김경종
53 lines
2.6 KiB
Markdown
53 lines
2.6 KiB
Markdown
---
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type: concept
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title: "Midas FEA Linear Dynamics and Buckling Analyses"
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created: 2026-06-02
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updated: 2026-06-02
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address: c-000151
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aliases:
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- MIDAS FEA modal analysis
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- MIDAS FEA time history analysis
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- MIDAS FEA response spectrum analysis
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- MIDAS FEA linear buckling analysis
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tags:
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- concept
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- finite-element-method
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- dynamics
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- eigenproblems
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- buckling
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- midas-fea
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status: current
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related:
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- "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
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- "[[Direct Time Integration Methods]]"
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- "[[Finite Element Eigenproblem Solvers]]"
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- "[[Geometric Stiffness Matrix]]"
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- "[[Dynamic Buckling Analysis]]"
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sources:
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- "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
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---
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# Midas FEA Linear Dynamics and Buckling Analyses
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## Definition
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Midas FEA linear dynamics and buckling analyses are the manual's linear static, modal, time history, response spectrum, and eigenvalue buckling procedure family.
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## How It Works
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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.
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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.
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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.
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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.
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## Connections
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- [[Finite Element Eigenproblem Solvers]] covers modal and buckling eigenvalue algorithms.
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- [[Direct Time Integration Methods]] covers transient dynamics and direct integration.
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- [[Geometric Stiffness Matrix]] connects internal stress to buckling stiffness.
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- [[Dynamic Buckling Analysis]] extends stability thinking to time-dependent loading.
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