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Training Manual
Linear Stat ic Structu ral Analysis
February 2, 2004
Inventory #002010
4-2
Chapter Overview
•
In this chapter, performing linear static structural analysesin Design Simulation will be covered:
– Geometry and Elements
– Contact and Types of Supported Assemblies
– Environment, including Loads and Supports
– Solving Models
– Results and Postprocessing
• The capabilities described in this section are generally
applicable to ANSYS DesignSpace Entra licenses andabove.
– Some options discussed in this chapter may require more
advanced licenses, but these are noted accordingly.
– Modal, harmonic, and nonlinear static structural analyses are
not discussed here but in their respective chapters.
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Training Manual
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4-4
Basics of L inear Stat ic Analysis
•
For a linear static structural analysis, the displacements {x}are solved for in the matrix equation below:
This results in certain assumptions related to the analysis:
– [K] is essentially constant
• Linear elastic material behavior is assumed
• Small deflection theory is used
• Some nonlinear boundary conditions may be included
– {F} is statically applied
• No time-varying forces are considered
• No inertial effects (mass, damping) are included
• It is important to remember these assumptions related to
l inear static analysis. Non linear static and dynamic
analyses are covered in later chapters.
F x K
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4-5
A. Geometry
•
In structural analyses, all types of bodies supported byDesign Simulation may be used.
• For surface bod ies , thickness must be
supplied in the “Details” view of the
“Geometry” branch.
• The cross-section and orientation of l ine bod ies is defined
within DesignModeler and is imported into Design
Simulation automatically.
– For line bodies, only displacement results are available.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
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… Elements Used
•
In Design Simulation, the following elements are used: – Solid bodies are meshed with 10-node tetrahedral or 20-node
hexahedral elements
• SOLID187 and SOLID186
– Surface bodies are meshed with 4-node quad shell elements
•
SHELL181 using real constants• Section definition (and offsets) are not used
– Line bodies are meshed with 2-node beam elements
• BEAM188 (with 3rd orientation node)
• Section definition and offsets are supported
Advanced ANSYS Details
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4-7
… Material Properties
•
The required structural material properties are Young’sModulus and Poisson’s Ratio for linear static structural
analyses
– Material input is under the “Engineering Data” branch, and
material assignment is per part under the “Geometry” branch
– Mass densi ty is required if any inertial loads are present
– Thermal expansio n coeff ic ient and thermal cond uct iv i ty are
required if any thermal loads are present
• Thermal loading not available with an ANSYS Structural license
– Stress Lim i ts are needed if a Stress Tool result is present
–Fatigue Propert ies are needed if Fatigue Tool result is present• Requires Fat igue Modu le add-on license
– Specific loading and result tools will be discussed later
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional xStructural /
Mechanical/Multiphysics x
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4-8
B. Assemb l ies – Sol id Body Contact
•
When importing assemblies of solid parts, contact regionsare automatically created between the solid bodies.
– Surface-to-surface contact allows non-matching meshes at
boundaries between solid parts
– Tolerance controls under “Contact” branch allows the user to
specify distance of auto contact detection via slider bar
ANSYS License Availability
DesignSpace Entra
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
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… Assemblies – Sol id Body Contact
•
In Design Simulation, the concept of contact and target surfaces are used for each contact region.
– One side of the contact region is comprised of “contact”
face(s), the other side of the region is made of “target” face(s).
– The integration points of the contact surfaces are restricted
from penetrating through the target surfaces (within a given
tolerance). The opposite is not true, however.
• When one side is the contact and the other side is the target, this
is called asymmetr ic contac t . On the other hand, if both sides are
made to be contact & target, this is called symmetr ic co ntac t since
neither side can penetrate the other.
•
By default, Design Simulation usessymm etr ic contac t for solid assemblies.
For ANSYS Professional licenses and
above, the user may change to asymmetric
contact, as desired.
ANSYS License Availability
DesignSpace Entra
DesignSpace /
Professional xStructural x
Mechanical/Multiphysics x
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… Assemblies – Sol id Body Contact
•
Four contact types are available:
– Bonded and No Separation contact are basically
linear behavior and require only 1 iteration
– Frict ionless and Rough contact are nonlinear
and require multiple iterations. However, no te
that small def lect ion theory is s t i l l assumed.
• When using these options, an interface treatment
option is available, set either as “Actual Geometry (and Specified Offset)” or “Adjusted to Touch.”
The latter allows the user to have ANSYS close the
gap to ‘just touching’ position.
