nonlinear Quasi-static Analysis Results
Non-Follower Loady-Displacement
(mm) Follower Loady-Displacement
(mm)
Bisshopp and Drucker 240 Bisshopp and Drucker 291
CBEAM 242 CBEAM 277
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OptiStruct Verification ProblemsVerification Problems p.60
Non-Follower Loady-Displacement
(mm) Follower Loady-Displacement
(mm)
Normalized 0.99173554 Normalized 1.05054152
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification/Tiploadfllwer.fem
ReferenceBisshopp, K. E., and D. C. Drucker, “Large Deflections of Cantilever Beams,” Quarterly of AppliedMathematics, vol. 3 272, 1945
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OptiStruct Verification ProblemsVerification Problems p.61
NAFEMS Frequency Response Analysis
OS-V: 0300 Deep Simply-Supported Beam HarmonicForced Vibration ResponseTest 5HOptiStruct is used to investigate the Peak Displacement in y-direction and extreme fiber bending stressat undamped Natural Frequency (at the mid-span node).
Figure 38:
Benchmark ModelTimoshenko beam and Engineer’s beam elements are used to model the simply-supported beam whichconsists of 10 elements. The displacements in x, y, and z direction, as well as the rotation in x directionare fixed at the end A. In addition, the displacements in y and z direction are constrained at end B. Asteady state harmonic forced vibration F=F0 sin ωt is induced in the y-direction. (F0=106 N/m uniformlydistributed, ω=2πf, f=0 to 4.16 Hz). For modal analysis solution, a damping ratio of 0.02 is applied in all16 modes and for direct solution, Rayleigh damping factor α1=5.36 and α2=7.46×10
-5 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
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OptiStruct Verification ProblemsVerification Problems p.62
Peak Displacement(mm)
Peak Stress (N/mm2)
Frequency (Hz)
Reference Solution 13.45 241.9 42.65
PBEAML
Direct Solution 13.42 236.1 43.02
Normalized 1.002235469 1.024565862 0.991399349
Modal Solution 13.56 238.61 43.16
Normalized 0.991887906 1.01378819 0.988183503
PBEAM
Direct Solution 12.27 238.21 45.28
Normalized 1.096169519 1.015490534 0.941916961
Modal Solution 12.3 238.89 45.34
Normalized 1.093495935 1.012599941 0.94067049
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
Test5HPBEAMLD.fem
Test5HPBEAMLM.fem
Test5HPBEAMD.fem
Test5HPBEAMM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
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OptiStruct Verification ProblemsVerification Problems p.63
OS-V: 0310 Deep Simply-Supported Beam Periodic ForcedVibration ResponseTest 5POptiStruct is used to investigate the Peak Displacement in y-direction and extreme fiber bending stressat the mid-span node.
Figure 39:
Benchmark ModelTimoshenko beam and Engineer’s beam elements are used to model the simply-supported beam whichconsists of 10 elements. The displacements in x, y, and z direction, as well as the rotation in x directionare fixed at the end A. In addition, the displacements in y and z direction are constrained at end B. Asteady state periodic forced vibration F=F0 (sin ωt-sin 3ωt) is induced in the y-direction. (F0=10
6 N/muniformly distributed, ω=2ωf, f=20 Hz). For modal analysis solution, a damping ratio of 0.02 is appliedin all 16 modes and for direct solution, Rayleigh damping factor α1=5.36 and α2=7.46×10
-5 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak Displacement(mm)
Peak Stress (N/mm2)
Reference Solution 0.951 17.10
HOE:
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OptiStruct Verification ProblemsVerification Problems p.64
Peak Displacement(mm)
Peak Stress (N/mm2)
Direct Solution 0.982 17.367
Normalized 0.968431772 0.984626015
Modal Solution 0.982 17.369
Normalized 0.968431772 0.984512637
LOE:
Direct Solution 1 19.6
Normalized 0.951 0.87244898
Modal Solution 1 0.951
Normalized 19.6 0.87244898
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
Test5PPBEAMLD.fem
Test5PPBEAMLM.fem
Test5PPBEAMD.fem
Test5PPBEAMM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.65
OS-V: 0320 Deep Simply-Supported Beam Random ForcedVibration ResponseTest 5ROptiStruct is used to investigate the Peak Displacement in y-direction and extreme fiber bending stressat undamped Natural Frequency (at the mid-span node).
