김경종
74 lines
3.0 KiB
Markdown
74 lines
3.0 KiB
Markdown
---
|
|
type: concept
|
|
title: "Plane Stress and Plane Strain Elements"
|
|
complexity: intermediate
|
|
domain: computational-mechanics
|
|
created: 2026-05-29
|
|
updated: 2026-05-29
|
|
address: c-000066
|
|
aliases:
|
|
- plane stress elements
|
|
- plane strain elements
|
|
- constant strain triangle
|
|
- CST element
|
|
- linear strain triangle
|
|
- LST element
|
|
tags:
|
|
- concept
|
|
- finite-element-method
|
|
- continuum-elements
|
|
- plane-stress
|
|
- plane-strain
|
|
status: current
|
|
related:
|
|
- "[[Finite Element Method]]"
|
|
- "[[Displacement-Based Finite Element Formulation]]"
|
|
- "[[Finite Element Modeling and Convergence Checks]]"
|
|
- "[[Isoparametric Finite Elements]]"
|
|
- "[[Finite Element Load Vector Assembly]]"
|
|
sources:
|
|
- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
|
|
source_refs:
|
|
- source: "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
|
|
raw_path: ".raw/AFirstCourseInTheFiniteElementMethod/"
|
|
raw_files:
|
|
- "AFirstCourseInTheFiniteElementMethod_033.md"
|
|
- "AFirstCourseInTheFiniteElementMethod_001.md"
|
|
- "AFirstCourseInTheFiniteElementMethod_043.md"
|
|
- "AFirstCourseInTheFiniteElementMethod_037.md"
|
|
md_indices:
|
|
- 33
|
|
- 1
|
|
- 43
|
|
- 37
|
|
match: "heuristic-heading-keyword"
|
|
confidence: high
|
|
---
|
|
|
|
# Plane Stress and Plane Strain Elements
|
|
|
|
## Definition
|
|
|
|
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.
|
|
|
|
## How They Work
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
## Why It Matters
|
|
|
|
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.
|
|
|
|
## Connections
|
|
|
|
- [[Finite Element Modeling and Convergence Checks]] gives the practical checks needed before trusting plane element results.
|
|
- [[Isoparametric Finite Elements]] generalizes the plane element construction to quadrilateral and higher-order mappings.
|
|
- [[Finite Element Thermal Stress Analysis]] reuses plane stress and plane strain constitutive matrices with thermal strain terms.
|
|
|
|
## Sources
|
|
|
|
- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
|
|
|