ANSYS License Availability
DesignSpace Entra
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
Contact Type Iterations Normal Behavior (Separation) Tangential Behavior (Sliding)
Bonded 1 Closed Closed
No Separation 1 Closed Open
Frictionless Multiple Open Open
Rough Multiple Open Closed
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… Assemblies – Sol id Body Contact
•
For the advanced user, some of thecontact options can be modified
– Formulation can be changed from “Pure
Penalty” to “Augmented Lagrange” or “MPC”.
• “MPC” is applicable to bonded contact only
• “Augmented Lagrange” is used in regular ANSYS
– In bonded contact, the pure Penalty method canbe thought of as adding very high st i f fness
between interface of parts to prevent relative
movement. This results in negligible relative
movement between parts at contact inter face .
– MPC formulation writes con straint equat ions
relating movement of parts at interface , so norelative movement occurs. This is sometimes
an attractive alternative to penalty method.
ANSYS License Availability
DesignSpace Entra
DesignSpace
Professional xStructural x
Mechanical/Multiphysics x
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… Assemblies – Sol id Body Contact
•
Advanced options (continued): – As explained in Chapter 3, the pinball
region can be input and visualized
• The pinball region defines location of near-
f ield open co ntact . Outside of the pinball
region is far-f ield open con tact .
• Originally, the pinball region was meant tomore efficiently process contact searching,
but this is also used for other purposes,
such as bonded contact
• For bond ed or no separat ion co ntact , i f gap
or penetrat ion is sm al ler than pinbal l region,
the gap/penetrat ion is autom atical lyexcluded
– Other advanced contact options will be
discussed in later chapters.
ANSYS License Availability
DesignSpace Entra
DesignSpace
Professional xStructural x
Mechanical/Multiphysics x
In this case, the gap between
the two parts is bigger than the
pinball region, so no automatic
gap closure will be performed.
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… Assemblies – Sol id Body Contact
• Internally, the solid face contact regions are modeled in
ANSYS as CONTA174 and TARGE170 elements
– By default, pure penalty method is used with relative contact
stiffness of 10 with symmetric contact pairs being generated
– For bonded and no separation contact, any geometric
penetration or gap is ignored i f wi th in the pinbal l region .
– For frictionless and rough contact, considering “actualgeometry” makes any initial gap or penetration ramped
whereas “adjust to touch” closes gap with auto CNOF
– NEQIT is set to 1 for if only bonded or no separation contact
exist; it is set higher otherwise (15-40, depending on model).
Contact Type KEYOPT(2) KEYOPT(5) KEYOPT(9) KEYOPT(12)
Bonded 1 0 1 5
No Separation 1 0 1 4
Frictionless, Actual Geometry 1 0 2 0
Frictionless, Adjusted to Touch 1 1 1 0
Rough, Actual Geometry 1 0 2 1
Rough, Adjusted to Touch 1 1 1 1
Advanced ANSYS Details
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… Assemblies – Surface Body Con tact
• For ANSYS Profess ional 1 licenses and above, mixed
assemblies of shells and solids are supported
– Allows for more complex modeling of assemblies, taking
advantage of the benefits of shells, when applicable
– More contact options are exposed to the user
–
Contact postprocessing is also available (discussed later)
ANSYS License Availability
DesignSpace Entra
DesignSpace
Professional x1
Structural x
Mechanical/Multiphysics x 1 For ANSYS Professional, surface contact supported with ANSYS 8.0 Service Pack 1 and above
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… Assemblies – Surface Body Con tact
• Edge contact is a subset of general contact
– For contact including shell faces or solid
edges, only bonded or no separation
behavior is allowed.
– For contact involving shell edges, only
bonded behavior using MPC formulation is
allowed.
• For MPC-based bonded contact, user can set
the search direction (the way in which the
multi-point constraints are written) as either
the target norm al or pinbal l region .
• If a gap exists (as is often the case with
shell assemblies), the pinbal l region can be
used for the search direction to detect
contact beyond a gap.
ANSYS License Availability
DesignSpace Entra
DesignSpace
Professional x1Structural x
Mechanical/Multiphysics x
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… Assemblies – Surface Body Con tact
• Internally, any contact including an edge (solid body edge
or surface edge) results in asymmetric contact with
CONTA175 for the edge and TARGE170 for the edge/face
– Contact involving solid edges default to pure penalty method
– Contact involving surface edges use MPC formulation.
Instead of “target normal,” if search direction is “pinball
region,” KEYOPT(5)=4 set on companion TARGE170 element.