Figure 40:
Benchmark ModelTimoshenko beam and Engineer’s beam elements are used to model the simply-supported beam whichconsists of 10 elements. The displacements in x, y, and z direction, as well as the rotation in x directionare fixed at the end A. In addition, the displacements in y and z direction are constrained at end B.A steady state random forcing with uniform power spectral density (of force) PSD= (106 N/m)2/Hzis induced in the y-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16modes and for direct solution, Rayleigh damping factor α1=5.36 and α2=7.46×10
-5 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak Displacement(mm)
Peak Stress (N/mm2)
Frequency (Hz)
Reference Solution 180.90 58516 42.65
HOE:
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.66
Peak Displacement(mm)
Peak Stress (N/mm2)
Frequency (Hz)
Direct Solution 184.03 56999.67 43.14
Normalized 0.982991903 1.026602435 0.988641632
Modal Solution 183.93 56973.24 43.16
Normalized 0.983526342 1.027078678 0.988183503
LOE:
Direct Solution 150.9 56917.35 45.34
Normalized 1.198807157 1.028087218 0.94067049
Modal Solution 151.4 57105.24 45.34
Normalized 1.194848085 1.024704563 0.94067049
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test5RPBEAMLD.fem
/Test5RPBEAMLM.fem
/Test5RPBEAMD.fem
/Test5RPBEAMM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.67
OS-V: 0330 Deep Simply-Supported Beam TransientForced Vibration ResponseTest 5TOptiStruct is used to investigate the Peak Displacement in y-direction, the time at the peakdisplacement, extreme fiber bending stress at undamped Natural Frequency and the Staticdisplacement at the mid-span node.
Benchmark ModelTimoshenko beam and Engineer’s beam elements are used to model the simply-supported beam whichconsists of 10 elements. The displacements in x, y, and z direction, as well as the rotation in x directionare fixed at the end A. In addition, the displacements in y and z direction are constrained at end B.A suddenly applied step load F0=10
6 N/m is induced in the y-direction. For modal analysis solution, adamping ratio of 0.02 is applied in all 16 modes at a time step of 0.0001 secs and for direct solution,Rayleigh damping factor α1=5.36 and α2=7.46×10
-5 at a time step of 0.0001 secs are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
PeakDisplacement(mm)
Time at PeakDisplacement(sec)
Peak Stress (N/mm2)
StaticDisplacement(mm)
Reference Solution 1.043 0.0117 18.76 0.538
HOE:
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.68
PeakDisplacement(mm)
Time at PeakDisplacement(sec)
Peak Stress (N/mm2)
StaticDisplacement(mm)
Direct Solution 1.036 0.0116 18.02 0.533
Normalized 1.006756757 1.00862069 1.041065483 1.009380863
Modal Solution 1.03 0.0115 17.99 0.533
Normalized 1.012621359 1.017391304 1.042801556 1.009380863
LOE:
Direct Solution 0.94 0.0109 18.02 0.48
Normalized 1.109574468 1.073394495 1.041065483 1.120833333
Modal Solution 0.939 0.01109 17.92 0.48
Normalized 1.110756124 1.055004509 1.046875 1.120833333
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test5TPBEAMLD.fem
/Test5TPBEAMLM.fem
/Test5TPBEAMD.fem
/Test5TPBEAMM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.69
OS-V: 0340 Simply-Supported Thin Square Plate HarmonicForced Vibration ResponseTest 13HOptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat undamped Natural Frequency (at the center of the plate).
Figure 41:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A steady state harmonic forced vibration F=F0 sin ωt is induced in the z-direction. (F0=100 N/m
2 overwhole plate, ω=2ωf, f=0 to 4.16 Hz). For modal analysis solution, a damping ratio of 0.02 is applied inall 16 modes and for direct solution, Rayleigh damping factor α1=0.299 and α2=1.339×10
-3 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.70
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak Displacement(mm)
Peak Stress (N/mm2) Frequency (HZ)
Reference Solution 45.42 30.03 2.377
HOE:
Direct Solution 47.254 37.57 2.323
Normalized 0.961188471 0.799307958 1.023245803
Modal Solution 47.34 37.64 2.324
Normalized 0.959442332 0.797821467 1.022805508
LOE:
Direct Solution 45.22 30.84 2.349
Normalized 1.004422822 0.973735409 1.011919966
Modal Solution 45.45 30.98 2.345
Normalized 0.999339934 0.969335055 1.013646055
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test13HHOED.fem
/Test13HHOEM.fem
/Test13HLOED.fem
/Test13HLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.71
OS-V: 0350 Simply-Supported Thin Square Plate PeriodicForced Vibration ResponseTest 13POptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat the center of the plate.
