김경종
59 lines
2.5 KiB
Markdown
59 lines
2.5 KiB
Markdown
---
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type: concept
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title: "Plane Stress and Plane Strain Elements"
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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: 2026-05-29
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address: c-000066
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aliases:
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- plane stress elements
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- plane strain elements
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- constant strain triangle
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- CST element
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- linear strain triangle
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- LST element
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tags:
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- concept
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- finite-element-method
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- continuum-elements
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- plane-stress
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- plane-strain
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status: current
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related:
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- "[[Finite Element Method]]"
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- "[[Displacement-Based Finite Element Formulation]]"
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- "[[Finite Element Modeling and Convergence Checks]]"
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- "[[Isoparametric Finite Elements]]"
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- "[[Finite Element Load Vector Assembly]]"
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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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---
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# Plane Stress and Plane Strain Elements
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## Definition
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Plane stress and plane strain elements are two-dimensional continuum finite elements used when a three-dimensional body can be idealized by behavior in a representative plane.
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## How They Work
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Plane stress assumes the out-of-plane normal and shear stresses are negligible, which is appropriate for thin plates loaded in their plane. Plane strain assumes the out-of-plane normal strain and shear strains are negligible, which is appropriate for long bodies whose geometry and loading do not vary significantly along the length.
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The textbook develops the constant-strain triangular element as the simplest plane element. Each node carries in-plane displacement components, and the element uses a linear displacement field that produces constant strain over the triangle. It then introduces the linear-strain triangle as a higher-order alternative and compares element behavior.
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## Why It Matters
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Plane elements are the first continuum step beyond line elements. They expose key modeling issues that remain important in larger finite element work: element shape quality, stress recovery, compatibility along edges, boundary traction conversion, and convergence under mesh refinement.
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## Connections
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- [[Finite Element Modeling and Convergence Checks]] gives the practical checks needed before trusting plane element results.
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- [[Isoparametric Finite Elements]] generalizes the plane element construction to quadrilateral and higher-order mappings.
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- [[Finite Element Thermal Stress Analysis]] reuses plane stress and plane strain constitutive matrices with thermal strain terms.
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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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