– For bonded contact (default), both use KEYOPT(12)=5 and
KEYOPT(9)=1.
• For surface faces in contact with other
faces, standard surface-to-surfacecontact is used, namely CONTA174
and TARGE170Example of Design Simulation-
generated edge-to-edge
contact, which results in
CONTA175 on one edge and
TARGE170 on the other.Advanced ANSYS Details
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… Assemblies – Contact Summary
• A summary of contact types and options available in
Design Simulation is presented in the table below:
– This table is also in the Design Simulation online help.
Referring to this table will aid in determining what options areavailable to the user.
ANSYS License Availability
DesignSpace Entra
DesignSpace /
Professional xStructural x
Mechanical/Multiphysics x
Contact Geometry Solid Body Face Solid Body Edge Surface Body Face Surface Body Edge
All types Bonded, No Separation Bonded, No Separation Bonded only
All formulations All formulations All formulations MPC formulation
Symmetry respected Asymmetric only Symmetry respected Asymmetric only
Bonded, No Separation Bonded, No Separation Bonded only
All formulations All formulations MPC formulation
Asymmetric only Asymmetric only Asymmetric onlyBonded, No Separation Bonded only
All formulations MPC formulation
Symmetry respected Asymmetric only
Bonded only
MPC formulation
Asymmetric only
Solid Body Face
Solid Body Edge
Surface Body Face
Surface Body Edge
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… Assemblies – Spot Weld
• Spot welds provide a means of connecting shell assemblies
at discrete points
– For ANSYS DesignSpace licenses, shell contact is not
supported, so spotwelds are the only way to define a shell
assembly.
– Spotweld definition is done in the CAD software. Currently,
only DesignModeler and Unigraphics define spotwelds in a
manner that Design Simulation supports.
– Spotwelds can also be created in
Design Simulation manually, but
only at discrete vertices.
ANSYS License AvailabilityDesignSpace Entra
DesignSpace Structural x
DesignSpace x
Professional x
Structural x
Mechanical/Multiphysics x
DesignModeler x
Pro/ENGINEER
Unigraphics x
SolidWorks
Inventor
Solid Edge
Mechanical Desktop
CATIA V4
CATIA V5
ACIS (SAT)Parasolid
IGES
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… Assemblies – Spot Weld
• Internally, spot welds are defined as a set of BEAM188
elements. The spot weld is defined with one beam element,
and the top and bottom of the spot weld is connected to the
shell or solid elements with a ‘spider web’ of multiple
beams.
– The BEAM188 elements use
same material properties as
underlying materials but
with an appropriate circular
cross-section with radius=
5*thickness of underlying
shells
– Figure on right shows spot-
welds between two sets of
shell elements, which are
made translucent for clarity.
Advanced ANSYS Details
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C. Loads and Suppo rts
• There are four types of structural loads available:
– Inertial loads
• These loads act on the entire system
• Density is required for mass calculations
– Structural Loads
•
These are forces or moments acting on parts of the system – Structural Supports
• These are constraints that prevent movement on certain regions
– Thermal Loads
• Structurally speaking, the thermal loads result in a temperature
field, which causes thermal expansion on the model.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural /
Mechanical/Multiphysics x
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… Acceleration & Gravity
• An acceleration can be defined on the system
– Acceleration acts on entire model in length/time2 units.
– Users sometimes have confusion over notation of direction. If
acceleration is applied to system suddenly, the inertia resists
the change in acceleration, so the inertial forces are in the
oppos i te direction to applied acceleration
– Acceleration can be defined by Components or Vector
• Standard Earth Gravity can also be applied as a load
– Value applied is 9.80665 m/s2 (in SI units)
– Standard Earth Gravity direction can only be defined along
one of three World Coordinate System axes.
– Since “Standard Earth Gravity” is defined as an acceleration,
define the direction as opposite to gravitational force, as noted
above.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
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… Rotational Velocity
• Rotational velocity is another inertial load available
– Entire model spins about an axis at a given rate
– Can be defined as a vector, using geometry for axis and
magnitude of rotational velocity
– Can be defined by components, supplying origin and
components in World Coordinate System
– Note that location of axis is very important since model spins
around that axis.
– Default is to input rotational velocity in radians per second.
