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김경종
2026-05-29 17:05:53 +09:00
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wiki/concepts/Isoparametric Linear Solid Elements.md
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@@ -9,7 +9,7 @@ aliases:
- isoparametric solid elements
- 3D solid elements
created: 2026-05-28
updated: 2026-05-28
updated: 2026-05-29
address: c-000049
tags:
- concept
@@ -24,8 +24,10 @@ related:
- "[[Solid Element Shape Functions]]"
- "[[Solid Element Strain-Displacement Matrix]]"
- "[[Solid Element Stiffness Integration]]"
- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
sources:
- "[[Solid Element Notes]]"
- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
---
# Isoparametric Linear Solid Elements
@@ -47,6 +49,8 @@ u(xi) = sum N_i(xi) u_i
The covered topologies are 4-node tetrahedron, 5-node pyramid, 6-node wedge, and 8-node hexahedron. In each case, the element is defined in natural coordinates and mapped to physical space through the Jacobian.
[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]] adds the introductory three-dimensional stress path through tetrahedral solid elements and isoparametric solid formulation after the plane and axisymmetric element chapters.
## Practical Notes
- Solid elements are suited to three-dimensional volume response rather than beam or shell idealizations.
@@ -58,7 +62,9 @@ The covered topologies are 4-node tetrahedron, 5-node pyramid, 6-node wedge, and
- [[Solid Element Shape Functions]] defines the natural-coordinate interpolation for each covered topology.
- [[Solid Element Strain-Displacement Matrix]] converts the displacement interpolation into engineering strain components.
- [[Solid Element Stiffness Integration]] assembles the stiffness matrix from `B`, `D`, and the Jacobian.
- [[Axisymmetric Finite Elements]] are an efficient reduced-dimensional alternative when body and load symmetry permit.
## Sources
- [[Solid Element Notes]]
- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]