Table of Contents

1. Introduction
1.1. Overview of the Theory Reference
1.2. Understanding Theory Reference Notation
1.3. Applicable Products
2. Structures
2.1. Structural Fundamentals
2.1.1. Stress-Strain Relationships
2.1.2. Orthotropic Material Transformation for Axisymmetric Models
2.1.3. Temperature-Dependent Coefficient of Thermal Expansion
2.2. Derivation of Structural Matrices
2.3. Structural Strain and Stress Evaluations
2.3.1. Integration Point Strains and Stresses
2.3.2. Surface Stresses
2.3.3. Shell Element Output
2.4. Combined Stresses and Strains
2.4.1. Combined Strains
2.4.2. Combined Stresses
2.4.3. Failure Criteria
2.5. Perfectly Matched Layers (PML) in Elastic Media
3. Structures with Geometric Nonlinearities
3.1. Understanding Geometric Nonlinearities
3.2. Large Strain
3.2.1. Theory
3.2.2. Implementation
3.2.3. Definition of Thermal Strains
3.2.4. Element Formulation
3.2.5. Applicable Input
3.2.6. Applicable Output
3.3. Large Rotation
3.3.1. Theory
3.3.2. Implementation
3.3.3. Element Transformation
3.3.4. Deformational Displacements
3.3.5. Updating Rotations
3.3.6. Applicable Input
3.3.7. Applicable Output
3.3.8. Consistent Tangent Stiffness Matrix and Finite Rotation
3.4. Stress Stiffening
3.4.1. Overview and Usage
3.4.2. Theory
3.4.3. Implementation
3.4.4. Pressure Load Stiffness
3.4.5. Applicable Input
3.4.6. Applicable Output
3.5. Spin Softening
3.5.1. Spring-Mass System
3.5.2. General Equation
3.6. General Element Formulations
3.6.1. Fundamental Equations
3.6.2. Classical Pure Displacement Formulation
3.6.3. Mixed u-P Formulations
3.6.4. u-P Formulation I
3.6.5. u-P Formulation II
3.6.6. u-P Formulation III
3.6.7. Volumetric Constraint Equations in u-P Formulations
3.7. Constraints and Lagrange Multiplier Method
3.8. Steady State Rolling
3.8.1. General ALE Formulation
3.8.2. ALE Formulation for Steady State Rolling
3.8.3. Kinematics
4. Structures with Material Nonlinearities
4.1. Understanding Material Nonlinearities
4.2. Rate-Independent Plasticity
4.2.1. Theory
4.2.2. Yield Criterion
4.2.3. Flow Rule
4.2.4. Hardening Rule
4.2.5. Plastic Strain Increment
4.2.6. Implementation
4.2.7. Elastoplastic Stress-Strain Matrix
4.2.8. Specialization for Bilinear Isotropic Hardening
4.2.9. Specification for Nonlinear Isotropic Hardening
4.2.10. Specialization for Bilinear Kinematic Hardening
4.2.11. Specialization for Multilinear Kinematic Hardening
4.2.12. Specialization for Nonlinear Kinematic Hardening
4.2.13. Specialization for Anisotropic Plasticity (Hill Potential Theory)
4.2.14. Specialization for Drucker-Prager
4.2.15. Extended Drucker-Prager Cap Model
4.2.16. Gurson's Model
4.2.17. Cast Iron Material Model
4.3. Rate-Dependent Plasticity (Including Creep and Viscoplasticity)
4.3.1. Creep
4.3.2. Rate-Dependent Plasticity
4.3.3. Extended Drucker-Prager (EDP) Creep Model
4.3.4. Cap Creep Model
4.4. Gasket Material
4.4.1. Stress and Deformation
4.4.2. Material Definition
4.4.3. Thermal Deformation
4.5. Nonlinear Elasticity
4.5.1. Overview and Guidelines for Use
4.6. Hyperelasticity
4.6.1. Finite Strain Elasticity
4.6.2. Deviatoric-Volumetric Multiplicative Split
4.6.3. Isotropic Hyperelasticity
4.6.4. Anisotropic Hyperelasticity
4.6.5. USER Subroutine
4.6.6. Output Quantities
4.6.7. Hyperelasticity Material Curve Fitting
4.6.8. Experimental Response Functions
4.6.9. Material Stability Check
4.7. Bergstrom-Boyce
4.8. Mullins Effect
4.8.1. The Pseudo-elastic Model
4.9. Viscoelasticity
4.9.1. Small Strain Viscoelasticity
4.9.2. Constitutive Equations
4.9.3. Numerical Integration
4.9.4. Thermorheological Simplicity
4.9.5. Large-Deformation Viscoelasticity
4.9.6. Visco-Hypoelasticity
4.9.7. Large-Strain Visco-Hyperelasticity
4.9.8. Large-Strain Visco-Anisotropic Hyperelasticity
4.9.9. Shift Functions
4.10. Concrete
4.10.1. The Domain (Compression - Compression - Compression)
4.10.2. The Domain (Tension - Compression - Compression)
4.10.3. The Domain (Tension - Tension - Compression)
4.10.4. The Domain (Tension - Tension - Tension)
4.11. Swelling
4.12. Cohesive Zone Material (CZM) Model
4.12.1. Interface Elements
4.12.2. Contact Elements
4.13. Fluid Material Models
4.13.1. Liquid
4.13.2. Gas
4.13.3. Pressure-Volume Data
5. Electromagnetics
5.1. Electromagnetic Field Fundamentals
5.1.1. Magnetic Scalar Potential
5.1.2. Solution Strategies
5.1.3. Magnetic Vector Potential
5.1.4. Edge-Based Magnetic Vector Potential
5.1.5. Harmonic Analysis Using Complex Formalism
5.1.6. Electric Scalar Potential
5.2. Derivation of Electromagnetic Matrices
5.2.1. Magnetic Scalar Potential
5.2.2. Magnetic Vector Potential
5.2.3. Edge-Based Magnetic Vector Potential
5.2.4. Electric Scalar Potential
5.3. Electromagnetic Field Evaluations
5.3.1. Magnetic Scalar Potential Results
5.3.2. Magnetic Vector Potential Results
5.3.3. Edge-Based Magnetic Vector Potential
5.3.4. Magnetic Forces
5.3.5. Joule Heat in a Magnetic Analysis
5.3.6. Electric Scalar Potential Results
5.3.7. Electrostatic Forces
5.4. Stranded Coil Analyses
5.4.1. Governing Equations