Can be changed in “Tools > Control Panel > Miscellaneous >
Angular Velocity” to revolutions per minute (RPM) instead.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
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… Inertial Loads in ANSYS
• Inertial loads are modeled in ANSYS as follows:
– Acceleration and Standard Earth Gravity are represented via
ACEL command
– Rotational velocity is defined via CGLOC (defines origin) and
CGOMGA (defines rotational velocity about CGLOC)
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… Forces and Pressures
• Pressure loading:
– Pressures can only be applied to surfaces and always act
normal to the surface
– Positive value acts into surface (i.e., compressive)
negative value acts outward from surface (i.e., suction)
– Units of pressure are in force per area
• Force loading:
– Forces can be applied on vertices, edges, or surfaces.
– The force will be distr ib uted on al l ent i t ies . This
means that if a force is applied to two identical
surfaces, each surface will have half of the forceapplied. Units are mass*length/time2
– A force is defined via vector and magnitude or by
components
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional xStructural x
Mechanical/Multiphysics x
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… Bolt Load
• Bolt Load:
– A bolt load is for cylindrical surfaces only. Radial component
will be distributed on compressive side using projected area.
Example of radial component distribution shown below.
Axial component is distributed evenly on cylinder.
– Use only one bolt load per cylindrical surface. If the
cylindrical surface is split in two, however, be sure to selectboth halves of cylindrical surface when applying a bolt load.
– Load is in units of force
– Bolt load can be defined via
vector and magnitude or by
components.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural x
Mechanical/Multiphysics x
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… Moment Load
• Moment Load:
– For solid bodies, a moment can be applied on any
surface
– If multiple surfaces are selected, the moment load
gets apportioned about those selected surfaces
– A vector and magnitude or components can define the
moment. The moment acts about the vector using the right-
hand rule
– For surface bodies, a moment can also be applied to a vertex
or edge with similar definition via vector or components as
with a surface-based moment
– Units of moment are in Force*length.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural x
Mechanical/Multiphysics x
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… Remote Load
• Remote Load:
– Allows the user to apply an offset force on a surface
– The user supplies the origin of the force (using vertices, a
cylinder, or typing in (x, y, z) coordinates)
– The force can then be defined by vector and magnitude or by
components
– This results in an equivalent force on the surface plus a
moment caused by the moment arm of the offset force
– The force is distributed on the surface
but includes the effect of the moment
arm due to the offset of the force
– Units are in force (mass*length/time2)
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural x
Mechanical/Multiphysics x
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… Structural Loads in ANSYS
• Structural loads are modeled in ANSYS as follows:
– Pressures are applied directly on surfaces via SF,,PRES
– Forces on vertices and edges are applied as nodal loads via
F,,FX/FY/FZ
– Forces on surfaces are applied as pressures on face 5 of
surface effect elements SURF154 with KEYOPT(11)=2
• KEYOPT(11)=2 to use full area, including tangential component
– Bolt loads are applied as pressures on face 5 of surface effect
elements SURF154 along compressive half of cylinder
• KEYOPT(11)=0 uses projected area w/ tangential component
– Moments on vertices or edges of shells are applied as nodal
loads via F,,MX/MY/MZ
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… Structural Loads in ANSYS
• Moment load on surface is defined by surface constraint
– Surface constraint is RBE3-type of distributed loading
– Pilot node at surface CG defined by TARGE170 with
KEYOPT(2)=1 and KEYOPT(4)=xxx000
– Surface is defined by CONTA174 with KEYOPT(2)=2,
KEYOPT(4)=1, KEYOPT(12)=5
– Moment applied as nodal load on pilot node
• Remote force load is defined by surface constraint
– Surface constraint is RBE3-type of distributed force
– Pilot node at force origin defined by TARGE170 with
KEYOPT(2)=1 and KEYOPT(4)=000xxx
– Surface is defined by CONTA174 with KEYOPT(2)=2,
KEYOPT(4)=1, KEYOPT(12)=5
– Force applied as nodal load on pilot node
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… Supports (General)
• Fixed Support:
– Constraints all degrees of freedom on vertex, edge, or surface
– For solid bodies, prevents translations in x, y, and z
– For surface and line bodies, prevents translations and
rotations in x, y, and z
• Given Displacement:
– Applies known displacement on vertex, edge, or surface
– Allows for imposed translational displacement in x, y, and z
– Entering “0” means that the direction is constrained
–
Leaving the direction blank means that the entity is free tomove in that direction
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural x
Mechanical/Multiphysics x
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… Supports (Solid Bodies)
• Frictionless Support:
– Applies constraint in normal direction on surfaces
– For solid bodies, this support can be used to apply a
‘symmetry’ plane boundary condition since ‘symmetry’ plane
is same as normal constraint
•Cylindrical Constraint: – Applied on cylindrical surfaces
– User can specify whether axial, radial, or tangential
components are constrained
– Suitable for small-deflection (linear) analysis only
ANSYS License Availability
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DesignSpace x
Professional x
Structural x
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… Supports (Solid Bodies)
• Compression Only Support:
– Applies a compression-only constraint normal to any given
surface. This prevents the sur face to move in the po si t ive
normal direct ion on ly .
