김경종
126 lines
6.2 KiB
Markdown
126 lines
6.2 KiB
Markdown
---
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type: concept
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title: "Finite Element Thermal Stress Analysis"
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complexity: intermediate
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domain: computational-mechanics
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created: 2026-05-29
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updated: 2026-06-02
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address: c-000070
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aliases:
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- thermal stress finite element analysis
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- thermal strain load vector
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- temperature-induced stress
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tags:
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- concept
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- finite-element-method
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- thermal-stress
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- coupled-field
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status: current
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related:
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- "[[Finite Element Heat Transfer and Field Problems]]"
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- "[[Finite Element Load Vector Assembly]]"
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- "[[Plane Stress and Plane Strain Elements]]"
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- "[[Axisymmetric Finite Elements]]"
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- "[[Displacement-Based Finite Element Formulation]]"
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- "[[Abaqus Thermal Expansion and Damping Materials]]"
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- "[[Midas Civil Heat of Hydration and Thermal Stress Analysis]]"
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- "[[Midas FEA Heat Transfer and Hydration Analysis]]"
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- "[[Midas NFX Heat Transfer Joule Heating and Thermal Stress]]"
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sources:
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- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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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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source_refs:
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- source: "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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raw_path: ".raw/AFirstCourseInTheFiniteElementMethod/"
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raw_files:
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- "AFirstCourseInTheFiniteElementMethod_064.md"
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- "AFirstCourseInTheFiniteElementMethod_001.md"
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- "AFirstCourseInTheFiniteElementMethod_033.md"
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- "AFirstCourseInTheFiniteElementMethod_083.md"
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md_indices:
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- 64
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- 1
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- 33
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- 83
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide3/"
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raw_files:
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- "AbaqusAnalysisUserGuide3_062.md"
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]]"
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raw_path: ".raw/MidasCivilAnalysisReference/"
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raw_files:
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- "MidasCivilAnalysisReference_048.md"
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- "MidasCivilAnalysisReference_049.md"
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md_indices:
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- 48
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- 49
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
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raw_path: ".raw/MidasNFXAnalysisManual/"
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raw_files:
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- "MidasNFXAnalysisManual_010.md"
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- "MidasNFXAnalysisManual_012.md"
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- "MidasNFXAnalysisManual_007.md"
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- "MidasNFXAnalysisManual_011.md"
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md_indices:
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- 10
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- 12
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- 7
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match: "heuristic-heading-keyword"
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confidence: high
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---
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# Finite Element Thermal Stress Analysis
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## Definition
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Finite element thermal stress analysis computes stresses caused by temperature-induced strains, especially when expansion or contraction is constrained.
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## How It Works
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The source treats thermal strain as an initial strain contribution. For a uniform temperature change in an isotropic material, thermal strain is proportional to the coefficient of thermal expansion and the temperature change. The constitutive relation is written in terms of mechanical strain minus thermal strain, so the thermal contribution enters the finite element equations as an equivalent nodal force vector.
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The same idea is applied to one-dimensional bars, plane stress and plane strain elements, and axisymmetric triangular elements. If the structure is free to expand, thermal strain may produce displacement without stress. If constraints or material incompatibility prevent free expansion, thermal stresses appear.
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[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]] adds production material definitions for this mechanism: thermal expansion coefficients, reference temperatures, temperature/field dependencies, isotropic/orthotropic/anisotropic expansion, and user-defined expansion increments through `UEXPAN`.
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[[Midas-Civil-Analysis-Reference|Midas Civil Analysis Reference]] adds the civil concrete workflow: hydration heat first defines a temperature and equivalent-age history, then structural stress analysis combines thermal strain, shrinkage, creep, and age-dependent concrete strength.
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[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]] adds a general-purpose thermal-stress view: structural elements can be reused as thermal elements by changing the DOF to temperature, thermal gradients and fluxes are recovered as element results, and composite laminates can receive average temperature change plus through-thickness gradient terms that generate membrane and bending resultants.
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## Why It Matters
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Thermal loading is not just another external force. It changes the strain state inside the element and can create stress only through constraint, incompatibility, or temperature gradients. Treating it as an equivalent nodal contribution keeps the global equation format compatible with the displacement formulation.
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## Connections
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- [[Finite Element Heat Transfer and Field Problems]] can supply the temperature distribution.
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- [[Finite Element Load Vector Assembly]] explains the equivalent nodal force interpretation.
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- [[Plane Stress and Plane Strain Elements]] and [[Axisymmetric Finite Elements]] provide common structural discretizations for thermal stress.
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- [[Abaqus Thermal Expansion and Damping Materials]] supplies Abaqus-specific thermal expansion and field expansion material definitions.
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- [[Midas Civil Heat of Hydration and Thermal Stress Analysis]] connects thermal strain to equivalent age, shrinkage, creep, and concrete strength development.
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- [[Midas NFX Heat Transfer Joule Heating and Thermal Stress]] connects thermal stress to NFX heat-transfer, Joule-heating, and laminate temperature-gradient workflows.
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## Sources
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- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]
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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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