add wiki

wiki/concepts/Beam and Frame Finite Elements.md

@@ -4,7 +4,7 @@ title: "Beam and Frame Finite Elements"
 complexity: intermediate
 domain: computational-mechanics
 created: 2026-05-29
-updated: 2026-05-29
+updated: 2026-06-01
 address: c-000065
 aliases:
   - beam finite element
@@ -23,8 +23,11 @@ related:
   - "[[Finite Element Load Vector Assembly]]"
   - "[[Direct Time Integration Methods]]"
   - "[[Shell Locking Phenomenon]]"
+  - "[[Abaqus Structural Element Families]]"
+  - "[[Abaqus Beam and Shell Section Definitions]]"
 sources:
   - "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
+  - "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
 ---
 
 # Beam and Frame Finite Elements
@@ -39,6 +42,8 @@ The Euler-Bernoulli beam element uses transverse displacement and rotation degre
 
 For short or deep beams, transverse shear deformation can become significant, motivating Timoshenko beam theory. Frame elements then combine axial bar behavior with beam bending behavior and use coordinate transformation matrices so arbitrarily oriented members can be assembled into plane frames, grids, and spatial frames.
 
+[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]] connects this member theory to Abaqus beam, frame, pipe, and elbow element families. It also separates the element topology from the beam section definition, where cross-section geometry, orientation, material behavior, and integration rules are supplied.
+
 ## Why It Matters
 
 Beam and frame elements sit between simple axial trusses and full continuum or shell models. They are efficient for bridges, buildings, machine frames, and grid structures when member-level idealization is appropriate.
@@ -49,8 +54,10 @@ Beam and frame elements sit between simple axial trusses and full continuum or s
 - [[Finite Element Load Vector Assembly]] handles distributed loads and equivalent nodal forces on beams.
 - [[Direct Time Integration Methods]] uses beam mass matrices for vibration and transient structural analysis.
 - [[Shell Locking Phenomenon]] is conceptually related through transverse shear treatment, though shell locking is a different element pathology.
+- [[Abaqus Structural Element Families]] places beams and frames beside trusses, membranes, shells, and elbows in the Abaqus library.
+- [[Abaqus Beam and Shell Section Definitions]] covers the cross-section and orientation data that beam elements require.
 
 ## Sources
 
 - [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
-
+- [[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]