Figure 42:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10. Asteady state harmonic forced vibration F=F0 (sin ωt-sin 3ωt) is induced in the z-direction. (F0=100 N/m2 over whole plate, ω=2πf, f=1.2 Hz). For modal analysis solution, a damping ratio of 0.02 is appliedin all 16 modes and for direct solution, Rayleigh damping factor α1=0.299 and α2=1.339×10
-3 aregiven.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.72
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak Displacement (mm) Peak Stress (N/mm2)
Reference Solution 2.863 2.018
HOE:
Direct Solution 2.928 2.418
Normalized 0.977800546 0.834574028
Modal Solution 2.929 2.426
Normalized 0.977466712 0.831821929
LOE:
Direct Solution 2.825 1.956
Normalized 1.013451327 1.031697342
Modal Solution 2.826 1.961
Normalized 1.013092711 1.029066803
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test13PHOED.fem
/Test13PHOEM.fem
/Test13PLOED.fem
/Test13PLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.73
OS-V: 0360 Simply-Supported Thin Square Plate HarmonicForced Vibration ResponseTest 13ROptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat undamped Natural Frequency (at the center of the plate).
Figure 43:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A steady state random forcing with uniform power spectral density (of force) PSD= (100 N/m2)2/Hzis induced in the z-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16modes and for direct solution, Rayleigh damping factor α1=0.299 and α2=1.339×10-3 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.74
f*Closed form solution
Peak DisplacementPSD (mm2/Hz)
Peak Stress PSD ((N/mm2)2/Hz)
Frequency (Hz)
Reference Solution 2063.20 1025.44 2.377
HOE
Direct Solutions 2232.98 1411.14 2.322
Normalized 0.923967075 0.726674887 1.023686477
Modal Solution 2241.33 1416.89 2.324
Normalized 0.920524867 0.723725907 1.022805508
LOE
Direct Solutions 2045.23 951.00 2.349
Normalized 1.008786298 1.078275499 1.011919966
Modal Solution 2065.73 960.22 2.345
Normalized 0.998775251 1.067921935 1.013646055
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test13RHOED.fem
/Test13RHOEM.fem
/Test13RLOED.fem
/Test13RLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.75
OS-V: 0365 Simply-Supported Thin Square Plate TransientForced Vibration ResponseTest 13TOptiStruct is used to investigate the Peak Displacement in z-direction, the time at the peakdisplacement, extreme fiber bending stress at undamped Natural Frequency and the Staticdisplacement at the center of the plate.
Figure 44:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A suddenly applied step load F0=100 N/m
2 is induced in the z-direction. For modal analysis solution,a damping ratio of 0.02 is applied in all 16 modes at a time step of 0.002 secs and for direct solution,Rayleigh damping factor α1=0.299 and α2=1.339×10
-3 at a time step of 0.002 secs are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.76
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
PeakDisplacement(mm)
Time at PeakDisplacement(sec)
Peak Stress (N/mm2)
StaticDisplacement(mm)
Reference Solution 3.523 0.210 2.484 1.817
HOE:
Direct Solution 3.637 0.212 2.784 1.832
Normalized 0.968655485 0.990566038 0.892241379 0.991812227
Modal Solution 3.643 0.210 2.820 1.832
Normalized 0.967060115 1 0.880851064 0.991812227
LOE:
Direct Solution 3.465 0.210 2.244 1.780
Normalized 1.016738817 1 1.106951872 1.020786517
Modal Solution 3.454 0.214 2.203 1.779
Normalized 1.019976838 0.981308411 1.127553336 1.021360315
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test13THOED.fem
/Test13THOEM.fem
/Test13TLOED.fem
/Test13TLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.77
OS-V: 0370 Simply-Supported Thick Square PlateHarmonic Forced Vibration ResponseTest 21HOptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat undamped Natural Frequency (at the center of the plate).
Figure 45:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A steady state harmonic forced vibration F=F0 sin ωt is induced in the z-direction. (F0=10
6 N/m2 overwhole plate, ω=2πf, f=0 to 78.17 Hz). For modal analysis solution, a damping ratio of 0.02 is applied inall 16 modes and for direct solution, Rayleigh damping factor α1=5.772 and α2=6.926×10
-5 are given.
The material properties are;
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.78
f*Closed form solution
Peak Displacement(mm)
Peak Stress (N/mm2) Frequency (Hz)
Reference Solution 58.33 800.8 45.90
HOE:
Direct Solution 62.633 943.67 45.21
Normalized 0.931298197 0.848601736 1.01526211
Modal Solution 62.67 944.57 45.23
Normalized 0.930748364 0.847793176 1.014813177
LOE:
Direct Solution 60 774.73 45.62
Normalized 0.972166667 1.033650433 1.006137659
Modal Solution 60.05 774.54 45.59
Normalized 0.971357202 1.033903995 1.006799737
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test21HHOED.fem
/Test21HHOEM.fem
/Test21HLOED.fem
/Test21HLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.79
OS-V: 0375 Simply-Supported Thick Square Plate PeriodicForced Vibration ResponseTest 21POptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat the center of the plate.
