김경종
64 lines
4.7 KiB
Markdown
64 lines
4.7 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: 2026-05-28
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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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- "[[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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---
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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]], [[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]], and the shell FE review [[On-the-Finite-Element-Analysis-of-Shell-Structures|On the Finite Element Analysis of Shell Structures]].
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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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- [[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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## 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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