Solidworks Simulation – Theoretical Manual

Solidworks Simulation – Theoretical Manual
Dassault System
Table of Contents
Introduction . 3
Chapter 1. Fundamental Relations for Linearly Elastic Solids 6
1.1. Stresses . 7
1.1.1. Stress Matrix . 7
1.1.2. Rotated Coordinate Systems . 10
1.1.3. Principal Stresses 14
1.1.4. Equations of Equilibrium 16
1.2. Strains . 17
1.2.1. Strain Matrix . 17
1.2.2. Rotated Coordinate Axes 19
1.2.3. Principal Strains 21
1.3. Stress-Strain Relations . 21
1.3.1. Anisotropic Material . 21
1.3.2. Plane Strain . 26
1.3.3. Plane Stress . 28
1.3.4. Axisymmetric Stress State 31
Chapter 2. The Finite Element Method 36
2.1. The Principle of Minimum Potential Energy . 37
2.2. Strain Energy Expressions for Beams, Plates and Shells . 38
2.2.1. Straight Beams 39
2.2.2. Flat Plates 43
2.3. The Finite Element Method 47
2.4. Interpolation Functions 51
2.5. Isoparametric Elements 54
2.6. Numerical Integration 57
2.7. Reduced Integration . 59
2.8. Solution of simultaneous Linear Expressions 59
2.9. Stress Calculations . 602
Chapter 3. Vibration Frequencies of Structures . 61
3.1. Vibration Modes and Frequencies 62
3.2. Finite Element Analysis . 62
3.3. Solution of Linear Eigenvalue Problems . 64
3.3.1. Subspace Iteration[11, 13] 65
3.3.2. Lanczos Algorithm 66
Chapter 4. Buckling of Structures 70
4.1. The Phenomenon of Buckling 71
4.2. Calculation of Critical Loads . 71
4.3. Variational Principles for Buckling 72
4.3.1. Inplane Buckling for Plane Stress, Plane Strain, Axisymmetric Stress States . 73
4.3.2. Straight Beams 75
4.3.3. Flat Plates 76
4.4. Calculation of Eigenvalues . 76
Chapter 5. Heat Transfer 77
5.1. Equations of Heat Transfer[13] 78
5.2. Variational Statement and the Finite element Method . 81
5.3. Solution of Transient Heat Conduction[13] . 85
Chapter 6. The Element Library . 86
6.1. TRUSS3D: Linear 3-D Truss/Spar 87
6.2. BEAM3D:Linear 3-D Elastic Beam 90
6.3. RBAR: 2-Node Rigid Bar[20] 98
6.4. SPRING: Spring Element 99
6.5. SHELL3T: Triangular Thick Shell[24,25,26] . 100
6.6. SHELL3: Triangular Thin Shell . 103
Notation Table 106
References . 112
Index .
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