Assumptions of Linear Static Analysis

Linear static analysis makes the linearity assumption, the elasticity assumption, and the static assumption.
Simulation results are invalid if these assumptions are not satisfied.

Linearity Assumption

The induced response is directly proportional to the applied loads. For example, if you double the magnitude of loads, the model's response (displacements, strains, and stresses) doubles. You can make the linearity assumption if the following conditions are satisfied:
  • The calculated highest stress is in the linear range of the stress-strain curve characterized by a straight line starting from the origin.
  • The maximum calculated displacement is considerably smaller than the characteristic dimension of the part. For example, the maximum displacement of a plate must be considerably smaller than its thickness and the maximum displacement of a beam must be considerably smaller than the smallest dimension of its cross-section.

Use nonlinear analysis if the linearity assumption is not satisfied.

Elasticity Assumption

The part returns to its original shape if the loads are removed (no permanent deformation).

Use nonlinear analysis if the elasticity assumption is not satisfied.

Static Assumption

Loads are applied slowly and gradually until they reach their full magnitudes. Suddenly applied loads cause additional displacements, strains, and stresses.

Use dynamic analysis if the static assumption is not satisfied.

Linearity Assumption

Stress-Strain Relation for Linear Material

In a linear material, the stress-strain relation is linear. The slope of the line is the elastic modulus of the material (E).