5.4.2. A-VOLT-EMF Formulation
5.5. Inductance, Flux and Energy Computation
5.5.1. Differential Inductance Definition
5.5.2. Review of Inductance Computation Methods
5.5.3. Inductance Computation Method Used
5.5.4. Transformer and Motion Induced Voltages
5.5.5. Absolute Flux Computation
5.5.6. Inductance Computations
5.5.7. Absolute Energy Computation
5.6. Electromagnetic Particle Tracing
5.7. Capacitance Computation
5.8. Conductance Computation
5.9. Hall Effect
6. Heat Flow
6.1. Heat Flow Fundamentals
6.1.1. Conduction and Convection
6.1.2. Radiation
6.2. Derivation of Heat Flow Matrices
6.3. Heat Flow Evaluations
6.3.1. Integration Point Output
6.3.2. Surface Output
6.4. Radiation Matrix Method
6.4.1. View Factor Calculation (2-D): Radiation Matrix Method
6.4.2. View Factors of Axisymmetric Bodies
6.4.3. Space Node
6.5. Radiosity Solution Method
6.5.1. View Factor Calculation (3-D): Hemicube Method
7. Thin Fluid Film Flow
7.1. Squeeze Film
7.1.1. Flow Between Flat Surfaces
7.1.2. Flow in Channels
7.2. Slide Film
7.3. Hydrodynamic Bearing
7.3.1. Finite Length Formulation for 2-D Elements
7.3.2. Finite Element Formulation for 3-D Element
8. Acoustics
8.1. Acoustic Fundamentals
8.1.1. Governing Equations
8.1.2. Finite Element Formulation of the Wave Equation
8.1.3. Governing Equations with Mean Flow Effect
8.1.4. Finite Element Formulation of the Convective Wave Equation
8.2. Derivation of Acoustic Matrices
8.3. Propagation, Radiation, and Scattering of Acoustic Pressure Waves
8.3.1. Acoustic Boundary Conditions
8.3.2. Absorbing Boundary Condition (ABC)
8.3.3. Artificially Matched Layers
8.3.4. Acoustic Excitation Sources
8.3.5. Sophisticated Acoustic Media
8.4. Acoustic Fluid-Structural Interaction (FSI)
8.4.1. Coupled Acoustic Fluid-Structural System with an Unsymmetric Matrix Equation
8.4.2. Coupled Acoustic Fluid-Structural System with Symmetric Matrix Equation for Full Harmonic Analysis
8.5. Pure Scattered Pressure Formulation
8.6. Acoustic Output Quantities
8.6.1. Sound Pressure
8.6.2. Far-field Parameters
8.6.3. Sound Power
8.6.4. Acoustic Surface Quantities
8.6.5. Acoustic Volumetric Quantities
8.6.6. Band Sound Pressure Level
8.6.7. Equivalent Radiated Power
8.7. Transfer Admittance Matrix
8.7.1. Transfer Admittance Matrix Connected to Acoustic Domains
8.7.2. Transfer Admittance Matrix Connected to the Structural and Acoustic Domain
8.8. Random Acoustics
8.8.1. Acoustic Diffuse Sound Field
8.8.2. Diffuse Sound Field Power Spectral Density
8.8.3. Diffuse Sound Field Physical Sampling
9. Diffusion
9.1. Diffusion Fundamentals
9.2. Normalized Concentration Approach
9.3. Derivation of Diffusion Matrices
9.4. Diffusion Analysis Results
10. Coupling
10.1. Coupled Effects
10.1.1. Elements
10.1.2. Coupling Methods
10.2. Thermoelasticity
10.3. Thermoplasticity
10.4. Piezoelectrics
10.5. Electroelasticity
10.6. Piezoresistivity
10.7. Thermoelectrics
10.8. Review of Coupled Electromechanical Methods
10.9. Porous Media Flow
10.10. Structural-Diffusion Coupling
10.11. Thermal-Diffusion Coupling
10.12. Electric-Diffusion Coupling
11. Shape Functions
11.1. Understanding Shape Function Labels
11.2. 2-D Lines
11.2.1. 2-D Lines without RDOF
11.2.2. 2-D Lines with RDOF
11.3. 3-D Lines
11.3.1. 3-D 2-Node Lines (Not Combining Translations and Rotations)
11.3.2. 3-D 2-Node Lines (Combining Translations and Rotations)
11.3.3. 3-D 3-Node Lines
11.3.4. 3-D 4-Node Lines
11.4. Axisymmetric Shells
11.4.1. Axisymmetric Shell without ESF
11.5. Axisymmetric Harmonic Shells and General Axisymmetric Surfaces
11.5.1. Axisymmetric Harmonic Shells
11.5.2. General Axisymmetric Surfaces
11.6. 3-D Shells
11.6.1. 3-D 3-Node Triangular Shells without RDOF (CST)
11.6.2. 3-D 6-Node Triangular Shells without RDOF (LST)
11.6.3. 3-D 3-Node Triangular Shells with RDOF but without SD
11.6.4. 3-D 4-Node Quadrilateral Shells without RDOF and without ESF (Q4)
11.6.5. 3-D 4-Node Quadrilateral Shells without RDOF but with ESF (QM6)
11.6.6. 3-D 8-Node Quadrilateral Shells without RDOF
11.6.7. 3-D 4-Node Quadrilateral Shells with RDOF but without SD and without ESF
11.6.8. 3-D 4-Node Quadrilateral Shells with RDOF but without SD and with ESF
11.7. 2-D and Axisymmetric Solids
11.7.1. 2-D and Axisymmetric 3-Node Triangular Solids (CST)
11.7.2. 2-D and Axisymmetric 6-Node Triangular Solids (LST)
11.7.3. 2-D and Axisymmetric 4-node Quadrilateral Solid without ESF (Q4)
11.7.4. 2-D and Axisymmetric 4-node Quadrilateral Solids with ESF (QM6)
11.7.5. 2-D and Axisymmetric 8-Node Quadrilateral Solids (Q8)
11.7.6. 2-D and Axisymmetric 4-Node Quadrilateral Infinite Solids
11.7.7. 2-D and Axisymmetric 8-Node Quadrilateral Infinite Solids
11.8. Axisymmetric Harmonic Solids
11.8.1. Axisymmetric Harmonic 3-Node Triangular Solids
11.8.2. Axisymmetric Harmonic 6-Node Triangular Solids
11.8.3. Axisymmetric Harmonic 4-Node Quadrilateral Solids without ESF
11.8.4. Axisymmetric Harmonic 4-Node Quadrilateral Solids with ESF
11.8.5. Axisymmetric Harmonic 8-Node Quadrilateral Solids
