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Theory Manual – Table of Contents ​

1. Introduction ​

  • 1.1 Purpose of the Theory Manual
  • 1.2 Scope of the Theory Manual
  • 1.3 Simulation Workflow Overview
  • 1.4 Supported Physics Domains in ESD
  • 1.5 Assumptions, Limitations, and Conventions

2. Fundamentals of Numerical Simulation ​

  • 2.1 Continuum Mechanics
  • 2.2 Stress and Strain
  • 2.3 Constitutive Laws
  • 2.4 Equilibrium Equations
  • 2.5 Virtual Work Principle

3. Structural Mechanics Theory ​

  • 3.1 Linear Elastic Material
  • 3.2 Isotropic Materials
  • 3.3 Orthotropic Materials
  • 3.4 Material Property Definitions

4. Static Structural Analysis ​

  • 4.1 Governing Equations
  • 4.2 Stiffness Matrix Formulation
  • 4.3 Assembly Process
  • 4.4 Boundary Conditions
  • 4.5 Load Application
  • 4.6 Solver Fundamentals

5. Meshing Theory ​

  • 5.1 Nodes and Elements
  • 5.2 Element Types
  • 5.3 Mesh Quality Metrics
  • 5.4 Convergence Concepts

6. Solver Theory ​

  • 6.1 Direct Solvers
  • 6.2 Iterative Solvers
  • 6.3 Sparse Matrix Storage
  • 6.4 Numerical Stability

7. Loads, Boundary Conditions, and Constraints ​

  • 7.1 Point Loads
  • 7.2 Distributed Loads
  • 7.3 Pressure Loads
  • 7.4 Fixed Supports
  • 7.5 Symmetry Constraints
  • 7.6 Multi-Point Constraints

8. Results and Post-Processing Theory ​

  • 8.1 Displacement Calculation
  • 8.2 Stress Recovery
  • 8.3 Strain Recovery
  • 8.4 Nodal vs Element Results
  • 8.5 Result Interpolation