Wiki Index

Last updated: 2026-05-28 | Total pages: 63 | Sources ingested: 7

Concepts

Finite Element Method - numerical procedure for solving discretized engineering and physics models (status: current)
Engineering Mathematical Models - idealized physical models selected before finite element solution (status: current)
Displacement-Based Finite Element Formulation - primary solid mechanics formulation using nodal displacements (status: current)
Isoparametric Finite Elements - shape-function framework for element geometry, interpolation, and matrices (status: current)
Isoparametric Linear Solid Elements - first-order 3D continuum elements with translational nodal degrees of freedom (status: current)
Solid Element Shape Functions - natural-coordinate interpolation functions for tetrahedron, pyramid, wedge, and hexahedron elements (status: current)
Solid Element Strain-Displacement Matrix - 3D solid element B matrix and Jacobian derivative mapping (status: current)
Solid Element Stiffness Integration - B^T D B volume integration for solid element stiffness matrices (status: current)
Incompatible Mode Solid Elements - internal displacement mode enrichment and static condensation for solid elements (status: current)
Mixed Finite Element Formulations - multi-field formulations for incompressibility, constraints, and pressure-like variables (status: current)
Nonlinear Finite Element Analysis - incremental solution of geometric, material, contact, and load nonlinearities (status: current)
Continuum Mechanics Based Four-Node Shell Element - low-order shell element derived from continuum mechanics (status: current)
Assumed Transverse Shear Strain Interpolation - shell locking remedy using a separately interpolated shear strain field (status: current)
Total Lagrangian Shell Formulation - reference-configuration formulation for nonlinear shell response (status: current)
MITC4 Shell Element - four-node quadrilateral shell element using mixed interpolation to avoid shear locking (status: current)
MITC Shell Kinematics - director-vector shell kinematics for MITC-style degenerated continuum shells (status: current)
Green-Lagrange Strain Linearization - nonlinear strain expansion for residual and tangent construction (status: current)
Nonlinear Newmark-Beta Integration - Newton-iterated Newmark time integration for nonlinear FE dynamics (status: current)
Dynamic Buckling Analysis - instability analysis under time-varying axial compression (status: current)
Dynamic Instability Region - load-frequency region where dynamic buckling occurs (status: current)
Geometric Stiffness Matrix - stress and geometry dependent stiffness contribution used in buckling analysis (status: current)
Scordelis-Lo Shell Benchmark - cylindrical shell benchmark for shell element convergence (status: current)
Basic Shell Mathematical Model - midsurface/director shell model underlying continuum shell finite elements (status: current)
Shell Structure Asymptotic Behavior - thin-shell response classes under decreasing thickness (status: current)
Shell Locking Phenomenon - thickness-dependent artificial stiffness in shell finite elements (status: current)
Uniform Optimal Convergence - shell element convergence that remains optimal across thickness regimes (status: current)
Shell Element Benchmark Testing - structured shell element performance testing across geometry, thickness, and meshes (status: current)
Finite Element Heat Transfer and Field Problems - FE treatment of heat transfer, fields, flow, and coupled problems (status: current)
Static Equilibrium Equation Solvers - direct, iterative, and nonlinear solvers for static FE equations (status: current)
Direct Time Integration Methods - transient FE dynamics and first-order field integration (status: current)
Finite Element Eigenproblem Solvers - modal and eigenvalue algorithms for FE matrices (status: current)
Finite Element Program Implementation - software data flow for FE codes and STAP-style implementation (status: current)

Entities

Klaus-Jurgen Bathe - professor of mechanical engineering, author of Finite Element Procedures, and co-author of A Continuum Mechanics Based Four-Node Shell (status: current)
Eduardo N. Dvorkin - co-author of A Continuum Mechanics Based Four-Node Shell (status: current)
Edita Dvorakova - co-author of Four-Node-Quadrilateral-Shell-Element-MITC4 (status: current)
Borek Patzak - co-author of Four-Node-Quadrilateral-Shell-Element-MITC4 and OOFEM-related researcher (status: current)
OOFEM - finite element code used for the MITC4 implementation (status: current)
Hee Jun Lee - author of Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method (status: current)
Phill-Seung Lee - author of On-the-Finite-Element-Analysis-of-Shell-Structures (status: current)
Hyuk-Chun Noh - author of On-the-Finite-Element-Analysis-of-Shell-Structures (status: current)
Inha University - degree-granting institution for the dynamic shell buckling thesis (status: current)
BLZPACK - Block Lanczos eigenvalue solver used in the dynamic buckling implementation (status: current)
ABAQUS - commercial finite element software used for validation comparisons (status: current)

Sources

Finite Element Procedures - 2014 textbook by Klaus-Jurgen Bathe; finite element theory, solvers, and implementation
A Continuum Mechanics Based Four-Node Shell - Dvorkin and Bathe paper on a four-node shell element for nonlinear analysis
Four-Node-Quadrilateral-Shell-Element-MITC4 - Dvorakova and Patzak paper on MITC4 implementation and Scordelis-Lo validation
MITC Study Notes - local derivation notes for MITC shell kinematics, nonlinear strain linearization, and Newmark-beta dynamics
Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method - 2012 thesis on MITC4 shell dynamic buckling analysis
On-the-Finite-Element-Analysis-of-Shell-Structures - review paper on shell mathematical models, asymptotic behavior, locking, convergence, and benchmark testing
Solid Element Notes - local notes on isoparametric linear solid element formulation, stiffness integration, and incompatible modes

Domains

Computational Mechanics - finite element analysis, numerical methods, and engineering simulation

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