Figure 46:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10. Asteady state harmonic forced vibration F=F0 (sin ωt-sin 3ωt) is induced in the z-direction. (F0=10
6 N/m2
over whole plate, ω=2πf, f=20 Hz). For modal analysis solution, a damping ratio of 0.02 is applied in all16 modes and for direct solution, Rayleigh damping factor α1=5.772 and α2=6.929×10
-5 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.80
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak Displacement (mm) Peak Stress (N/mm2)
Reference Solution 4.929 67.67
HOE:
Direct Solution 5.134 79.26
Normalized 0.960070121 0.853772395
Modal Solution 5.134 79.291
Normalized 0.960070121 0.8534386
LOE:
Direct Solution 5.016 65.48
Normalized 0.982655502 1.033445327
Modal Solution 5.018 65.595
Normalized 0.98226385 1.031633509
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test21PHOED.fem
/Test21PHOEM.fem
/Test21PLOED.fem
/Test21PLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.81
OS-V: 0380 Simply-Supported Thick Square Plate RandomForced Vibration ResponseTest 21ROptiStruct is used to investigate the Peak Displacement in z-direction and extreme fiber bending stressat undamped Natural Frequency (at the center of the plate).
Figure 47:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A steady state random forcing with uniform power spectral density (of force) PSD= (106 N/m2)2/Hzis induced in the z-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16modes and for direct solution, Rayleigh damping factor α1=5.772 and α2=6.929×10
-5 are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.82
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
Peak DisplacementPSD (mm2/Hz)
Peak Stress PSD ((N/mm2)2
Frequency (Hz)
Reference Solution 3401.81 641200.00 45.90
HOE:
Direct Solution 3929.62 892303.43 45.24
Normalized 0.865684214 0.718589639 1.014588859
Modal Solution 3928.88 892421.36 45.27
Normalized 0.865847264 0.718494681 1.013916501
LOE:
Direct Solution 3607.25 600979.1 45.62
Normalized 0.943048028 1.066925622 1.006137659
Modal Solution 3606.23 600094.2 45.63
Normalized 0.943314764 1.068498912 1.00591716
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test21RHOED.fem
/Test21RHOEM.fem
/Test21RLOED.fem
/Test21RLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.83
OS-V: 0385 Simply-Supported Thick Square PlateTransient Forced Vibration ResponseTest 21TOptiStruct is used to investigate the Peak Displacement in z-direction, the time at the peakdisplacement, extreme fiber bending stress at undamped Natural Frequency and the Staticdisplacement at the center of the plate.
Figure 48:
Benchmark ModelThe 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0m. Thez-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.A suddenly applied step load F0=10
6 N/m2 is induced in the z-direction. For modal analysis solution, adamping ratio of 0.02 is applied in all 16 modes at a time step of 0.0001 secs and for direct solution,Rayleigh damping factor α1=5.772 and α2=6.929×10
-5 at a time step of 0.0001 secs are given.
The material properties are:
Young’s Modulus200 × 109 N/m2
Poisson’s Ratio0.3
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.84
Density8000 kg/m3
Frequency Response SummaryThe frequency of each targeted mode is normalized with the closed form solution.
f*Closed form solution
PeakDisplacement(mm)
Time at PeakDisplacement(sec)
Peak Stress (N/mm2)
StaticDisplacement(mm)
Reference Solution 4.524 0.0108 62.11 2.333
HOE:
Direct Solution 4.838 0.011 72.67 2.42
Normalized 0.935097148 0.981818182 0.854685565 0.964049587
Modal Solution 4.870 0.011 75.16 2.42
Normalized 0.928952772 0.981818182 0.82637041 0.964049587
LOE:
Direct Solution 4.604 0.0108 57.98 2.34
Normalized 0.982623805 1 1.071231459 0.997008547
Modal Solution 4.611 0.0107 58.44 2.341
Normalized 0.981132075 1.009345794 1.062799452 0.996582657
Model FilesThe model files used in this example include:
/demos/hwsolvers/optistruct/verification
/Test21THOED.fem
/Test21THOEM.fem
/Test21TLOED.fem
/Test21TLOEM.fem
ReferenceNAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish EnterpriseTechnology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.
Proprietary Information of Altair Engineering
-
OptiStruct Verification ProblemsVerification Problems p.85
NAFEMS Normal Modes Analysis
OS-V: 0400 Pin-ended Double CrossTest No. FV2A pin-ended