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7.8 KiB
7.8 KiB
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Computational Mechanics
Scope
Computational mechanics uses numerical methods to model, discretize, and solve physical problems in solids, structures, heat transfer, fluids, field problems, and coupled multiphysics systems. This vault currently enters the domain through Finite Element Procedures, A-First-Course-in-the-Finite-Element-Method, Solid Element Notes, the shell element paper A Continuum Mechanics Based Four-Node Shell, the MITC4 implementation paper Four-Node-Quadrilateral-Shell-Element-MITC4, MITC Study Notes, the shell buckling thesis Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method, the shell FE review On-the-Finite-Element-Analysis-of-Shell-Structures, the industrial theory reference Abaqus Theory Manual, and the operational references Abaqus-Analysis-User-s-Guide-Volume-I and Abaqus-Analysis-User-s-Guide-Volume-II.
Core Threads
- Engineering Mathematical Models - how physical problems become solvable mathematical models.
- Finite Element Method - the central discretization workflow.
- Displacement-Based Finite Element Formulation - the primary formulation for linear solid and structural mechanics.
- Isoparametric Finite Elements - the element construction and matrix computation framework.
- Isoparametric Linear Solid Elements, Solid Element Shape Functions, Solid Element Strain-Displacement Matrix, Solid Element Stiffness Integration, and Incompatible Mode Solid Elements - 3D continuum solid element formulation and enrichment.
- Mixed Finite Element Formulations - stable formulations for incompressibility and constrained fields.
- Nonlinear Finite Element Analysis - incremental, iterative treatment of geometric, material, and contact nonlinearities.
- Abaqus Analysis Procedures, Abaqus Element Library, Reduced Integration and Hourglass Control, Hybrid Incompressible Elements, Abaqus Constitutive Integration, and Finite Element Contact Formulation - production finite element procedure, element, material, integration, and interface modeling choices.
- 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, and Abaqus Output Database and Results Files - production Abaqus model definition, execution, resource, and output workflow.
- 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, and Abaqus User Subroutines and Utility Routines - production Abaqus analysis procedure, continuation, reduction, adaptivity, coupling, optimization, and extension workflows.
- 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, and Finite Element Thermal Stress Analysis - introductory element-by-element FE formulation, loading, modeling, and thermal coupling threads.
- Continuum Mechanics Based Four-Node Shell Element, Assumed Transverse Shear Strain Interpolation, and Total Lagrangian Shell Formulation - shell-element formulation details for nonlinear thin and thick shell analysis.
- MITC4 Shell Element and Scordelis-Lo Shell Benchmark - implementation-oriented shell element validation and locking assessment.
- Basic Shell Mathematical Model, Shell Structure Asymptotic Behavior, Shell Locking Phenomenon, Uniform Optimal Convergence, and Shell Element Benchmark Testing - shell FE reliability criteria for thin-shell behavior and element testing.
- MITC Shell Kinematics, Green-Lagrange Strain Linearization, and Nonlinear Newmark-Beta Integration - derivation-level bridge from shell kinematics to nonlinear dynamics.
- Dynamic Buckling Analysis, Dynamic Instability Region, and Geometric Stiffness Matrix - stability workflow for dynamically compressed shell and plate structures.
- Static Equilibrium Equation Solvers, Direct Time Integration Methods, and Finite Element Eigenproblem Solvers - solver families for different equation types.
- Finite Element Program Implementation - the practical data flow from input to element calculations, assembly, solution, and stress recovery.
Current Source Base
- Finite Element Procedures by Klaus-Jurgen Bathe.
- Solid Element Notes from
.raw/SolidElement/. - A Continuum Mechanics Based Four-Node Shell by Eduardo N. Dvorkin and Klaus-Jurgen Bathe.
- Four-Node-Quadrilateral-Shell-Element-MITC4 by Edita Dvorakova and Borek Patzak.
- MITC Study Notes from
.raw/MITC공부/. - Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method by Hee Jun Lee.
- On-the-Finite-Element-Analysis-of-Shell-Structures by Phill-Seung Lee and Hyuk-Chun Noh.
- Abaqus Theory Manual from
.raw/AbaqusTheoriesManual/. - Abaqus-Analysis-User-s-Guide-Volume-I from
.raw/AbaqusAnalysisUserGuide1/. - Abaqus-Analysis-User-s-Guide-Volume-II from
.raw/AbaqusAnalysisUserGuide2/. - A-First-Course-in-the-Finite-Element-Method by Daryl L. Logan.