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GEO5

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Solution Method

The program FEM serves to analyze geotechnical problems characterized by nonlinear response of the soil or rock body. A successful analysis of most of such problems calls for an iterative solution of a given boundary value problem. Applying the finite element method (FEM) then leads to an incremental form of the equilibrium conditions written as:

where:

ΚΤ

-

instantaneous stiffness matrix

Δu

-

vector of nodal displacement increments

Δf

-

vector of out-of-balance force increments

This equation can be solved only approximately using a suitable numerical method. The goal of the method is to arrive, during the process of iteration, at such a state of stress and strain that satisfies the condition Δf = 0. To that end, the program offers two basic methods:

  1. Newton-Raphson method - NRM
  2. Arc-length method - ALM

Analysis settings - setting the solution method