Linear Transient Analysis

Calculates the response of a structure to time-dependent loads. Typical applications are structures subject to earthquakes, wind, explosions, or a vehicle going through a pothole.

The loads are time-dependent forces and displacements. Initial conditions define the initial displacement and initial velocities in grid points.

The results of a transient response analysis are displacements, velocities, accelerations, forces, stresses, and strains. The responses are usually time-dependent.

The transient response analysis computes the structural responses solving the following equation of motion with initial conditions in matrix form.(1)

M \ddot{u} + C \dot{u} + K u = f (t)

(2)

u_{t = 0} = u_{0}

(3)

{\dot{u}}_{t = 0} = v_{0}

The matrix $K$ is the global stiffness matrix, the matrix $M$ the mass matrix, and the matrix $C$ is the damping matrix formed by the damping elements. The initial conditions are part of the problem formulation and are applicable for the direct transient response only. The equation of motion is integrated over time using the Newmark beta method. A time step and an end time need to be defined.

Direct and modal transient response analysis methods are implemented as follows.