11.9. 3-D Solids
11.9.1. 4-Node Tetrahedra
11.9.2. 10-Node Tetrahedra
11.9.3. 5-Node Pyramids
11.9.4. 13-Node Pyramids
11.9.5. 6-Node Wedges without ESF
11.9.6. 6-Node Wedges with ESF
11.9.7. 15-Node Wedges
11.9.8. 8-Node Bricks without ESF
11.9.9. 8-Node Bricks with ESF
11.9.10. 20-Node Bricks
11.9.11. 8-Node Infinite Bricks
11.9.12. 20-Node Infinite Bricks
11.9.13. General Axisymmetric Solids
11.10. Electromagnetic Tangential Vector Elements
11.10.1. Tetrahedral Elements
11.10.2. Hexahedral Elements
12. Element Tools
12.1. Element Shape Testing
12.1.1. Overview
12.1.2. 3-D Solid Element Faces and Cross-Sections
12.1.3. Aspect Ratio
12.1.4. Aspect Ratio Calculation for Triangles
12.1.5. Aspect Ratio Calculation for Quadrilaterals
12.1.6. Parallel Deviation
12.1.7. Parallel Deviation Calculation
12.1.8. Maximum Corner Angle
12.1.9. Maximum Corner Angle Calculation
12.1.10. Jacobian Ratio
12.1.11. Warping Factor
12.2. Integration Point Locations
12.2.1. Lines (1, 2, or 3 Points)
12.2.2. Quadrilaterals (2 x 2 or 3 x 3 Points)
12.2.3. Bricks and Pyramids (2 x 2 x 2 Points)
12.2.4. Triangles (1, 3, or 6 Points)
12.2.5. Tetrahedra (1, 4, 5, or 11 Points)
12.2.6. Triangles and Tetrahedra (2 x 2 or 2 x 2 x 2 Points)
12.2.7. Wedges (3 x 2 or 3 x 3 Points)
12.2.8. Wedges (2 x 2 x 2 Points)
12.2.9. Bricks (14 Points)
12.2.10. Nonlinear Bending (5 Points)
12.2.11. General Axisymmetric Elements
12.3. Temperature-Dependent Material Properties
12.4. Positive Definite Matrices
12.4.1. Matrices Representing the Complete Structure
12.4.2. Element Matrices
12.5. Lumped Matrices
12.5.1. Diagonalization Procedure
12.5.2. Limitations of Lumped Mass Matrices
12.6. Reuse of Matrices
12.6.1. Element Matrices
12.6.2. Structure Matrices
12.6.3. Override Option
12.7. Hydrostatic Loads
12.7.1. Internal and External Pressures
12.7.2. Buoyancy
12.7.3. Effective Tension
12.7.4. Instability Checking
12.7.5. Effect of Water Pressure on Some Elements
12.8. Hydrodynamic Loads
12.8.1. Regular Waves on Line Elements
12.8.2. Irregular Waves on Line Elements (Kw = 5 through 7)
12.8.3. Diffracted Wave on Line and Surface Elements (Kw = 8)
12.8.4. Presence of Both Waves and Current
12.8.5. MacCamy-Fuchs Corrections
12.8.6. Morison's Equation
12.8.7. Dynamic Pressure Head
12.9. Nodal and Centroidal Data Evaluation
13. Element Library
13.1. Reserved for Future Use
13.2. Not Documented
13.3. Reserved for Future Use
13.4. Reserved for Future Use
13.5. SOLID5 - 3-D Coupled-Field Solid
13.5.1. Other Applicable Sections
13.6. Reserved for Future Use
13.7. Reserved for Future Use
13.8. Reserved for Future Use
13.9. Reserved for Future Use
13.10. Reserved for Future Use
13.11. LINK11 - Linear Actuator
13.11.1. Assumptions and Restrictions
13.11.2. Element Matrices and Load Vector
13.11.3. Force, Stroke, and Length
13.12. Reserved for Future Use
13.13. PLANE13 - 2-D Coupled-Field Solid
13.13.1. Other Applicable Sections
13.14. COMBIN14 - Spring-Damper
13.14.1. Types of Input
13.14.2. Stiffness Pass
13.14.3. Output Quantities
13.15. Reserved for Future Use
13.16. Reserved for Future Use
13.17. Reserved for Future Use
13.18. Reserved for Future Use
13.19. Reserved for Future Use
13.20. Reserved for Future Use
13.21. MASS21 - Structural Mass
13.22. Reserved for Future Use
13.23. Reserved for Future Use
13.24. Reserved for Future Use
13.25. PLANE25 - Axisymmetric-Harmonic 4-Node Structural Solid
13.25.1. Other Applicable Sections
13.25.2. Assumptions and Restrictions
13.25.3. Use of Temperature
13.26. Not Documented
13.27. MATRIX27 - Stiffness, Damping, or Mass Matrix
13.27.1. Assumptions and Restrictions
13.28. Reserved for Future Use
13.29. FLUID29 - 2-D Acoustic Fluid
13.29.1. Other Applicable Sections
13.30. FLUID30 - 3-D Acoustic Fluid
13.30.1. Other Applicable Sections
13.31. LINK31 - Radiation Link
13.31.1. Standard Radiation (KEYOPT(3) = 0)
13.31.2. Empirical Radiation (KEYOPT(3) = 1)
13.31.3. Solution
13.32. Reserved for Future Use
13.33. LINK33 - 3-D Conduction Bar
13.33.1. Other Applicable Sections
13.33.2. Matrices and Load Vectors
13.33.3. Output
13.34. LINK34 - Convection Link
13.34.1. Conductivity Matrix
13.34.2. Output
13.35. PLANE35 - 2-D 6-Node Triangular Thermal Solid
13.35.1. Other Applicable Sections
13.36. SOURC36 - Current Source
13.36.1. Description
13.37. COMBIN37 - Control
13.37.1. Element Characteristics
13.37.2. Element Matrices
13.37.3. Adjustment of Real Constants
13.37.4. Evaluation of Control Parameter
13.38. FLUID38 - Dynamic Fluid Coupling
13.38.1. Description
13.38.2. Assumptions and Restrictions
13.38.3. Mass Matrix Formulation
13.38.4. Damping Matrix Formulation
13.39. COMBIN39 - Nonlinear Spring
13.39.1. Input
13.39.2. Element Stiffness Matrix and Load Vector
13.39.3. Choices for Element Behavior
13.40. COMBIN40 - Combination
13.40.1. Characteristics of the Element
13.40.2. Element Matrices for Structural Applications
13.40.3. Determination of F1 and F2 for Structural Applications
13.40.4. Thermal Analysis
13.41. Reserved for Future Use
