This most basic type of FEA analysis is also known as small displacement analysis. The matrix equation for this type of analysis can be represented as {F} = [K]{U} where:

{F} is the applied force vector

[K] is the stiffness matrix

{U} is the displacement vector

The following three assumptions must be true for the system to be linear.

1) The material used in the analysis must follow Hooke's Law where the stress is proportional to strain. The constant of proportionality is called Young's modulus.

2) The stiffness matrix does not change throughout the problem.

3) The boundary conditions do not change from the initial load application to the final deformed shape. The loading must be constant in magnitude, orientation and distribution.

Static refers to the assumption that all loads are applied slowly up to their full magnitude.