Chapter 9 Meshing 1

Chapter 9Meshing9.1 Step-by-Step: Pneumatic Fingers

9.2 More Exercise: Cover of Pressure Cylinder

9.3 More Exercise: Convergence Study of 3D Solid Elements

9.4 Review

Chapter 9 Meshing Section 9.1 Pneumatic Fingers 2

Section 9.1Pneumatic Fingers

Problem Description

Unit: mm.

80

5

1 2

5.1 4

3 3.2 1 (19.2)

Plane of symmetry.

Chapter 9 Meshing Section 9.1 Pneumatic Fingers 3

Techniques/Concepts

• Mesh Metric: Skewness

• Hex Dominant Method

• Sweep Method

• MultiZone Method

• Section View

• Nonlinear Simulations

• Line Search

• Displacement Convergence

Chapter 9 Meshing Section 9.2 Cover of Pressure Cylinder 4

Section 9.2Cover of Pressure Cylinder

Techniques/Concepts

• Patch Conforming Method

• Patch Independent Method

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 5

Section 9.3Convergence Study of 3D Solid Elements

Problem Description

100 mm

10 mm

[1] The beam is made of steel.

[2] The width of the beam is 10 mm. A uniform load of 1 MPa applies on the upper face of the beam.

[3] We will record the vertical tip deflection.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 6

Element Shapes

[1] hexahedron. [2] Tetrahedron.

[4] Perpendicular prism.

[3] Parallel prism.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 7

0.60

0.64

0.68

0.72

0.76

0 3000 6000 9000 12000 15000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Lower-Order Elements

[1] Lower-order tetrahedron.

[2] Lower-order perpendicular

prism.

[3] Lower-order parallel prism.

[4] Lower-order hexahedron.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 8

0.746

0.747

0.748

0.749

0.750

0.751

0.752

0 2000 4000 6000 8000 10000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Higher-Order Elements

[1] Higher-order tetrahedron.

[2] Higher-order perpendicular prism.

[3] Higher-order parallel prism.

[4] Higher-order hexahedron.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 9

0.746

0.747

0.748

0.749

0.750

0.751

0.752

0 2000 4000 6000 8000 10000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Hexahedra

[2] Higher-order hexahedron.

[1] Lower-order hexahedron.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 10

0.600

0.640

0.680

0.720

0.760

0 2000 4000 6000 8000 10000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Tetrahedra

[1] Lower-order tetrahedron.

[2] Higher-order tetrahedron.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 11

0.66

0.68

0.70

0.72

0.74

0.76

0 2000 4000 6000 8000 10000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Parallel Prisms

[2] Higher-order parallel prism.

[1] Lower-order parallel prism.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 12

0.66

0.68

0.70

0.72

0.74

0.76

0 2000 4000 6000 8000 10000

Tip

Def

lect

ion

(mm

)

Number of Nodes

Perpendicular Prisms

[2] Higher-order perpendicular prism.

[1] Lower-order perpendicular prism.

Chapter 9 Meshing Section 9.3 Convergence Study of 3D Solid Elements 13

Guidelines

• Never use lower-order tetrahedra/triangles.

• Higher-order tetrahedra/triangles can be as good as other elements as long as the

mesh is fine enough. In cases of coarse mesh, however, they perform poorly and

are not recommended.

• Lower-order prisms are not recommended.

• Lower-order hexahedra/quadrilaterals can be used, but they are not as efficient as

their higher-order counterparts.

• Higher-order hexahedra, prisms, and quadrilaterals are among the most efficient

elements so far we have discussed. Mesh your models with these elements

whenever possible. If that is not possible, then at least try to achieve a higher-

order hexahedra-dominant or quadrilateral-dominant mesh.