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2026-05-29 17:05:53 +09:00
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wiki/concepts/Displacement-Based Finite Element Formulation.md
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@@ -7,7 +7,7 @@ aliases:
- displacement formulation
- displacement method
created: 2026-05-28
updated: 2026-05-28
updated: 2026-05-29
address: c-000008
tags:
- concept
@@ -22,10 +22,15 @@ related:
- "[[Solid Element Strain-Displacement Matrix]]"
- "[[Solid Element Stiffness Integration]]"
- "[[Assumed Transverse Shear Strain Interpolation]]"
- "[[Direct Stiffness Method]]"
- "[[Bar and Truss Finite Elements]]"
- "[[Beam and Frame Finite Elements]]"
- "[[Plane Stress and Plane Strain Elements]]"
sources:
- "[[Finite Element Procedures]]"
- "[[A Continuum Mechanics Based Four-Node Shell]]"
- "[[Solid Element Notes]]"
- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
---
# Displacement-Based Finite Element Formulation
@@ -46,15 +51,19 @@ The four-node shell paper gives a concrete locking example: direct displacement
[[Solid Element Notes]] gives the corresponding 3D continuum path: interpolate nodal translations, compute small strains with the solid `B` matrix, apply the Hooke-law `D` matrix, and integrate `B^T D B` over the element volume.
[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]] gives the introductory sequence: start from the [[Direct Stiffness Method]], then apply displacement interpolation to springs, bars, trusses, beams, frames, plane elements, axisymmetric elements, and thermal stress problems.
## Practical Checks
- Does the interpolation reproduce rigid-body motion and constant strain states where required?
- Are displacement boundary conditions imposed consistently?
- Are stresses recovered in a way that reflects the approximation quality?
- Does mesh refinement improve the relevant response quantities?
- Are distributed, body, surface, and thermal loads converted into compatible equivalent nodal forces?
## Sources
- [[Finite Element Procedures]]
- [[A Continuum Mechanics Based Four-Node Shell]]
- [[Solid Element Notes]]
- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]