13.42. Reserved for Future Use
13.43. Reserved for Future Use
13.44. Reserved for Future Use
13.45. Reserved for Future Use
13.46. Reserved for Future Use
13.47. INFIN47 - 3-D Infinite Boundary
13.47.1. Introduction
13.47.2. Theory
13.47.3. Reduced Scalar Potential
13.47.4. Difference Scalar Potential
13.47.5. Generalized Scalar Potential
13.48. Not Documented
13.49. Not Documented
13.50. MATRIX50 - Superelement (or Substructure)
13.50.1. Other Applicable Sections
13.51. Not Documented
13.52. Reserved for Future Use
13.53. Reserved for Future Use
13.54. Reserved for Future Use
13.55. PLANE55 - 2-D Thermal Solid
13.55.1. Other Applicable Sections
13.55.2. Mass Transport Option
13.56. Not Documented
13.57. Reserved for Future Use
13.58. Not Documented
13.59. Reserved for Future Use
13.60. Reserved for Future Use
13.61. SHELL61 - Axisymmetric-Harmonic Structural Shell
13.61.1. Other Applicable Sections
13.61.2. Assumptions and Restrictions
13.61.3. Stress, Force, and Moment Calculations
13.62. Reserved for Future Use
13.63. Reserved for Future Use
13.64. Not Documented
13.65. SOLID65 - 3-D Reinforced Concrete Solid
13.65.1. Assumptions and Restrictions
13.65.2. Description
13.65.3. Linear Behavior - General
13.65.4. Linear Behavior - Concrete
13.65.5. Linear Behavior - Reinforcement
13.65.6. Nonlinear Behavior - Concrete
13.65.7. Modeling of a Crack
13.65.8. Modeling of Crushing
13.66. Reserved for Future Use
13.67. Reserved for Future Use
13.68. LINK68 - Coupled Thermal-Electric Line
13.68.1. Other Applicable Sections
13.69. Reserved for Future Use
13.70. SOLID70 - 3-D Thermal Solid
13.70.1. Other Applicable Sections
13.70.2. Fluid Flow in a Porous Medium
13.71. MASS71 - Thermal Mass
13.71.1. Specific Heat Matrix
13.71.2. Heat Generation Load Vector
13.72. Reserved for Future Use
13.73. Reserved for Future Use
13.74. Not Documented
13.75. PLANE75 - Axisymmetric-Harmonic 4-Node Thermal Solid
13.75.1. Other Applicable Sections
13.76. Reserved for Future Use
13.77. PLANE77 - 2-D 8-Node Thermal Solid
13.77.1. Other Applicable Sections
13.77.2. Assumptions and Restrictions
13.78. PLANE78 - Axisymmetric-Harmonic 8-Node Thermal Solid
13.78.1. Other Applicable Sections
13.78.2. Assumptions and Restrictions
13.79. Reserved for Future Use
13.80. Reserved for Future Use
13.81. Reserved for Future Use
13.82. Reserved for Future Use
13.83. PLANE83 - Axisymmetric-Harmonic 8-Node Structural Solid
13.83.1. Other Applicable Sections
13.83.2. Assumptions and Restrictions
13.84. Not Documented
13.85. Reserved for Future Use
13.86. Not Documented
13.87. SOLID87 - 3-D 10-Node Tetrahedral Thermal Solid
13.87.1. Other Applicable Sections
13.88. Reserved for Future Use
13.89. Reserved for Future Use
13.90. SOLID90 - 3-D 20-Node Thermal Solid
13.90.1. Other Applicable Sections
13.91. Reserved for Future Use
13.92. Reserved for Future Use
13.93. Reserved for Future Use
13.94. CIRCU94 - Piezoelectric Circuit
13.94.1. Electric Circuit Elements
13.94.2. Piezoelectric Circuit Element Matrices and Load Vectors
13.95. Reserved for Future Use
13.96. SOLID96 - 3-D Magnetic Scalar Solid
13.96.1. Other Applicable Sections
13.97. Reserved for Future Use
13.98. SOLID98 - Tetrahedral Coupled-Field Solid
13.98.1. Other Applicable Sections
13.99. Reserved for Future Use
13.100. Reserved for Future Use
13.101. Reserved for Future Use
13.102. Reserved for Future Use
13.103. Reserved for Future Use
13.104. Reserved for Future Use
13.105. Reserved for Future Use
13.106. Reserved for Future Use
13.107. Reserved for Future Use
13.108. Reserved for Future Use
13.109. Reserved for Future Use
13.110. INFIN110 - 2-D Infinite Solid
13.110.1. Mapping Functions
13.110.2. Matrices
13.111. INFIN111 - 3-D Infinite Solid
13.111.1. Other Applicable Sections
13.112. Reserved for Future Use
13.113. Reserved for Future Use
13.114. Reserved for Future Use
13.115. Reserved for Future Use
13.116. FLUID116 - Coupled Thermal-Fluid Pipe
13.116.1. Assumptions and Restrictions
13.116.2. Combined Equations
13.116.3. Thermal Matrix Definitions
13.116.4. Fluid Equations
13.117. Reserved for Future Use
13.118. Reserved for Future Use
13.119. Reserved for Future Use
13.120. Reserved for Future Use
13.121. PLANE121 - 2-D 8-Node Electrostatic Solid
13.121.1. Other Applicable Sections
13.121.2. Assumptions and Restrictions
13.122. SOLID122 - 3-D 20-Node Electrostatic Solid
13.122.1. Other Applicable Sections
13.123. SOLID123 - 3-D 10-Node Tetrahedral Electrostatic Solid
13.123.1. Other Applicable Sections
13.124. CIRCU124 - Electric Circuit
13.124.1. Electric Circuit Elements
13.124.2. Electric Circuit Element Matrices
13.125. CIRCU125 - Diode
13.125.1. Diode Elements
13.125.2. Norton Equivalents
13.125.3. Element Matrix and Load Vector
13.126. TRANS126 - Electromechanical Transducer
13.127. Reserved for Future Use
13.128. Reserved for Future Use
13.129. FLUID129 - 2-D Infinite Acoustic
13.129.1. Other Applicable Sections
13.130. FLUID130 - 3-D Infinite Acoustic
13.130.1. Mathematical Formulation and F.E. Discretization
