Two-step recursive method for dynamic response computation based on principle of minimum transformed energy

摘要

A fourth-order accurate method is presented for the computation of dynamic response in the field of structural vibration. Based on Benthien-Gurtin's principle of minimum transformed energy in linear elastodynamics in Laplace space, functional in the form of single convolution integral is obtained by restoring the functional in the Laplace space back into the original space. Based on the functional after spatial discretization, five-order Hermite interpolation functions are adopted to approximate the nodal displacement in local time domain. A unconditionally stable two-step recursive method is presented after the variational operation. The value of parameter θ is selected according to the unconditionally stable analysis. Accuracy analyses and examples show that the algorithm is a higher accurate method. The method provided an useful tool with simple code and easy implementation for the investigations of dynamic response computations in practical engineering.