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Purpose

This vault is currently focused on computational mechanics, seeded from Finite Element Procedures by Klaus-Jurgen Bathe, solid element notes, shell element sources, MITC derivation notes, shell buckling analysis, and On-the-Finite-Element-Analysis-of-Shell-Structures by Phill-Seung Lee and Hyuk-Chun Noh.

Current Seed Content

Domain:

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

Concepts:

Finite Element Method - central computational mechanics workflow
Engineering Mathematical Models - how physical problems become solvable models
Displacement-Based Finite Element Formulation - primary solid mechanics derivation
Isoparametric Finite Elements - element construction and integration framework
Isoparametric Linear Solid Elements - 3D continuum element formulation with translational nodal DOFs
Solid Element Shape Functions - linear solid element interpolation functions
Solid Element Strain-Displacement Matrix - 3D strain-displacement relation and Jacobian mapping
Solid Element Stiffness Integration - Gauss integration of solid element stiffness matrices
Incompatible Mode Solid Elements - internal-mode enrichment for solid element flexibility
Mixed Finite Element Formulations - pressure and constraint-aware formulations
Nonlinear Finite Element Analysis - incremental nonlinear solution workflow
Continuum Mechanics Based Four-Node Shell Element - four-node shell formulation derived from continuum mechanics
Assumed Transverse Shear Strain Interpolation - transverse shear locking remedy for shell elements
Total Lagrangian Shell Formulation - large displacement and rotation shell analysis framework
MITC4 Shell Element - mixed-interpolation four-node shell element implementation
MITC Shell Kinematics - shell director kinematics for MITC derivations
Green-Lagrange Strain Linearization - nonlinear strain expansion for tangent construction
Nonlinear Newmark-Beta Integration - Newmark time stepping with Newton iterations
Dynamic Buckling Analysis - finite element stability analysis under time-varying axial compression
Dynamic Instability Region - instability boundary in excitation/load parameter space
Geometric Stiffness Matrix - stress stiffness contribution needed for buckling eigenproblems
Scordelis-Lo Shell Benchmark - shell element convergence benchmark
Basic Shell Mathematical Model - general shell model beneath continuum shell finite elements
Shell Structure Asymptotic Behavior - bending, membrane, and mixed behavior as thickness decreases
Shell Locking Phenomenon - thickness-dependent artificial stiffness in shell finite element results
Uniform Optimal Convergence - convergence target that remains stable across shell thickness regimes
Shell Element Benchmark Testing - benchmark methodology for shell element reliability
Finite Element Heat Transfer and Field Problems - FE treatment beyond structural mechanics
Static Equilibrium Equation Solvers - linear and nonlinear static equation solution
Direct Time Integration Methods - transient dynamics and time integration
Finite Element Eigenproblem Solvers - modal and eigenvalue algorithms
Finite Element Program Implementation - FE code data flow and STAP-style implementation

Entity:

Klaus-Jurgen Bathe - author of Finite Element Procedures and co-author of A Continuum Mechanics Based Four-Node Shell
Eduardo N. Dvorkin - co-author of A Continuum Mechanics Based Four-Node Shell
Edita Dvorakova - co-author of Four-Node-Quadrilateral-Shell-Element-MITC4
Borek Patzak - co-author of Four-Node-Quadrilateral-Shell-Element-MITC4
OOFEM - finite element code used in the MITC4 implementation
Hee Jun Lee - author of the dynamic shell buckling thesis
Phill-Seung Lee - author of the shell finite element review
Hyuk-Chun Noh - author of the shell finite element review
Inha University - degree-granting institution for the thesis
BLZPACK - Block Lanczos eigenvalue solver used in the thesis
ABAQUS - validation comparison software used in the thesis

Source:

Finite Element Procedures - finite element analysis textbook
A Continuum Mechanics Based Four-Node Shell - shell element formulation paper
Four-Node-Quadrilateral-Shell-Element-MITC4 - MITC4 implementation and validation paper
MITC Study Notes - local MITC shell derivation notes
Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method - thesis on MITC4 shell dynamic buckling analysis
On-the-Finite-Element-Analysis-of-Shell-Structures - review of shell mathematical models, asymptotic behavior, locking, convergence, and benchmark testing
Solid Element Notes - local notes on linear isoparametric solid elements

Current State

Sources ingested: 7
Wiki pages: 63
Last activity: 2026-05-28 (ingested solid element notes)

Canvases

main - default visual reference canvas with a General zone

Key Themes

Model first, solve second. The finite element result is only meaningful relative to the selected mathematical model, boundary conditions, materials, loads, and discretization.

Formulation controls reliability. Displacement, mixed, isoparametric, nonlinear, transient, and eigenproblem formulations each impose different stability and accuracy requirements.

Solid elements ground the 3D continuum path. The solid element notes connect natural-coordinate interpolation, Jacobian derivative mapping, B/D matrices, stiffness integration, and incompatible-mode enrichment.

Shell elements expose formulation tradeoffs. Low-order shell elements need careful shear strain interpolation and nonlinear kinematics to avoid locking while preserving computational economy.

Benchmarks close the loop. The MITC4 source ties formulation to implementation by using patch tests and the Scordelis-Lo shell benchmark before comparing convergence.

Derivations connect formulations to solvers. The MITC study notes link shell director kinematics, Green-Lagrange strain linearization, tangent construction, and nonlinear Newmark-beta dynamics.

Stability analysis closes the structural loop. The dynamic buckling thesis connects MITC4 shell modeling, geometric stiffness, eigenvalue solvers, validation benchmarks, and instability-region prediction.

Thin-shell asymptotics explain shell FE failure modes. The shell FE review connects basic shell models, bending/membrane/mixed asymptotic behavior, locking, uniform convergence, and benchmark design.

Implementation matters. Element-level calculations, assembly, storage, solvers, and stress recovery are part of the method, not afterthoughts.

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