13.130.2. Finite Element Discretization
13.131. SHELL131 - 4-Node Layered Thermal Shell
13.131.1. Other Applicable Sections
13.132. SHELL132 - 8-Node Layered Thermal Shell
13.132.1. Other Applicable Sections
13.133. Reserved for Future Use
13.134. Reserved for Future Use
13.135. Reserved for Future Use
13.136. FLUID136 - 3-D Squeeze Film Fluid Element
13.136.1. Other Applicable Sections
13.136.2. Assumptions and Restrictions
13.137. Reserved for Future Use
13.138. FLUID138 - 3-D Viscous Fluid Link Element
13.138.1. Other Applicable Sections
13.139. FLUID139 - 3-D Slide Film Fluid Element
13.139.1. Other Applicable Sections
13.140. Reserved for Future Use
13.141. Reserved for Future Use
13.142. Reserved for Future Use
13.143. Not Documented
13.144. ROM144 - Reduced Order Electrostatic-Structural
13.144.1. Element Matrices and Load Vectors
13.144.2. Combination of Modal Coordinates and Nodal Displacement at Master Nodes
13.144.3. Element Loads
13.145. Reserved for Future Use
13.146. Reserved for Future Use
13.147. Reserved for Future Use
13.148. Reserved for Future Use
13.149. Reserved for Future Use
13.150. Reserved for Future Use
13.151. SURF151 - 2-D Thermal Surface Effect
13.152. SURF152 - 3-D Thermal Surface Effect
13.152.1. Matrices and Load Vectors
13.152.2. Adiabatic Wall Temperature as Bulk Temperature
13.152.3. Film Coefficient Adjustment
13.152.4. Radiation Form Factor Calculation
13.153. SURF153 - 2-D Structural Surface Effect
13.154. SURF154 - 3-D Structural Surface Effect
13.155. SURF155 - 3-D Thermal Surface Line Load
13.156. SURF156 - 3-D Structural Surface Line Load Effect
13.157. SHELL157 - Thermal-Electric Shell
13.157.1. Other Applicable Sections
13.158. Not Documented
13.159. SURF159 - General Axisymmetric Surface with 2 or 3 Nodes
13.159.1. Other Applicable Sections
13.159.2. Assumptions and Restrictions
13.160. LINK160 - Explicit 3-D Spar (or Truss)
13.161. BEAM161 - Explicit 3-D Beam
13.162. PLANE162 - Explicit 2-D Structural Solid
13.163. SHELL163 - Explicit Thin Structural Shell
13.164. SOLID164 - Explicit 3-D Structural Solid
13.165. COMBI165 - Explicit Spring-Damper
13.166. MASS166 - Explicit 3-D Structural Mass
13.167. LINK167 - Explicit Tension-Only Spar
13.168. SOLID168 - Explicit 3-D 10-Node Tetrahedral Structural Solid
13.169. TARGE169 - 2-D Target Segment
13.169.1. Other Applicable Sections
13.169.2. Segment Types
13.170. TARGE170 - 3-D Target Segment
13.170.1. Introduction
13.170.2. Segment Types
13.170.3. Reaction Forces
13.171. CONTA171 - 2-D 2-Node Surface-to-Surface Contact
13.171.1. Other Applicable Sections
13.172. CONTA172 - 2-D 3-Node Surface-to-Surface Contact
13.172.1. Other Applicable Sections
13.173. CONTA173 - 3-D 4-Node Surface-to-Surface Contact
13.173.1. Other Applicable Sections
13.174. CONTA174 - 3-D 8-Node Surface-to-Surface Contact
13.174.1. Introduction
13.174.2. Contact Kinematics
13.174.3. Frictional Model
13.174.4. Contact Algorithm
13.174.5. Viscous Damping
13.174.6. Energy and Momentum Conserving Contact
13.174.7. Debonding
13.174.8. Contact Surface Wear
13.174.9. Thermal/Structural Contact
13.174.10. Electric Contact
13.174.11. Magnetic Contact
13.174.12. Pore Fluid Contact
13.174.13. Diffusive Contact
13.175. CONTA175 - 2-D/3-D Node-to-Surface Contact
13.175.1. Other Applicable Sections
13.175.2. Contact Models
13.175.3. Contact Forces
13.176. CONTA176 - 3-D Line-to-Line Contact
13.176.1. Other Applicable Sections
13.176.2. Contact Kinematics
13.176.3. Contact Models
13.176.4. Contact Forces
13.177. CONTA177 - 3-D Line-to-Surface Contact
13.177.1. Other Applicable Sections
13.177.2. Contact Kinematics
13.177.3. Contact Model
13.177.4. Contact Forces
13.178. CONTA178 - 3-D Node-to-Node Contact
13.178.1. Introduction
13.178.2. Contact Algorithms
13.178.3. Element Damper
13.178.4. Rigid Coulomb Friction
13.179. PRETS179 - Pretension
13.179.1. Introduction
13.179.2. Assumptions and Restrictions
13.180. LINK180 - 3-D Spar (or Truss)
13.180.1. Assumptions and Restrictions
13.181. SHELL181 - 4-Node Shell
13.181.1. Other Applicable Sections
13.181.2. Assumptions and Restrictions
13.181.3. Assumed Displacement Shape Functions
13.181.4. Membrane Option
13.181.5. Warping
13.181.6. Shear Correction
13.182. PLANE182 - 2-D 4-Node Structural Solid
13.182.1. Other Applicable Sections
13.182.2. Theory
13.183. PLANE183 - 2-D 8-Node Structural Solid
13.183.1. Other Applicable Sections
13.183.2. Assumptions and Restrictions
13.184. MPC184 - Multipoint Constraint
13.184.1. Slider Element
13.184.2. Joint Elements
13.185. SOLID185 - 3-D 8-Node Structural Solid
13.185.1. SOLID185 - 3-D 8-Node Structural Solid
13.185.2. SOLID185 - 3-D 8-Node Layered Solid
13.185.3. Other Applicable Sections
13.185.4. Theory
13.185.5. Shear Correction
13.186. SOLID186 - 3-D 20-Node homogeneous/Layered Structural Solid
13.186.1. SOLID186 - 3-D 20-Node homogeneous Structural Solid
13.186.2. SOLID186 - 3-D 20-Node Layered Structural Solid
13.186.3. Other Applicable Sections
13.186.4. Shear Correction
