김경종
52 lines
2.1 KiB
Markdown
52 lines
2.1 KiB
Markdown
---
|
|
type: concept
|
|
title: "Elasto-Plastic Timoshenko Beam Analysis"
|
|
complexity: advanced
|
|
domain: computational-mechanics
|
|
created: 2026-06-02
|
|
updated: 2026-06-02
|
|
address: c-000137
|
|
aliases:
|
|
- plastic Timoshenko beam
|
|
- beam plasticity finite element
|
|
tags:
|
|
- concept
|
|
- finite-element-method
|
|
- plasticity
|
|
- beam-elements
|
|
status: current
|
|
related:
|
|
- "[[Finite Element Plasticity]]"
|
|
- "[[Beam and Frame Finite Elements]]"
|
|
- "[[Abaqus Structural Element Families]]"
|
|
- "[[Abaqus Beam and Shell Section Definitions]]"
|
|
- "[[Incremental Elasto-Plastic Solution Methods]]"
|
|
sources:
|
|
- "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
|
|
---
|
|
|
|
# Elasto-Plastic Timoshenko Beam Analysis
|
|
|
|
## Definition
|
|
|
|
Elasto-plastic Timoshenko beam analysis extends beam finite elements to include shear deformation and plastic material response under bending and axial effects.
|
|
|
|
## How It Works
|
|
|
|
The beam element retains Timoshenko kinematics, so rotations and transverse shear deformation are part of the formulation. Plasticity is evaluated through section stress resultants or through integration over the cross-section, depending on the implementation detail.
|
|
|
|
The source uses this as a bridge between one-dimensional plasticity and higher-dimensional continuum plasticity. It shows that plasticity is not only a continuum-element issue: structural elements also need state storage, section integration, and incremental equilibrium.
|
|
|
|
## Why It Matters
|
|
|
|
Beam plasticity is useful for frames, members, and reduced structural models where a continuum mesh is unnecessary or too expensive. It also exposes solver issues that recur in shells and plates: section integration, through-thickness yielding, and tangent stiffness degradation.
|
|
|
|
## Connections
|
|
|
|
[[Beam and Frame Finite Elements]] provides the elastic structural-element base. [[Abaqus Structural Element Families]] and [[Abaqus Beam and Shell Section Definitions]] provide the production element and section-definition counterpart.
|
|
|
|
## Sources
|
|
|
|
- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]
|
|
|