add wiki

2026-05-28 17:16:48 +09:00
parent 665c5ab4e4
commit 4cc312954f
5693 changed files with 66683 additions and 4087 deletions
@@ -0,0 +1,71 @@
+---
+type: source
+title: "Solid Element Notes"
+source_type: study-notes
+created: 2026-05-28
+updated: 2026-05-28
+address: c-000048
+aliases:
+  - SolidElement
+  - "등매개 선형 솔리드 요소"
+tags:
+  - source
+  - finite-element-method
+  - solid-elements
+  - isoparametric-elements
+status: current
+confidence: high
+raw_path: ".raw/SolidElement/"
+source_files:
+  markdown_files: 1
+  image_files: 65
+related:
+  - "[[Isoparametric Linear Solid Elements]]"
+  - "[[Solid Element Shape Functions]]"
+  - "[[Solid Element Strain-Displacement Matrix]]"
+  - "[[Solid Element Stiffness Integration]]"
+  - "[[Incompatible Mode Solid Elements]]"
+  - "[[Isoparametric Finite Elements]]"
+---
+
+# Solid Element Notes
+
+## Summary
+
+These local notes derive linear isoparametric solid elements for three-dimensional continuum modeling. They cover nodal displacement interpolation, common first-order solid element topologies, natural-coordinate shape functions, the strain-displacement matrix, Hooke-law material stiffness, Gaussian integration for element stiffness, and incompatible modes for locking relief.
+
+The local source is a converted Markdown/image extraction: one Markdown file and 65 extracted images under `.raw/SolidElement/`.
+
+## Coverage Map
+
+| Section | Topic |
+|---|---|
+| 1 | [[Isoparametric Linear Solid Elements]] and practical modeling notes |
+| 2.1 | Position and displacement interpolation with shape functions |
+| 2.1 | [[Solid Element Shape Functions]] for 4-node tetrahedron, 5-node pyramid, 6-node wedge, and 8-node hexahedron |
+| 2.2 | [[Solid Element Strain-Displacement Matrix]] and Jacobian derivative mapping |
+| 2.3 | Three-dimensional Hooke-law stress-strain matrix |
+| 2.4 | [[Solid Element Stiffness Integration]] using `B^T D B` and element-specific Gauss points |
+| 2.5 | [[Incompatible Mode Solid Elements]] and static condensation of internal mode degrees of freedom |
+
+## Key Takeaways
+
+- Linear solid elements model three-dimensional volume response with three translational degrees of freedom per node and no rotational degrees of freedom.
+- The same shape functions interpolate both geometry and displacement, making the notes a direct extension of [[Isoparametric Finite Elements]] into 3D continuum elements.
+- The Jacobian maps derivatives from natural coordinates to physical coordinates, allowing the `B` matrix to be assembled in global coordinates.
+- The element stiffness follows the standard displacement-based form `K = integral B^T D B dV`, evaluated in natural coordinates with the Jacobian determinant.
+- Incompatible modes add internal displacement modes to selected wedge and hexahedral elements, then eliminate those extra degrees of freedom by static condensation.
+
+## Concepts Introduced
+
+- [[Isoparametric Linear Solid Elements]]
+- [[Solid Element Shape Functions]]
+- [[Solid Element Strain-Displacement Matrix]]
+- [[Solid Element Stiffness Integration]]
+- [[Incompatible Mode Solid Elements]]
+
+## Source Notes
+
+- Source path: `.raw/SolidElement/`
+- Composite source hash recorded in `.raw/.manifest.json`.
+- The note contains a few OCR/math transcription issues in the quadrature expressions, but the formulation sequence and element topology coverage are usable.