13.187. SOLID187 - 3-D 10-Node Tetrahedral Structural Solid
13.187.1. Other Applicable Sections
13.188. BEAM188 - 3-D 2-Node Beam
13.188.1. Assumptions and Restrictions
13.188.2. Ocean Effects
13.188.3. Stress Evaluation
13.189. BEAM189 - 3-D 3-Node Beam
13.190. SOLSH190 - 3-D 8-Node Layered Solid Shell
13.190.1. Other Applicable Sections
13.190.2. Theory
13.190.3. Shear Correction
13.191. Reserved for Future Use
13.192. INTER192 - 2-D 4-Node Gasket
13.192.1. Other Applicable Sections
13.193. INTER193 - 2-D 6-Node Gasket
13.193.1. Other Applicable Sections
13.194. INTER194 - 3-D 16-Node Gasket
13.194.1. Element Technology
13.195. INTER195 - 3-D 8-Node Gasket
13.195.1. Other Applicable Sections
13.196. Reserved for Future Use
13.197. Reserved for Future Use
13.198. Reserved for Future Use
13.199. Reserved for Future Use
13.200. Reserved for Future Use
13.201. Reserved for Future Use
13.202. INTER202 - 2-D 4-Node Cohesive
13.202.1. Other Applicable Sections
13.203. INTER203 - 2-D 6-Node Cohesive
13.203.1. Other Applicable Sections
13.204. INTER204 - 3-D 16-Node Cohesive
13.204.1. Element Technology
13.205. INTER205 - 3-D 8-Node Cohesive
13.205.1. Other Applicable Sections
13.206. Reserved for Future Use
13.207. Reserved for Future Use
13.208. SHELL208 - 2-Node Axisymmetric Shell
13.208.1. Other Applicable Sections
13.208.2. Assumptions and Restrictions
13.208.3. Shear Correction
13.209. SHELL209 - 3-Node Axisymmetric Shell
13.209.1. Other Applicable Sections
13.209.2. Assumptions and Restrictions
13.209.3. Shear Correction
13.210. Reserved for Future Use
13.211. Reserved for Future Use
13.212. CPT212 - 2-D 4-Node Coupled Pore-Pressure-Thermal Mechanical Solid
13.212.1. Other Applicable Sections
13.213. CPT213 - 2-D 8-Node Coupled Pore-Pressure-Thermal Mechanical Solid
13.213.1. Other Applicable Sections
13.213.2. Assumptions and Restrictions
13.214. COMBI214 - 2-D Spring-Damper Bearing
13.214.1. Matrices
13.214.2. Output Quantities
13.215. CPT215 - 3-D 8-Node Coupled Pore-Pressure-Thermal Mechanical Solid
13.215.1. Other Applicable Sections
13.216. CPT216 - 3-D 20-Node Coupled Pore-Pressure-Thermal Mechanical Solid
13.216.1. Other Applicable Sections
13.217. CPT217 - 3-D 10-Node Coupled Pore-Pressure-Thermal Mechanical Solid
13.217.1. Other Applicable Sections
13.218. FLUID218 - 3-D Hydrodynamic Bearing Element
13.218.1. Other Applicable Sections
13.218.2. Assumptions and Restrictions
13.219. Reserved for Future Use
13.220. Reserved for Future Use
13.221. Reserved for Future Use
13.222. PLANE222 - 2-D 4-Node Coupled-Field Solid
13.222.1. Other Applicable Sections
13.222.2. Theory
13.223. PLANE223 - 2-D 8-Node Coupled-Field Solid
13.223.1. Other Applicable Sections
13.224. Reserved for Future Use
13.225. Reserved for Future Use
13.226. SOLID226 - 3-D 20-Node Coupled-Field Solid
13.226.1. Other Applicable Sections
13.227. SOLID227 - 3-D 10-Node Coupled-Field Solid
13.227.1. Other Applicable Sections
13.228. Reserved for Future Use
13.229. Reserved for Future Use
13.230. PLANE230 - 2-D 8-Node Electric Solid
13.230.1. Other Applicable Sections
13.230.2. Assumptions and Restrictions
13.231. SOLID231 - 3-D 20-Node Electric Solid
13.231.1. Other Applicable Sections
13.232. SOLID232 - 3-D 10-Node Tetrahedral Electric Solid
13.232.1. Other Applicable Sections
13.233. PLANE233 - 2-D 8-Node Electromagnetic Solid
13.233.1. Other Applicable Sections
13.233.2. Assumptions and Restrictions
13.234. Reserved for Future Use
13.235. Reserved for Future Use
13.236. SOLID236 - 3-D 20-Node Electromagnetic Solid
13.236.1. Other Applicable Sections
13.237. SOLID237 - 3-D 10-Node Electromagnetic Solid
13.237.1. Other Applicable Sections
13.238. PLANE238 - 2-D 8-Node Diffusion Solid
13.238.1. Other Applicable Sections
13.238.2. Assumptions and Restrictions
13.239. SOLID239 - 3-D 20-Node Diffusion Solid
13.239.1. Other Applicable Sections
13.240. SOLID240 - 3-D 10-Node Tetrahedral Diffusion Solid
13.240.1. Other Applicable Sections
13.241. HSFLD241 - 2-D Hydrostatic Fluid
13.242. HSFLD242 - 3-D Hydrostatic Fluid
13.242.1. Introduction
13.242.2. Element Matrices and Load Vectors
13.243. Reserved for Future Use
13.244. Reserved for Future Use
13.245. Reserved for Future Use
13.246. Reserved for Future Use
13.247. Reserved for Future Use
13.248. Reserved for Future Use
13.249. Reserved for Future Use
13.250. Reserved for Future Use
13.251. SURF251 - 2-D Radiosity Surface
13.252. SURF252 - 3-D Thermal Radiosity Surface
13.253. Reserved for Future Use
13.254. Reserved for Future Use
13.255. Reserved for Future Use
13.256. Reserved for Future Use
13.257. INFIN257 - Structural Infinite Solid
13.257.1. Structural Infinite Element for Static Analysis
13.257.2. Structural Infinite Element for Dynamic Analysis
13.258. Reserved for Future Use
13.259. Reserved for Future Use
13.260. Reserved for Future Use
13.261. Reserved for Future Use
13.262. Reserved for Future Use
13.263. REINF263 - 2-D Smeared Reinforcing
13.263.1. Other Applicable Sections
