A post‐correction integration algorithm for non‐linear dynamic analysis of structures

Abstract

AbstractA simple and practical post‐correction direct integration approach to compute the dynamic response of structures with non‐linear stiffness properties is introduced. This approach is based on the assumption that the effect of a non‐linear restoring force is equivalent to a series of impulse functions acting on the so called fundamental linear system. Applying this basic idea with unconditionally stable step‐by‐step integration methods, the non‐linear dynamic analysis of structures can be executed by a linear one‐step direct integration procedure by modifying the velocity and acceleration at the end of the time step (post‐correction) instead of modifying the structural properties at the beginning of each time step. A general description of the proposed post‐correction approach for the direct integration of the equations of motion is presented. The algorithm to combine the proposed approach with the unconditionally stable Wilson θ method is discussed in great detail. Numerical results are included to verify the accuracy of the method and to illustrate the computing procedure.