modify wiki

wiki/concepts/Finite Element Eigenproblem Solvers.md

@@ -8,7 +8,7 @@ aliases:
   - finite element eigenvalue analysis
   - modal analysis
 created: 2026-05-28
-updated: 2026-05-28
+updated: 2026-05-29
 address: c-000015
 tags:
   - concept
@@ -22,9 +22,13 @@ related:
   - "[[Dynamic Buckling Analysis]]"
   - "[[Geometric Stiffness Matrix]]"
   - "[[BLZPACK]]"
+  - "[[Abaqus Analysis Procedures]]"
+  - "[[Abaqus General and Linear Perturbation Steps]]"
 sources:
   - "[[Finite Element Procedures]]"
   - "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
+  - "[[Abaqus Theory Manual]]"
+  - "[[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]"
 ---
 
 # Finite Element Eigenproblem Solvers
@@ -39,6 +43,10 @@ The source introduces eigenvector properties, shifting, zero-mass effects, stand
 
 The dynamic buckling thesis adds an implementation example: [[BLZPACK]], based on Block Lanczos, is used for vibration and buckling eigenvalue analyses in a shell dynamic buckling program.
 
+[[Abaqus Analysis Procedures]] adds the commercial-code procedure context: eigenvalue extraction supports vibration modes, modal dynamics, harmonic response, and buckling or postbuckling workflows.
+
+[[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]] adds the step-level user workflow: eigenvalue buckling, natural frequency extraction, complex eigenvalue extraction, modal dynamics, response spectrum, and random response are treated as Abaqus procedure choices, usually through linear perturbation or modal procedure contexts.
+
 ## Why It Matters
 
 Large finite element models can have many degrees of freedom, but engineering decisions often require only selected modes or eigenvalues. Solver choice determines whether the analysis can efficiently find the physically relevant part of the spectrum.
@@ -48,8 +56,12 @@ Large finite element models can have many degrees of freedom, but engineering de
 - [[Direct Time Integration Methods]] can be contrasted with mode superposition.
 - [[Static Equilibrium Equation Solvers]] shares matrix factorization and conditioning concerns.
 - [[Finite Element Program Implementation]] must support sparse matrix operations and vector iteration workflows.
+- [[Abaqus Analysis Procedures]] frames eigen extraction as one procedure family among static, transient, and coupled analyses.
+- [[Abaqus General and Linear Perturbation Steps]] explains why many eigen and modal procedures are interpreted as perturbations about a base state.
 
 ## Sources
 
 - [[Finite Element Procedures]]
 - [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]
+- [[Abaqus Theory Manual]]
+- [[Abaqus-Analysis-User-s-Guide-Volume-II|Abaqus Analysis User's Guide Volume II]]