---
type: concept
title: "Midas NFX Nonlinear Static and Dynamic Algorithms"
created: 2026-06-02
updated: 2026-06-02
address: c-000179
aliases:
  - NFX nonlinear algorithms
  - NFX nonlinear dynamics
tags:
  - concept
  - finite-element-method
  - midas-nfx
  - nonlinear-analysis
  - dynamics
status: current
related:
  - "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
  - "[[midas NFX]]"
  - "[[Nonlinear Finite Element Analysis]]"
  - "[[Direct Time Integration Methods]]"
  - "[[Geometric Stiffness Matrix]]"
  - "[[Midas NFX Equation Solvers and Eigen Extraction]]"
sources:
  - "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
---

# 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.