A Step-by-Step Time Integration Method Based on the Principle of Minimum Transformed Energy

Abstract

A step-by-step time integration method is presented for dynamic response analysis based on Benthien-Gurtin's principle of minimum transformed energy in linear elastodynamics. First of all, a single convolution-type (Gurtin-type) functional in the real space is obtained from the functional in Laplace space. Then the concrete functional, that can be used to construct time integration methods by adopting some interpolation functions, is established after successively spatial and temporal discretization. The cubic Hermite interpolation functions in temporal domain are adopted to show the procedure of constructing time integration method and the new numerical method is developed finally. The specific stability characteristics about the unconditional and conditional stabilities of the numerical method are investigated in detail. The numerical examples show that the algorithm is of satisfying accuracy and is an effective method for the numerical calculations of dynamic response problems in engineering.