– A way to think of this support is to imagine a ‘rigid’ structure
which has the same shape of the selected surface. Note that
the con tact ing (compressiv e) areas are not known beforehand.
– Can be used on a cylindrical surface to model a
“Pinned Cylinder Support”, which was available
in 7.1 but is a special case of the “Compression
Only Support”. Notice the example on the right,
where the outline of the undeformed cylinder isshown. The compressive side retains the shape
of the original cylinder, but the tensile side is free to deform.
– This requ ires an iterat ive (nonl in ear) so lut ion .
• Compressive behavior is not known a pr ior i , so an iterative
solution is required to determine what sides exhibit
compressive behavior.
ANSYS License Availability
DesignSpace Entra x
DesignSpace x
Professional x
Structural xMechanical/Multiphysics x
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… Supports (Line/Surface Bodies)
• Simply Supported:
– Can be applied on edge or vertex of surface or line bodies
– Prevents all translations but all rotations are free
• Fixed Rotation:
– Can be applied on surface, edge, or vertex of surface or line
bodies
– Constrains rotations but translations are free
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… Structural Supports in ANSYS
• The following are applied internally in ANSYS:
– Fixed support constraints result in D,,ALL for given entity
– Given displacement is D,,UX/UY/UZ for specified direction
– Frictionless surface involves nodal rotation such that UX is in
normal direction, and D,,UX is applied
–
Cylindrical constraint rotates nodal coordinates in cylindricalCS and constrains appropriate direction with D,,UX/UY/UZ
– Simply supported constraints apply D on UX, UY, and UZ on
shells or beams
– Fixed rotation constraints apply D on ROTX, ROTY, and ROTZ
on shells or beams
– For compression-only supports, the surface mesh is copied to
form a rigid target surface (TARGE170) on top of the original
surface (CONTA174). Standard contact behavior is used to
model this support, and that is why it is a nonl inear solution.
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… Summary of Supports
• Suppor ts and Contact Regions may both be thought of as
being boundary con d i t ions .
– Contact Regio ns provides a ‘flexible’ boundary condition
between two existing parts explicitly modeled
– Suppor ts provide a ‘rigid’ boundary condition between the
modeled part an a rigid, immovable part not explicitly modeled
• If Part A, which is of interest, is connected to Part B,
consider whether both parts need to be analyzed (withcontact) or whether supports will suffice in providing the
effect Part B has on Part A.
– In other words, is Part B ‘rigid’ compared to Part A? If so, a
support can be used and only Part A modeled. If not, one may
need to model both Parts A and B with contact.
Type of Support Equivalent Contact Condition at Surfaces of Part
Fixed Support Bonded contact with a rigid, immovable part
Frictionless Support No Separation contact with a rigid, immovable part
Compression Only Support Frictionless contact with a rigid, immovable part
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… Thermal Loading
• Temperature causes thermal expansion in the model
– Thermal strains are calculated as follows:
where is the thermal expansion coefficient (CTE), T ref is the
reference temperature at which thermal strains are zero, T is
the applied temperature, and eth is the thermal strain. – Thermal strains do not cause stress by themselves. It is the
constraint, temperature gradient, or CTE mismatch that
produce stress.
– CTE is defined in the “Engineering” branch
and has units of strain per temperature
– The reference temperature is defined in the
“Environment” branch
ref
z
th
y
th
x
th T T a e e e
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… Thermal Loading
• Thermal loads can be applied on the model
– Any temperature loading can be applied (see Chapter 6 on
Thermal Analysis for details)
– Design Simulation will always perform a thermal solution first,
then use the calculated temperature field as input when
solving the structural solution.
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… Thermal Loading in ANSYS
• In ANSYS, for any thermal loads present in the model:
– ANSYS will always solve a thermal solution first
• Even if a uniform temperature field is applied, a thermal solution
will be performed. This is why temperature body loads in a
structural analysis is not possible with an ANSYS Structural
license.
