Frequency‐domain fundamental solutions and boundary element method for consistent couple stress elastodynamic problems

Abstract

AbstractIn this article, the elastodynamic problems are investigated within the framework of a consistent couple‐stress theory (CCST). The basic equations for the CCST elastodynamic problems are derived at first. These dynamic formulas are then analyzed in the frequency domain by the Fourier transform. The frequency‐domain fundamental solutions to the transformed elastodynamic problems are subsequently derived for the two‐dimensional (2D) plane‐strain state. Based on the fundamental solutions and the elastodynamic reciprocal theorem, the frequency‐domain boundary integral equations (BIEs) are established. Then, the BIEs are numerically solved by a collocation method in conjunction with analytical and numerical treatments of the arising singular integrals. To obtain the time‐domain dynamic responses, an exponential window method (EWM) is adopted to transform the frequency‐domain results to the time‐domain solutions. By using the developed boundary element method (BEM), several typical couple‐stress elastodynamic problems are numerically investigated and the size‐effects are studied by using different values of the length‐scale parameter in the CCST. Good agreements between the results obtained by the developed BEM for a tiny length‐scale parameter and the corresponding classical BEM results or analytical solutions are achieved, which validates the high accuracy of the present BEM.