Governing Equations

Linear static structural analysis solves for the displacement field caused by applied loads under the assumption of static equilibrium. The governing finite element equation is:

K u = f

The equation is linear when the stiffness matrix K does not depend on the unknown displacement u. This requires small deformations, linear elastic materials, and fixed boundary/contact conditions.

Once displacements are obtained, strains and stresses are recovered using:

epsilon = B u_e
sigma = D epsilon

The accuracy of the solution depends on the mathematical model, material data, mesh quality, load representation, boundary conditions, and solver tolerances.