# Linear Static versus Linear Dynamic Analysis

In linear static analysis, the loads are applied gradually and slowly until they reach their full magnitude. After reaching their full magnitude, the loads remain constant (time-invariant). The accelerations and velocities of the excited system are negligible, therefore, no inertial and damping forces are considered in the formulation:

where:

[K]: stiffness matrix

{u}: displacement vector

The solution produces displacements, stresses, that are constant.

In linear dynamic analysis, the applied loads are time-dependent. The loads can be deterministic (periodic, non-periodic), or non-deterministic which means that they cannot be precisely predicted but they can be described statistically. The accelerations and velocities of the excited system are significant, therefore, inertial and damping forces should be considered in the formulation:

where:

[K]: stiffness matrix

[C]: damping matrix

[M]: mass matrix

{u(t)}: time varying displacement vector

: time varying acceleration vector

: time varying velocity vector