13.264. REINF264 - 3-D Discrete Reinforcing
13.264.1. Other Applicable Sections
13.265. REINF265 - 3-D Smeared Reinforcing
13.265.1. Other Applicable Sections
13.265.2. Stiffness and Mass Matrices of a Reinforcing Layer
13.266. Reserved for Future Use
13.267. Reserved for Future Use
13.268. Reserved for Future Use
13.269. Reserved for Future Use
13.270. Reserved for Future Use
13.271. Reserved for Future Use
13.272. SOLID272 - General Axisymmetric Solid with 4 Base Nodes
13.272.1. Other Applicable Sections
13.272.2. Assumptions and Restrictions
13.273. SOLID273 - General Axisymmetric Solid with 8 Base Nodes
13.273.1. Other Applicable Sections
13.273.2. Assumptions and Restrictions
13.274. Reserved for Future Use
13.275. Reserved for Future Use
13.276. Reserved for Future Use
13.277. Reserved for Future Use
13.278. SOLID278 - 3-D 8-Node homogeneous/Layered Thermal Solid
13.278.1. SOLID278 - 3-D 8-Node homogeneous Thermal Solid
13.278.2. SOLID278 - 3-D 8-Node Layered Thermal Solid
13.279. SOLID279 - 3-D 20-Node Homogeneous/Layered Thermal Solid
13.279.1. SOLID279 - 3-D 20-Node Homogeneous Thermal Solid
13.279.2. SOLID279 - 3-D 20-Node Layered Thermal Solid
13.280. Reserved for Future Use
13.281. SHELL281 - 8-Node Shell
13.281.1. Other Applicable Sections
13.281.2. Assumptions and Restrictions
13.281.3. Membrane Option
13.281.4. Shear Correction
13.282. Reserved for Future Use
13.283. Reserved for Future Use
13.284. Reserved for Future Use
13.285. SOLID285 - 3-D 4-Node Tetrahedral Structural Solid with Nodal Pressures
13.285.1. Other Applicable Sections
13.285.2. Theory
13.286. Reserved for Future Use
13.287. Reserved for Future Use
13.288. PIPE288 - 3-D 2-Node Pipe
13.288.1. Assumptions and Restrictions
13.288.2. Ocean Effects
13.288.3. Stress Evaluation
13.289. PIPE289 - 3-D 3-Node Pipe
13.290. ELBOW290 - 3-D 3-Node Elbow
13.290.1. Other Applicable Sections
13.290.2. Assumptions and Restrictions
13.290.3. Shear Correction
14. Analysis Tools
14.1. Acceleration Effect
14.1.1. Acceleration Due to One Rotation
14.1.2. Acceleration Due to Two Rotations
14.2. Inertia Relief
14.2.1. Mass-Related Information Calculation
14.3. Damping Matrices
14.3.1. Transient (FULL) Analysis
14.3.2. Damped Modal Analysis
14.3.3. Harmonic (FULL) Analysis
14.3.4. Mode-Superposition Analysis
14.4. Rotating Structures
14.4.1. Rotating Reference Frame Equations
14.4.2. Stationary Reference Frame Equations
14.5. Automatic Time Stepping
14.5.1. Time Step Prediction
14.5.2. Time Step Bisection
14.5.3. The Response Eigenvalue for 1st Order Transients
14.5.4. The Response Frequency for Structural Dynamics
14.5.5. Creep Time Increment
14.5.6. Plasticity Time Increment
14.5.7. Midstep Residual for Structural Dynamic Analysis
14.6. Solving for Unknowns and Reactions
14.6.1. Reaction Forces
14.6.2. Disequilibrium
14.7. Equation Solvers
14.7.1. Direct Solvers
14.7.2. Sparse Direct Solver
14.7.3. Iterative Solver
14.8. Mode-Superposition Method
14.8.1. General Equations
14.8.2. Equations for QR Damped Eigensolver Based Analysis
14.8.3. Equations for Unsymmetric Eigensolver Based Analysis
14.8.4. Modal Damping
14.8.5. Residual Vector Method
14.8.6. Residual Response Method
14.9. Extraction of Modal Damping Parameter for Squeeze Film Problems
14.10. Reduced Order Modeling of Coupled Domains
14.10.1. Selection of Modal Basis Functions
14.10.2. Element Loads
14.10.3. Mode Combinations for Finite Element Data Acquisition and Energy Computation
14.10.4. Function Fit Methods for Strain Energy
14.10.5. Coupled Electrostatic-Structural Systems
14.10.6. Computation of Capacitance Data and Function Fit
14.11. Newton-Raphson Procedure
14.11.1. Overview
14.11.2. Convergence
14.11.3. Predictor
14.11.4. Adaptive Descent
14.11.5. Line Search
14.11.6. Arc-Length Method
14.12. Constraint Equations
14.12.1. Derivation of Matrix and Load Vector Operations
14.12.2. Constraints: Automatic Selection of Slave DOFs
14.13. Eigenvalue and Eigenvector Extraction
14.13.1. Supernode Method
14.13.2. Block Lanczos
14.13.3. PCG Lanczos
14.13.4. Unsymmetric Method
14.13.5. Subspace Method
14.13.6. Damped Method
14.13.7. QR Damped Method
14.13.8. Shifting
14.13.9. Repeated Eigenvalues
14.13.10. Complex Eigensolutions
14.14. Analysis of Cyclically Symmetric Structures
14.14.1. Modal Analysis
14.14.2. Complete Mode Shape Derivation
14.14.3. Mode-Superposition Harmonic Analysis
14.14.4. Aerodynamic Coupling
14.14.5. Expansion to Output Quantities
14.14.6. Mistuning
14.14.7. Cyclic Symmetry Transformations
14.15. Mass Related Information
14.15.1. Precise Calculation of Mass Related Information
14.15.2. Lumped Calculation of Mass Related Information
14.16. Energies
14.17. Reduced-Order Modeling for State-Space Matrices Export
14.18. Enforced Motion in Structural Analysis
14.18.1. Full Method for Transient and Harmonic Analyses
14.18.2. Enforced Motion Method for Transient and Harmonic Analyses
14.18.3. Large Mass Method
15. Analysis Procedures
15.1. Static Analysis
15.1.1. Assumptions and Restrictions
15.1.2. Description of Structural Systems