– Reference temperature is defined with TREF (not MP,REFT) – Coefficient of thermal expansion per material is supplied with
MP,ALPX (not MP,CTEX or MP,THSX)
– Temperature loading is input via BF commands after thermal
solution
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… Solution Options
– Weak springs can be added to stabilize model
• If “Program Controlled” is set, Design Simulation
tries to anticipate under-constrained models. If no
“Fixed Support” is present, it may add weak springs
and provide an informative message letting the user
know that it has done so
• This can be set to “On” or “Off”. To set the default
behavior, go to “Tools > Control Panel > Solution> Use Weak Springs”.
• In some cases, the user expects the model to be in
equilibrium and does not want to constrain all
possible rigid-body modes. Weak springs will help
by preventing matrix singularity.
• It is good practice to constrain all possible rigid-bodymotion, however.
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… Solution Options
– Informative messages are also present:
• The type of analysis is shown, such as “Static
Structural” for the cases described in this section.
• If a nonlinear solution is required, it will be indicated
as such. Recall that for some contact behavior and
compression-only support, the solution becomes
nonlinear. These type of solutions require multiple
iterations and take longer than linear solutions.
• The solver working directory is where scratch files
are saved during the solution of the matrix equation.
By default, the TEMP directory of your Windows
system environment variable is used, although this
can be changed in “Tools > Control Panel > Solution
> Solver Working Directory”. Sufficient free space must be on that partition.
• Any solver messages which appear after solution
can be checked afterwards under “Solver Messages”
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… Solving the Model
• To solve the model, request resu lts f i rst (covered next) and
click on the “Solve” button on the Standard Toolbar
– By default, two processors (if present) will be used for parallel
processing. To set the number of processors, use “Tools >
Control Panel > Solution > Number of Processors to Use”
– Recall that under “Worksheet” tab of the “Solution” branch,
the details of the solution output can be examined.
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… Solution Options in ANSYS
• The solver selection for direct vs. iterative:
– The solvers used are either the direct sparse solver
(EQSLV,SPARSE) or the PCG solver (EQSLV,PCG)
– A simplified discussion between the two solvers:• If given the linear static case of [K]{x} = {F}, Direct solvers factorize [K] to solve for [K]-1.
Then, {x} = [K]-1{F}.
–
This factorization is computationally expensive but is done once.• Iterative solvers use a preconditioner [Q] to solve the equation [Q][K]{x} = [Q]{F}. Assume
that [Q] = [K]-1. In this trivial case, [I]{x} = [K]-1{F}. However, the preconditioner is not
usually [K]-1. The closer [Q] is to [K]-1, the better the preconditioning is, and this process
is repeated - hence the name, i terat ive solver .
– For iterative solvers, matrix multiplication (not factorization) is
performed. This is much faster than matrix inversion if done entirely in
RAM, so, as long as the number of iterations is not very high (which
happens for well-conditioned matrices), iterative solvers can be moreefficient than sparse solvers.
– The main difference between the iterative solvers in ANSYS — PCG,
JCG, ICCG — is the type of pre-condit ioner used.
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… Solution Options in ANSYS
• Weak spring option:
– If used, weak springs are added to the mesh. These are
modeled with COMBIN14 with small stiffness and added to the
extreme dimensions of the part.
• Solver working directory:
–The ANSYS input file is written as “ds.dat” in the solverdirectory. The output file is “solve.out” and can be viewed in
the “Worksheet” tab of the “Solution” branch.
– ANSYS is executed in batch mode (-b) as a separate process.
During solution, the results file .rst is written. The results are
also read in and XML results files are generated in batch
mode. The XML files are then read into Design Simulation.
– All associated ANSYS files have default jobname of “file” and
are deleted after solution, unless changed in “Tools > Control
Panel > Solution > Save Ansys Files”.
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… Solution Options in ANSYS
• Various defaults in ANSYS are turned off when solving in
Design Simulation:
– Solution control (SOLCON,OFF) is turned off
– Multiframe restart is turned off (RESCON,,NONE)
– ANSYS shape checking is turned off (SHPP,OFF)
–
Number of equilibrium iterations (NEQIT) is set to 1 if contactis not present or if all contact is bonded or no separation.
• Otherwise, it is automatically determined, such as NEQIT,20
(frictionless contact) or NEQIT,40 (rough contact). NSUBST,1,10,1
is also set in these cases.
