VERSION 4.3

User s Guide

Structural Mechanics Module

C o n t a c t I n f o r m a t i o n

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Part No. CM021101

S t r u c t u r a l M e c h a n i c s M o d u l e U s e r s G u i d e 19982012 COMSOL

Protected by U.S. Patents 7,519,518; 7,596,474; and 7,623,991. Patents pending.

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Version: May 2012 COMSOL 4.3

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C o n t e n t s

C h a p t e r 1 : I n t r o d u c t i o n

About the Structural Mechanics Module 14

Why Structural Mechanics is Important for Modeling . . . . . . . . . 14

What Problems Can It Solve? . . . . . . . . . . . . . . . . . . 15

The Structural Mechanics Physics Guide . . . . . . . . . . . . . . 18

Available Study Types . . . . . . . . . . . . . . . . . . . . . 21

Geometry Levels for Study Capabilities . . . . . . . . . . . . . . 25

Show More Physics Options . . . . . . . . . . . . . . . . . . 26

Where Do I Access the Documentation and Model Library? . . . . . . 28

Typographical Conventions . . . . . . . . . . . . . . . . . . . 30

Overview of the Users Guide 34

C h a p t e r 2 : S t r u c t u r a l M e c h a n i c s M o d e l i n g

Applying Loads 39

Units, Orientation, and Visualization . . . . . . . . . . . . . . . 39

Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . 40

Singular Loads . . . . . . . . . . . . . . . . . . . . . . . . 41

Moments in the Solid Mechanics Interface . . . . . . . . . . . . . 42

Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Acceleration Loads . . . . . . . . . . . . . . . . . . . . . . 43

Temperature LoadsThermal Expansion. . . . . . . . . . . . . . 43

Total Loads . . . . . . . . . . . . . . . . . . . . . . . . . 43

Defining Constraints 44

Orientation . . . . . . . . . . . . . . . . . . . . . . . . . 44

Symmetry Constraints . . . . . . . . . . . . . . . . . . . . . 44

Kinematic Constraints . . . . . . . . . . . . . . . . . . . . . 46

Rotational Joints . . . . . . . . . . . . . . . . . . . . . . . 46

C O N T E N T S | 3

4 | C O N T E N T S

Calculating Reaction Forces 47

Using Predefined Variables to Evaluate Reaction Forces . . . . . . . . 47

Using Weak Constraints to Evaluate Reaction Forces . . . . . . . . . 48

Using Surface Traction to Evaluate Reaction Forces . . . . . . . . . . 49

Introduction to Material Models 50

Introduction to Linear Elastic Materials . . . . . . . . . . . . . . 50

Introduction to Linear Viscoelastic Materials . . . . . . . . . . . . 51

Mixed Formulation . . . . . . . . . . . . . . . . . . . . . . 51

Defining Multiphysics Models 52

Thermal-Structural Interaction. . . . . . . . . . . . . . . . . . 52

Acoustic-Structure Interaction. . . . . . . . . . . . . . . . . . 52

Thermal-Electric-Structural Interaction . . . . . . . . . . . . . . 53

Modeling with Geometric Nonlinearity 54

Geometric Nonlinearity for the Solid Mechanics Interface . . . . . . . 55

Geometric Nonlinearity for the Shell, Plate, Membrane and Truss Interfaces 56

Prestressed Structures. . . . . . . . . . . . . . . . . . . . . 57

Geometric Nonlinearity, Frames, and the ALE Method . . . . . . . . 57

Linearized Buckling Analysis 61

Introduction to Contact Modeling 63

Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 63

Contact Pairs . . . . . . . . . . . . . . . . . . . . . . . . 64

Boundary Settings for Contact Pairs . . . . . . . . . . . . . . . 65

Time-Dependent Analysis . . . . . . . . . . . . . . . . . . . 66

Multiphysics Contact . . . . . . . . . . . . . . . . . . . . . 66

Solver and Mesh Settings for Contact Modeling . . . . . . . . . . . 67

Monitoring the Solution . . . . . . . . . . . . . . . . . . . . 68

Eigenfrequency Analysis 69

Using Modal Superposition 71

Modeling Damping and Losses 73

Overview of Damping and Loss . . . . . . . . . . . . . . . . . 73

Linear Viscoelastic Materials . . . . . . . . . . . . . . . . . . 77

Rayleigh Damping. . . . . . . . . . . . . . . . . . . . . . . 77

Equivalent Viscous Damping. . . . . . . . . . . . . . . . . . . 78

Loss Factor Damping . . . . . . . . . . . . . . . . . . . . . 79

Explicit Damping . . . . . . . . . . . . . . . . . . . . . . . 80

Piezoelectric Losses 81

About Piezoelectric Materials . . . . . . . . . . . . . . . . . . 81

Piezoelectric Material Orientation . . . . . . . . . . . . . . . . 82

Piezoelectric Losses. . . . . . . . . . . . . . . . . . . . . . 88

No Damping . . . . . . . . . . . . . . . . . . . . . . . . 91

References for Piezoelectric Damping . . . . . . . . . . . . . . . 91

Springs and Dampers 93

Tips for Selecting the Correct Solver 95

Symmetric Matrices . . . . . . . . . . . . . . . . . . . . . . 95

Selecting Iterative Solvers . . . . . . . . . . . . . . . . . . . 96

Specifying Tolerances and Scaling for the Solution Components . . . . . 97

Using Perfectly Matched Layers 98

PML Implementation . . . . . . . . . . . . . . . . . . . . . 98

Known Issues When Modeling Using PMLs . . . . . . . . . . . . 100

C h a p t e r 3 : S o l i d M e c h a n i c s

Solid Mechanics Geometry and Structural Mechanics Physics Symbols

104

3D Solid Geometry . . . . . . . . . . . . . . . . . . . . . 104

2D Geometry . . . . . . . . . . . . . . . . . . . . . . . 105

Axisymmetric Geometry . . . . . . . . . . . . . . . . . . . 106

Physics Symbols for Boundary Conditions . . . . . . . . . . . . 106

About Coordinate Systems and Physics Symbols . . . . . . . . . . 108

Displaying Physics Symbols in the Graphics WindowAn Example . . . 108

C O N T E N T S | 5

6 | C O N T E N T S

The Solid Mechanics Interface 111

Domain, Boundary, Edge, Point, and Pair Features for the Solid Mechanics

Interface . . . . . . . . . . . . . . . . . . . . . . . . . 113

Linear Elastic Material .