---
type: meta
title: "Concepts Index"
updated: 2026-05-28
tags:
  - meta
  - index
  - concept
domain: computational-mechanics
status: evergreen
related:
  - "[[index]]"
  - "[[dashboard]]"
  - "[[Wiki Map]]"
  - "[[Computational Mechanics]]"
  - "[[Finite Element Method]]"
  - "[[Continuum Mechanics Based Four-Node Shell Element]]"
  - "[[MITC4 Shell Element]]"
  - "[[MITC Shell Kinematics]]"
  - "[[Dynamic Buckling Analysis]]"
  - "[[Shell Structure Asymptotic Behavior]]"
  - "[[Isoparametric Linear Solid Elements]]"
---

# Concepts Index

Navigation: [[index]] | [[entities/_index|Entities]] | [[sources/_index|Sources]]

All concept pages: finite-element and computational-mechanics concepts extracted from sources.

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## Computational Mechanics

- [[Finite Element Method]] - numerical procedure for solving discretized engineering and physics models
- [[Engineering Mathematical Models]] - idealized physical models selected before finite element solution
- [[Displacement-Based Finite Element Formulation]] - primary solid mechanics formulation using nodal displacements
- [[Isoparametric Finite Elements]] - shape-function framework for geometry mapping and element matrix calculation
- [[Isoparametric Linear Solid Elements]] - first-order 3D continuum elements using isoparametric interpolation
- [[Solid Element Shape Functions]] - interpolation functions for tetrahedral, pyramid, wedge, and hexahedral solid elements
- [[Solid Element Strain-Displacement Matrix]] - 3D solid element `B` matrix and Jacobian derivative mapping
- [[Solid Element Stiffness Integration]] - numerical integration of `B^T D B` over element volume
- [[Incompatible Mode Solid Elements]] - internal-mode enrichment and static condensation for solid elements
- [[Mixed Finite Element Formulations]] - multi-field formulations for incompressibility, constraints, and pressure-like variables
- [[Nonlinear Finite Element Analysis]] - incremental solution of geometric, material, contact, and load nonlinearities
- [[Continuum Mechanics Based Four-Node Shell Element]] - low-order shell element derived from continuum mechanics for nonlinear analysis
- [[Assumed Transverse Shear Strain Interpolation]] - shell locking remedy using a separately interpolated transverse shear field
- [[Total Lagrangian Shell Formulation]] - reference-configuration formulation for large displacement and rotation shell response
- [[MITC4 Shell Element]] - four-node quadrilateral shell element using mixed interpolation of tensorial components
- [[MITC Shell Kinematics]] - director-vector kinematic model for MITC shell elements
- [[Green-Lagrange Strain Linearization]] - nonlinear strain expansion for internal force and tangent stiffness terms
- [[Nonlinear Newmark-Beta Integration]] - implicit Newmark time stepping with Newton-Raphson nonlinear iterations
- [[Dynamic Buckling Analysis]] - instability analysis of structures under time-varying compressive loading
- [[Dynamic Instability Region]] - load-frequency instability boundary for parametric buckling
- [[Geometric Stiffness Matrix]] - initial stress stiffness contribution used in nonlinear and buckling analysis
- [[Scordelis-Lo Shell Benchmark]] - cylindrical shell benchmark for shell element convergence and locking behavior
- [[Basic Shell Mathematical Model]] - midsurface/director shell model underlying continuum shell finite elements
- [[Shell Structure Asymptotic Behavior]] - bending, membrane, and mixed thin-shell response classes
- [[Shell Locking Phenomenon]] - membrane and shear locking as artificial stiffness in thin-shell FE solutions
- [[Uniform Optimal Convergence]] - thickness-uniform optimal convergence target for shell elements
- [[Shell Element Benchmark Testing]] - structured performance testing for shell finite elements
- [[Finite Element Heat Transfer and Field Problems]] - finite element treatment of heat transfer, field equations, flow, and coupled problems
- [[Static Equilibrium Equation Solvers]] - direct, iterative, and nonlinear solvers for static FE equations
- [[Direct Time Integration Methods]] - transient finite element dynamics and first-order field integration
- [[Finite Element Eigenproblem Solvers]] - modal and eigenvalue algorithms for FE matrices
- [[Finite Element Program Implementation]] - software data flow for FE codes and STAP-style implementation

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## Add new concepts here as they are extracted from sources.