--- type: meta title: "Concepts Index" updated: 2026-05-29 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]]" - "[[Abaqus Analysis Procedures]]" - "[[Abaqus Element Library]]" - "[[Abaqus Input File Syntax]]" - "[[Abaqus Spatial Model Definition]]" - "[[Abaqus Surface and Assembly Modeling]]" - "[[Abaqus Matrix-Based Model Definition]]" - "[[Abaqus Job Execution Workflow]]" - "[[Abaqus Resource and Parallel Execution]]" - "[[Abaqus Output Database and Results Files]]" - "[[Abaqus General and Linear Perturbation Steps]]" - "[[Abaqus Nonlinear Solution Control]]" - "[[Abaqus Restart and Results Transfer]]" - "[[Abaqus Substructuring and Submodeling]]" - "[[Abaqus Matrix Generation and Reduced Models]]" - "[[Abaqus Fracture and Enriched Discontinuity Modeling]]" - "[[Abaqus Adaptivity and Mesh Replacement]]" - "[[Abaqus Explicit Analysis Efficiency Techniques]]" - "[[Abaqus Eulerian and Particle Methods]]" - "[[Abaqus Multiphysics Coupling and Co-simulation]]" - "[[Abaqus Structural Optimization and Parametric Studies]]" - "[[Abaqus User Subroutines and Utility Routines]]" - "[[Reduced Integration and Hourglass Control]]" - "[[Hybrid Incompressible Elements]]" - "[[Abaqus Constitutive Integration]]" - "[[Finite Element Contact Formulation]]" - "[[Direct Stiffness Method]]" - "[[Bar and Truss Finite Elements]]" - "[[Beam and Frame Finite Elements]]" - "[[Plane Stress and Plane Strain Elements]]" - "[[Axisymmetric Finite Elements]]" - "[[Finite Element Load Vector Assembly]]" - "[[Finite Element Modeling and Convergence Checks]]" - "[[Finite Element Thermal Stress Analysis]]" --- # Concepts Index Navigation: [[index]] | [[entities/_index|Entities]] | [[sources/_index|Sources]] All concept pages: finite-element and computational-mechanics concepts extracted from sources. --- ## 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 - [[Abaqus Analysis Procedures]] - Abaqus procedure families for nonlinear, dynamic, modal, buckling, coupled-field, and special analyses - [[Abaqus Element Library]] - Abaqus element formulations, interpolation, numerical integration, and multi-field element choices - [[Abaqus Input File Syntax]] - keyword, data-line, model-data, and history-data syntax for Abaqus input files - [[Abaqus Spatial Model Definition]] - nodes, elements, sets, coordinate systems, and spatial model topology in Abaqus - [[Abaqus Surface and Assembly Modeling]] - named surfaces and part-instance assemblies for contact, loads, constraints, and output - [[Abaqus Matrix-Based Model Definition]] - direct matrix input and assembly for stiffness, mass, and damping components - [[Abaqus Job Execution Workflow]] - command-line analysis, checks, recovery, conversion, and utilities - [[Abaqus Resource and Parallel Execution]] - environment, memory, scratch, CPU, MPI/thread, domain, and GPU settings - [[Abaqus Output Database and Results Files]] - ODB, SIM, selected results, status, message, restart, and diagnostic files - [[Abaqus General and Linear Perturbation Steps]] - step classes, state propagation, perturbation procedures, and load-case interpretation - [[Abaqus Nonlinear Solution Control]] - increments, Newton iterations, residual convergence, stabilization, and time-integration controls - [[Abaqus Restart and Results Transfer]] - restart, import, state transfer, and staged analysis continuation - [[Abaqus Substructuring and Submodeling]] - reduced substructures and global-to-local refined submodels - [[Abaqus Matrix Generation and Reduced Models]] - generated stiffness, mass, damping, and load matrices for reuse or exchange - [[Abaqus Fracture and Enriched Discontinuity Modeling]] - contour integrals, crack propagation, line springs, and XFEM discontinuities - [[Abaqus Adaptivity and Mesh Replacement]] - ALE adaptive meshing, adaptive remeshing, and mesh-to-mesh solution mapping - [[Abaqus Explicit Analysis Efficiency Techniques]] - mass scaling, selective subcycling, and steady-state detection for Abaqus/Explicit - [[Abaqus Eulerian and Particle Methods]] - Eulerian volume fractions, CEL analysis, DEM, SPH, and particle generation - [[Abaqus Multiphysics Coupling and Co-simulation]] - sequential predefined-field coupling and runtime solver co-simulation - [[Abaqus Structural Optimization and Parametric Studies]] - structural optimization, design sensitivity, and scripted parametric studies - [[Abaqus User Subroutines and Utility Routines]] - compiled extension points, utility routines, and external database hooks - [[Reduced Integration and Hourglass Control]] - under-integration tradeoffs, zero-energy modes, and stabilization - [[Hybrid Incompressible Elements]] - mixed displacement-pressure treatment for incompressible and nearly incompressible materials - [[Abaqus Constitutive Integration]] - material-point stress updates, state variables, and consistent material tangents - [[Finite Element Contact Formulation]] - surface interaction, contact constraints, and nonlinear interface behavior - [[Direct Stiffness Method]] - displacement-based stiffness assembly workflow for element systems - [[Bar and Truss Finite Elements]] - axial structural elements, coordinate transformation, and truss analysis - [[Beam and Frame Finite Elements]] - beam, frame, grid, and spatial member finite element formulations - [[Plane Stress and Plane Strain Elements]] - two-dimensional continuum elements for plane idealizations - [[Axisymmetric Finite Elements]] - reduced-dimensional elements for bodies of revolution under symmetric loading - [[Finite Element Load Vector Assembly]] - equivalent nodal force construction for distributed, body, surface, and thermal loads - [[Finite Element Modeling and Convergence Checks]] - mesh quality, symmetry, stress interpretation, and convergence checks - [[Finite Element Thermal Stress Analysis]] - thermal strain and equivalent force treatment for constrained temperature change - [[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 --- ## Add new concepts here as they are extracted from sources.