– Only requested results is output with OUTRES, not everything
by default
• Results are later written to XML files in /POST1, which are then
read back into Design Simulation. Hence, Design Simulation does
not directly read the results from the .rst file
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E. Resu l ts and Postpro cessing
• Various results are available for postprocessing:
– Directional and total deformation
– Components, principal, or invariants of stresses and strains
– Contact output
• Requires ANSYS Professional and above
–
Reaction forces
• In Design Simulation, results are usually requested before
solving, but they can be requested afterwards, too.
– If you solve a model then request results afterwards, click onthe “Solve” button , and the results will be retrieved. A
new solution is not required i f that type of result h as been
requested previously (i.e., total deformation was requested
previously but now direction deformation is added).
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… Plotting Results
• All of the contour and vector plots are usually shown on the
deformed geometry. Use the Context Toolbar to change the
scaling or display of results to desired settings.
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… Deformation
• The deformation of the model can be plotted:
– Total deformation is a scalar quantity:
– The x, y, and z components of deformation can be
requested under “Directional.” Because there is
direction associated with the components, if a
“Coordinate System” branch is present, users can
request deformation in a given coordinate system.
• For example, it may be easier to interpret displacement for a
cylindrical geometry in a ‘radial’ direction by using a cylindrical
coordinate system to display the result.
– Vector plots of deformation are available.
Recall that wireframe mode is the easiest
to view vector plots.
222
z y xtotal U U U U
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… Deformation
• Deformation results are available for line, surface, and solid
bodies
– Note that “deformation results” are associated with
translational DOF only. Rotations associated with the DOF of
line and surface bodies are not directly viewable
– Because deformation (displacements) are DOF which Design
Simulation solves for, the convergence behavior is well-behaved when using the Convergence tool
– Vector deformation plots cannot use“Alert” or “Convergence”
tools because they are vector quantities (x, y, z) rather than a
unique quantity (x or y or z). Use Alert or Convergence tools
on “Total” or “Directional” quantities instead. – “Total” deformation is an invariant, so “Coordinate Systems”
cannot be used on this result quantity. Also, “Vector”
deformation is always shown in the world coordinate system.
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… Stresses and Strains
• Stresses and strains can be viewed:
– “Strains” are actually elastic strains
– Stresses and (elastic) strains are
tensors and have six components
(x, y, z, xy, yz, xz) while thermal
strains can be considered a vector
with three components (x, y, z)
– For stresses and strains, components can be
requested under “Normal” (x, y, z) and “Shear” (xy, yz, xz).
For thermal strains, components are under “Thermal”
• Can request in different results coordinate systems
•Not available with an ANSYS Structural license
• Only available for shell and solid bodies. Line bodies currently do
not report any results except for deformation.
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… Stresses and Strains
• Safety Factors can be used to evaluate designs:
– Because stress is a tensor, it is hard to evaluate
the response of the system by looking solely at
stress components
– The “Stress Tool” allows the user to
have Design Simulation calculate
scalar results related to factors ofsafety
– In the next slides, stress results will
be discussed, along with different
criteria of evaluating material response,
as available from the Stress Tool.
– The “Stress Tool” branch controls
what theory will be used and what
type of stress limit will be used.
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… Principal Stresses
• Principal Stresses and Strains:
– From basic mechanics review, the stress tensor can
be rotated such that only normal stresses appear.
These are the three pr inc ipal stresses s1 < s2 < s3.
– Principal values of stress and strain results can be requested.
The three principal values also have direction associated with
them, and a “Vector Principal” output can be selected. • Principal values can be exported to Excel with Euler angles
– In the example shown on the right, one
can easily see the three principal
stresses (white=max, blue=min). From
this, one can see that the part is under-going bending with one side in tension
and the other in compression.
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… Principal Stresses
• Maximum Tensile Stress Theory:
– The maximum tensi le st ress theory can be used for the
“Stress Tool”. It utilizes the maximum principal stress and is
generally suitable for brittle materials.
– The criterion can be thought of as the following:
where st is the ultimate (or yield) tensile strength
– If plotted in two-dimensional principal stress space, the failuresurface results in a square as shown below. A stress state
lying inside the square is assumed to be fine but any stress
state lying on the edges of the square will fail.
– The max tensile stress criterion, as its
name implies, only considers the tensilebehavior. For many brittle materials, the
compressive strength is much greater,
so this assumption may be valid.
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s1
s2
st
st
1s
s t safety F
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… Principal Stresses
• Mohr-Coulomb Theory:
– The Mohr-Coulom b theory can be used for the “Stress Tool”.
