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Plane Strain Analysis

This computational module is suitable for the analysis of longitudinal structures (tunnel, embankment, dam, etc.) characterized by a longitudinal dimensions being of the orders of magnitude larger than transverse dimensions of the analyzed domain.

Plane strain analysis

In such a case the analysis can be carried per 1 m run of the structure, see Figure. This complies with the plane strain assumption. Components of the strain vector developed on planes normal to the longitudinal axis can be then neglected. Therefore, we assume the soil body be loaded by the components of the strain and stress vector pertinent to the transverse plane normal to the longitudinal axis and by the longitudinal normal stress that arises due to Poisson’s effect. The corresponding non-zero components of the stress and strain vector are:

Considering beam elements the analysis corresponds to the solution of a plate strip having the cross-section width equal to 1 m. Non-zero components of nodal generalized displacements are evident from the following Figure for a two-node beam element compatible with a three-node triangular plane element and a three-node beam element compatible with a six-node triangular plane element.

Two-node and three-node beam element

The corresponding components of internal forces, see Figure, assumed with respect to 1 m of cross-sectional width are given by: