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wiki/concepts/Midas FEA Linear Dynamics and Buckling Analyses.md

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+---
+type: concept
+title: "Midas FEA Linear Dynamics and Buckling Analyses"
+created: 2026-06-02
+updated: 2026-06-02
+address: c-000151
+aliases:
+  - MIDAS FEA modal analysis
+  - MIDAS FEA time history analysis
+  - MIDAS FEA response spectrum analysis
+  - MIDAS FEA linear buckling analysis
+tags:
+  - concept
+  - finite-element-method
+  - dynamics
+  - eigenproblems
+  - buckling
+  - midas-fea
+status: current
+related:
+  - "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
+  - "[[Direct Time Integration Methods]]"
+  - "[[Finite Element Eigenproblem Solvers]]"
+  - "[[Geometric Stiffness Matrix]]"
+  - "[[Dynamic Buckling Analysis]]"
+sources:
+  - "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
+---
+
+# Midas FEA Linear Dynamics and Buckling Analyses
+
+## Definition
+
+Midas FEA linear dynamics and buckling analyses are the manual's linear static, modal, time history, response spectrum, and eigenvalue buckling procedure family.
+
+## How It Works
+
+Linear static analysis solves the assembled stiffness equation with loads, boundary conditions, coordinate transformations, and singularity checks. The manual also warns that nonlinear member cases such as tension-only or compression-only links use internal iteration, so their results should not be combined as if they were purely linear load cases.
+
+Modal analysis solves `K phi = lambda M phi` and reports mode shapes, participation factors, effective modal mass, and modal direction factors. Lanczos and subspace methods are described, including shift-invert ideas, rigid-mode handling, and Sturm sequence checks for missed eigenvalues.
+
+Time history analysis is organized through mode superposition and direct integration, with damping models such as Rayleigh damping and modal damping. The manual gives a practical time-step accuracy rule: choose a step small enough relative to the highest mode of interest and the load time interval.
+
+Response spectrum analysis approximates a multi-degree-of-freedom response through modal single-degree-of-freedom spectra and modal combination rules such as ABS, SRSS, and CQC. Linear buckling analysis forms a geometric stiffness contribution from a pre-buckling stress or internal force state and solves an eigenvalue problem for critical load factors and modes.
+
+## Connections
+
+- [[Finite Element Eigenproblem Solvers]] covers modal and buckling eigenvalue algorithms.
+- [[Direct Time Integration Methods]] covers transient dynamics and direct integration.
+- [[Geometric Stiffness Matrix]] connects internal stress to buckling stiffness.
+- [[Dynamic Buckling Analysis]] extends stability thinking to time-dependent loading.
+