15.1.3. Description of Thermal, Magnetic and Other First Order Systems
15.2. Transient Analysis
15.2.1. Assumptions and Restrictions
15.2.2. Description of Structural and Other Second Order Systems
15.2.3. Description of Thermal, Magnetic and Other First Order Systems
15.3. Mode-Frequency Analysis
15.3.1. Assumptions and Restrictions
15.3.2. Description of Analysis
15.4. Harmonic Analysis
15.4.1. Harmonic Analysis Assumptions and Restrictions
15.4.2. Description of Harmonic Analysis
15.4.3. Harmonic Analysis Complex Displacement Output
15.4.4. Nodal and Reaction Load Computation in a Harmonic Analysis
15.4.5. Harmonic Analysis Solution
15.4.6. Variational Technology Method
15.4.7. Automatic Frequency Spacing in a Harmonic Analysis
15.4.8. Logarithm Frequency Spacing in a Harmonic Analysis
15.4.9. Harmonic Analysis with Rotating Forces on Rotating Structures
15.4.10. Harmonic Ocean Wave Procedure (HOWP)
15.5. Buckling Analysis
15.5.1. Assumptions and Restrictions
15.5.2. Description of Analysis
15.6. Substructuring Analysis
15.6.1. Assumptions and Restrictions (within Superelement)
15.6.2. Description of Analysis
15.6.3. Statics
15.6.4. Transients
15.6.5. Component Mode Synthesis (CMS)
15.7. Spectrum Analysis
15.7.1. Assumptions and Restrictions
15.7.2. Description of Analysis
15.7.3. Single-Point Response Spectrum
15.7.4. Damping
15.7.5. Participation Factors and Mode Coefficients
15.7.6. Combination of Modes
15.7.7. Effective Mass and Cumulative Mass Fraction
15.7.8. Dynamic Design Analysis Method
15.7.9. Random Vibration Method
15.7.10. Description of Method
15.7.11. Response Power Spectral Densities and Mean Square Response
15.7.12. Cross Spectral Terms for Partially Correlated Input PSDs
15.7.13. Spatial Correlation
15.7.14. Wave Propagation
15.7.15. Multi-Point Response Spectrum Method
15.7.16. Missing-Mass Response
15.7.17. Rigid Responses
15.8. Linear Perturbation Analysis
15.8.1. Assumptions and Restrictions
15.8.2. Description of Analysis
15.8.3. Static Analysis Based on Linear Perturbation
15.8.4. Modal Analysis Based on Linear Perturbation
15.8.5. Eigenvalue Buckling Analysis Based on Linear Perturbation
15.8.6. Full Harmonic Analysis Based on Linear Perturbation
15.8.7. Substructure or CMS Generation Based on Linear Perturbation
15.8.8. Application of Perturbation Loads
15.8.9. Downstream Analysis Using the Solution of a Linear Perturbation Analysis
16. Preprocessing and Postprocessing Tools
16.1. Integration and Differentiation Procedures
16.1.1. Single Integration Procedure
16.1.2. Double Integration Procedure
16.1.3. Differentiation Procedure
16.1.4. Double Differentiation Procedure
16.2. Fourier Coefficient Evaluation
16.3. Statistical Procedures
16.3.1. Mean, Covariance, Correlation Coefficient
16.3.2. Random Samples of a Uniform Distribution
16.3.3. Random Samples of a Gaussian Distribution
16.3.4. Random Samples of a Triangular Distribution
16.3.5. Random Samples of a Beta Distribution
16.3.6. Random Samples of a Gamma Distribution
17. Postprocessing
17.1. POST1 - Derived Nodal Data Processing
17.1.1. Derived Nodal Data Computation
17.2. POST1 - Vector and Surface Operations
17.2.1. Vector Operations
17.2.2. Surface Operations
17.3. POST1 - Path Operations
17.3.1. Defining the Path
17.3.2. Defining Orientation Vectors of the Path
17.3.3. Mapping Nodal and Element Data onto the Path
17.3.4. Operating on Path Data
17.4. POST1 - Stress Linearization
17.4.1. Cartesian Case
17.4.2. Axisymmetric Case (General)
17.4.3. Axisymmetric Case
17.5. POST1 - Electromagnetic Macros
17.5.1. Flux Passing Thru a Closed Contour
17.5.2. Magnetomotive Forces
17.5.3. Power Loss
17.5.4. Energy Supplied
17.5.5. Terminal Inductance
17.5.6. Flux Linkage
17.5.7. Terminal Voltage
17.5.8. Energy in a Magnetic Field
17.5.9. Relative Error in Electrostatic or Electromagnetic Field Analysis
17.5.10. Electromotive Force
17.5.11. Computation of Equivalent Transmission-line Parameters
17.6. POST1 - Error Approximation Technique
17.6.1. Error Approximation Technique for Displacement-Based Problems
17.6.2. Error Approximation Technique for Temperature-Based Problems
17.6.3. Error Approximation Technique for Magnetics-Based Problems
17.7. POST1 - Crack Analysis
17.8. POST1 - Harmonic Solid and Shell Element Postprocessing
17.8.1. Thermal Solid Elements (PLANE75, PLANE78)
17.8.2. Structural Solid Elements (PLANE25, PLANE83)
17.8.3. Structural Shell Element (SHELL61)
17.9. POST26 - Data Operations
17.10. POST26 - Response Spectrum Generator (RESP)
17.10.1. Time Step Size
17.11. POST1 and POST26 - Interpretation of Equivalent Strains
17.11.1. Physical Interpretation of Equivalent Strain
17.11.2. Elastic Strain
17.11.3. Plastic Strain
17.11.4. Creep Strain
17.11.5. Total Strain
17.12. POST26 - Response Power Spectral Density
17.13. POST26 - Computation of Covariance
17.14. POST1 and POST26 – Complex Results Postprocessing
17.15. POST1 - Modal Assurance Criterion (MAC)
Bibliography

Release 18.2 - © ANSYS, Inc. All rights reserved.