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| concept | Midas NFX Nonlinear Static and Dynamic Algorithms | 2026-06-02 | 2026-06-02 | c-000179 |
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Midas NFX Nonlinear Static and Dynamic Algorithms
Definition
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.
Nonlinear Static
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.
Large Deformation
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.
Explicit Transient
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.
Implicit Transient
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.
Solver Development Use
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.
Connections
- Nonlinear Finite Element Analysis gives the common nonlinear solution context.
- Direct Time Integration Methods gives the time-integration base.
- Geometric Stiffness Matrix connects to large-deformation tangent stiffness and buckling.
- Midas FEA Nonlinear Solution Algorithms and Midas Civil Boundary and Material Nonlinear Analysis are sibling MIDAS nonlinear references.