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14 KiB
14 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, Finite-Elements-in-Plasticity-Theory-and-Practice, 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, the operational Abaqus Analysis User's Guide references, the Midas-FEA-Analysis-Manual, the Midas-Civil-Analysis-Reference, and the Midas-NFX-Analysis-Manual.
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.
- Finite Element Plasticity, Incremental Elasto-Plastic Solution Methods, Plasticity Yield Criteria, Plastic Flow Rules and Hardening, Elasto-Viscoplastic Finite Element Analysis, Elasto-Plastic Timoshenko Beam Analysis, Elasto-Plastic Mindlin Plate Analysis, Transient Dynamic Elasto-Plastic Analysis, Finite Element Plasticity Program Architecture, and Plasticity Benchmark and Input Data Cases - finite element plasticity theory, structural applications, dynamics, implementation, and verification cases.
- 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 Element Selection and Formulation, Abaqus Continuum Element Families, Abaqus Structural Element Families, Abaqus Beam and Shell Section Definitions, Abaqus Inertial Rigid and Capacitance Elements, Abaqus Connector Elements and Behaviors, Abaqus Cohesive and Gasket Elements, Abaqus Special-Purpose Interaction Elements, Abaqus Fluid Acoustic Eulerian and Particle Elements, Abaqus User-Defined Elements, and Abaqus Element Indexes and Naming Conventions - production Abaqus element-family, section, interaction, particle, user-element, and naming workflows.
- Abaqus Prescribed Conditions and Amplitudes, Abaqus Initial and Boundary Conditions, Abaqus Loads and Predefined Fields, Abaqus Kinematic Constraints and MPCs, Abaqus Surface-Based Constraints and Couplings, Abaqus Embedded Elements and Overconstraints, Abaqus Contact Interaction Definition, Abaqus Contact Property Models, Abaqus Contact Formulations and Enforcement, Abaqus Contact Diagnostics and Modeling Difficulties, Abaqus Standard Contact Elements, and Abaqus Cavity Radiation Interactions - production Abaqus prescribed-condition, constraint, contact, diagnostic, contact-element, and radiation-interaction workflows.
- 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.
- Abaqus Material Library and Data Definition, Abaqus Elastic Material Models, Abaqus Hyperelastic and Viscoelastic Materials, Abaqus Metal Plasticity Models, Abaqus Geomaterial and Concrete Plasticity, Abaqus Progressive Damage and Failure, Abaqus Hydrodynamic Equation of State Materials, Abaqus Thermal Expansion and Damping Materials, Abaqus Transport Acoustic and Electromagnetic Materials, Abaqus Porous Media and Pore Fluid Materials, and Abaqus User-Defined Material Behavior - production Abaqus material definition, constitutive modeling, damage, EOS, field-property, porous-media, and custom material 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.
- Midas FEA Analysis Workflow, Midas FEA Element Library, Midas FEA Concrete Cracking and Material Models, Midas FEA Nonlinear Solution Algorithms, Midas FEA Linear Dynamics and Buckling Analyses, Midas FEA Construction Stage Analysis, Midas FEA Heat Transfer and Hydration Analysis, Midas FEA Static Contact Analysis, Midas FEA Fatigue Analysis, and Midas FEA CFD Analysis - Midas production finite element workflows for civil nonlinear analysis, staged concrete behavior, contact, fatigue, and wind-CFD.
- Midas Civil Numerical Analysis Model, Midas Civil Element Library and Section Stiffness, Midas Civil Boundary Supports and Links, Midas Civil Dynamic and Seismic Analysis, Midas Civil Buckling P-Delta and Geometric Nonlinearity, Midas Civil Boundary and Material Nonlinear Analysis, Midas Civil Construction Stage and Time-Dependent Analysis, Midas Civil Heat of Hydration and Thermal Stress Analysis, Midas Civil PSC and Prestress Loss Analysis, and Midas Civil Moving Load Bridge Analysis - midas Civil bridge-oriented structural analysis workflows for model definition, supports, dynamics, nonlinear response, staged construction, hydration thermal stress, prestress, and moving loads.
- Midas NFX Analysis Workflow, Midas NFX Element Library, Midas NFX Material and Composite Models, Midas NFX Equation Solvers and Eigen Extraction, Midas NFX Linear Dynamics and Buckling Analyses, Midas NFX Nonlinear Static and Dynamic Algorithms, Midas NFX Contact Analysis, Midas NFX Fatigue Analysis, Midas NFX Heat Transfer Joule Heating and Thermal Stress, and Midas NFX Structural Optimization and Forming Limit Analysis - midas NFX general-purpose workflows for model setup, elements, materials, equation solving, eigen extraction, dynamics, nonlinear analysis, contact, fatigue, thermal/electrical coupling, optimization, and forming-limit checks.
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/. - Abaqus-Analysis-User-s-Guide-Volume-III from
.raw/AbaqusAnalysisUserGuide3/. - Abaqus-Analysis-User-s-Guide-Volume-IV from
.raw/AbaqusAnalysisUserGuide4/. - Abaqus-Analysis-User-s-Guide-Volume-V from
.raw/AbaqusAnalysisUserGuide5/. - A-First-Course-in-the-Finite-Element-Method by Daryl L. Logan.
- Finite-Elements-in-Plasticity-Theory-and-Practice by D. R. J. Owen and E. Hinton from
.raw/FiniteElementsinPlasticityTheoryandPractice/. - Midas-FEA-Analysis-Manual from
.raw/MidasFEAAnalysisManual/. - Midas-Civil-Analysis-Reference from
.raw/MidasCivilAnalysisReference/. - Midas-NFX-Analysis-Manual from
.raw/MidasNFXAnalysisManual/.