김경종
108 lines
14 KiB
Markdown
108 lines
14 KiB
Markdown
---
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type: domain
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title: "Computational Mechanics"
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created: 2026-05-28
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updated: 2026-06-02
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address: c-000005
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tags:
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- domain
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- computational-mechanics
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- finite-element-method
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status: current
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related:
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- "[[Finite Element Procedures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Solid Element Notes]]"
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]]"
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- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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- "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
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- "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
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- "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
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- "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
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- "[[Finite Element Method]]"
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- "[[Engineering Mathematical Models]]"
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sources:
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- "[[Finite Element Procedures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Solid Element Notes]]"
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]]"
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- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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- "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
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- "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
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- "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
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- "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
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---
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# Computational Mechanics
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## Scope
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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|A First Course in the Finite Element Method]], [[Finite-Elements-in-Plasticity-Theory-and-Practice|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|Four-Node Quadrilateral Shell Element MITC4]], [[MITC Study Notes]], the shell buckling thesis [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method|Dynamic Buckling Analysis of Shell Structures using Finite Element Method]], the shell FE review [[On-the-Finite-Element-Analysis-of-Shell-Structures|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|Midas FEA Analysis Manual]], the [[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]], and the [[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]].
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## Core Threads
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- [[Engineering Mathematical Models]] - how physical problems become solvable mathematical models.
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- [[Finite Element Method]] - the central discretization workflow.
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- [[Displacement-Based Finite Element Formulation]] - the primary formulation for linear solid and structural mechanics.
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- [[Isoparametric Finite Elements]] - the element construction and matrix computation framework.
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- [[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.
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- [[Mixed Finite Element Formulations]] - stable formulations for incompressibility and constrained fields.
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- [[Nonlinear Finite Element Analysis]] - incremental, iterative treatment of geometric, material, and contact nonlinearities.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[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.
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- [[MITC4 Shell Element]] and [[Scordelis-Lo Shell Benchmark]] - implementation-oriented shell element validation and locking assessment.
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- [[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.
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- [[MITC Shell Kinematics]], [[Green-Lagrange Strain Linearization]], and [[Nonlinear Newmark-Beta Integration]] - derivation-level bridge from shell kinematics to nonlinear dynamics.
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- [[Dynamic Buckling Analysis]], [[Dynamic Instability Region]], and [[Geometric Stiffness Matrix]] - stability workflow for dynamically compressed shell and plate structures.
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- [[Static Equilibrium Equation Solvers]], [[Direct Time Integration Methods]], and [[Finite Element Eigenproblem Solvers]] - solver families for different equation types.
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- [[Finite Element Program Implementation]] - the practical data flow from input to element calculations, assembly, solution, and stress recovery.
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- [[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.
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- [[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.
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- [[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.
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## Current Source Base
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- [[Finite Element Procedures]] by [[Klaus-Jurgen Bathe]].
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- [[Solid Element Notes]] from `.raw/SolidElement/`.
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- [[A Continuum Mechanics Based Four-Node Shell]] by [[Eduardo N. Dvorkin]] and [[Klaus-Jurgen Bathe]].
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]] by [[Edita Dvorakova]] and [[Borek Patzak]].
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- [[MITC Study Notes]] from `.raw/MITC공부/`.
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- [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method|Dynamic Buckling Analysis of Shell Structures using Finite Element Method]] by [[Hee Jun Lee]].
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- [[On-the-Finite-Element-Analysis-of-Shell-Structures|On the Finite Element Analysis of Shell Structures]] by [[Phill-Seung Lee]] and [[Hyuk-Chun Noh]].
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- [[Abaqus Theory Manual]] from `.raw/AbaqusTheoriesManual/`.
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- [[Abaqus-Analysis-User-s-Guide-Volume-I|Abaqus Analysis User's Guide Volume I]] from `.raw/AbaqusAnalysisUserGuide1/`.
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- [[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]] from `.raw/AbaqusAnalysisUserGuide2/`.
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- [[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]] from `.raw/AbaqusAnalysisUserGuide3/`.
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- [[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]] from `.raw/AbaqusAnalysisUserGuide4/`.
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- [[Abaqus-Analysis-User-s-Guide-Volume-V|Abaqus Analysis User's Guide Volume V]] from `.raw/AbaqusAnalysisUserGuide5/`.
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- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]] by [[Daryl L. Logan]].
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- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]] by [[D. R. J. Owen]] and [[E. Hinton]] from `.raw/FiniteElementsinPlasticityTheoryandPractice/`.
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- [[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]] from `.raw/MidasFEAAnalysisManual/`.
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- [[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]] from `.raw/MidasCivilAnalysisReference/`.
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- [[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]] from `.raw/MidasNFXAnalysisManual/`.
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