It utilizes the maximum and minimum principal stresses and is
suitable for brittle materials.
– The criterion is as follows:
where st and sc are the ultimate (or yield)
tensile and compressive strengths. – The failure surface is plotted in two-dimensional principal
stress space below. Unlike the maximum tensile stress
theory, the Mohr-Coulomb theory considers the
effects of the compressive strength.
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1
31
ct
safety F s
s
s
s
s1
s2
st
st
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… Equivalent Stress
• Equivalent Stress:
– The von Mises or equivalent stress se is defined as:
– This criterion is commonly used for ductile metals.
–When uniaxial tensile tests of specimens are performed todetermine the yield strength and stress-strain relationships,
the engineer needs a way to relate the uniaxial data to the
stress state (tensor). Hence, the equivalent stress is a
commonly used scalar invariant for this purpose.
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213
2
32
2
21
2
1s s s s s s s e
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… Equivalent Stress
• Maximum Equivalent Stress Theory:
– The Maximum Equ ivalent Stress Theory can be used for the
“Stress Tool”. It compares the equivalent stress with the yield
(or ultimate) strength and is suitable for ductile materials.
– The criterion is as follows:
where sy is the tensile yield (or ultimate) strength.
– The failure surface is plotted in two-dimensional principalstress space below.
– A stress state can be separated into hydrostatic and
distortional terms. The hydrostatic term
contributes to volume change but the
distortional term is associated withyielding. Hence, the maximum equivalent
stress criterion is also known as the
disto r t ion energy cr i ter ion.
e
y
safety F s
s
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s1
s2
sy
sy
sy
sy
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4-57
… Maximum Shear Stress
• Maximum Shear Stress:
– The maximum shear st ress tmax is defined as
which results in the largest principal shear stress
– This value can be compared to the yield strength to predictyielding for ductile materials
• Stress Intensity:
– The stress intensity is twice the value of the maximum shear
stress.
– The stress intensity provides the value of the largest
difference between principal stresses
2
31
max
s s
t
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… Maximum Shear Stress
• Maximum Shear Stress Theory:
– The Maximum Shear Stress Theory or the Tresca c r i ter ion can
be used for the “Stress Tool”. It is suitable for ductile
materials.
– The criterion is as follows:
where sy is the tensile yield (or ultimate) strength
and f is a factor (default=0.5) – The failure surface is plotted in two-dimensional principal
stress space below with the von Mises criterion superimposed
on in with a thin line. The two criteria are
quite similar, although the Tresca criterion
is slightly more conservative (maximum
difference between the two does not
exceed 15%).
maxt
s y
safety
f F
s1
s2
sy
sy
sy
sy
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… Contact Results
• Contact Results:
– Contact results can be requested for selected
bodies or surfaces which have contact elements.
– Contact elements in ANSYS use the concept of
contact and target surfaces. Only co ntact sur faces
repor t contact resul ts . MPC-based contact, the target surfaces
of any contact, and edge-based contact do not report results.Also, line bodies do not report any contact results.
• Contact Pressure shows distribution of normal contact pressure
• Contact penetration shows the resulting amount of penetration
whereas contact gap shows any gap (within pinball radius).
• Sliding distance is the amount one surface has slid with respect to
the other. Frictional stress is tangential contact traction due to
frictional effects.
• Contact status provides information on whether the contact is
established (closed state) or not touching (open state).
• For the open state, near-field means that it is within pinball
region, far-field means that it is outside of pinball region.
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… Reaction Forces
• Reaction forces and moments are output for each support
– For each support, look under the “Details” view
after solution. Reaction forces and moments are
printed. X, y, and z components are with respect
to the world coordinate system. Moments are
reported at the centroid of the support.
– The reaction force for weak springs, if used, isunder the “Environment” branch Details view
after solution. The weak spring reaction forces
should be small to ensure that the effect of weak
springs is negligible.
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… Reaction Forces
• The “Worksheet” tab for “Environment” branch has a
summary of reaction forces and moments
– If a support shares a vertex, edge, or surface with another
support, contact pair, or load, the reported reaction forces may
be incorrect. This is due to the fact that the underlying mesh
will have multiple supports and/or loads applied to the same
nodes. The solution will still be valid, but the reported valuesmay not be accurate because of this.
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• Workshop 4 – Linear Structural Analysis
• Goal:
– A 5 part assembly representing an impeller type pump is
analyzed with a 100N preload on the belt.
F. Workshop 4
http://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/workshops/DS80_Workshop_04.ppt