김경종
60 lines
3.0 KiB
Markdown
60 lines
3.0 KiB
Markdown
---
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type: concept
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title: "Midas NFX Nonlinear Static and Dynamic Algorithms"
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created: 2026-06-02
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updated: 2026-06-02
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address: c-000179
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aliases:
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- NFX nonlinear algorithms
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- NFX nonlinear dynamics
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tags:
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- concept
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- finite-element-method
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- midas-nfx
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- nonlinear-analysis
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- dynamics
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status: current
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related:
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- "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
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- "[[midas NFX]]"
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- "[[Nonlinear Finite Element Analysis]]"
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- "[[Direct Time Integration Methods]]"
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- "[[Geometric Stiffness Matrix]]"
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- "[[Midas NFX Equation Solvers and Eigen Extraction]]"
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sources:
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- "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
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---
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# Midas NFX Nonlinear Static and Dynamic Algorithms
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## Definition
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The NFX nonlinear algorithm thread covers nonlinear static, quasi-static, explicit transient, and implicit transient procedures, including large-deformation stress/strain recovery and nonlinear time stepping.
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## Nonlinear Static
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The manual discusses nonlinear finite element solution as an iterative incremental process. It includes Newton-Raphson style correction, line search, and convergence toward equilibrium under material, geometric, contact, and load nonlinearities.
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## Large Deformation
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For large deformation, the source treats stress and strain recovery separately from small-strain linear behavior. Geometric stiffness is derived from the tangent of internal virtual work and depends on current stress, objective stress rates, displacement gradients, and updated Lagrangian assumptions.
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## Explicit Transient
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The explicit transient procedure uses central difference ideas, diagonal/lumped mass, critical time step calculation, artificial bulk viscosity, damping, mass scaling, and penalty-based joint constraints. The manual stresses that low-order elements are usually preferred in explicit analysis because critical time step and computational cost are sensitive to element size and formulation.
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## Implicit Transient
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The implicit nonlinear transient procedure uses the HHT method, nonlinear iteration on the dynamic residual, automatic time-step control based on residual behavior, and damping matrices that account for current deformation and material nonlinearity.
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## Solver Development Use
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For a custom solver, this page suggests separate implementation tracks: nonlinear static residual/tangent tests, geometric stiffness tests, explicit stable-step tests, mass-scaling checks, implicit dynamic residual tests, and damping verification. Treating all nonlinear procedures as one solver loop would hide important differences in state update, stability, and verification.
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## Connections
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- [[Nonlinear Finite Element Analysis]] gives the common nonlinear solution context.
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- [[Direct Time Integration Methods]] gives the time-integration base.
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- [[Geometric Stiffness Matrix]] connects to large-deformation tangent stiffness and buckling.
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- [[Midas FEA Nonlinear Solution Algorithms]] and [[Midas Civil Boundary and Material Nonlinear Analysis]] are sibling MIDAS nonlinear references.
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