SCT-BEM for Transient Heat Conduction and Wave Propagation in 2D Thin-Walled Structures

Abstract

Traditional boundary element method (BEM) faces significant challenges in addressing dynamic problems in thin-walled structures. These challenges arise primarily from the complexities of handling time-dependent terms and nearly singular integrals in structures with thin-shapes. In this study, we reformulate time derivative terms as domain integrals and approximate the unknown functions using radial basis functions (RBFs). This reformulation simplifies the treatment of transient terms and enhances computational efficiency by reducing the complexity of time-dependent formulations. The resulting domain integrals are efficiently evaluated using the scaled coordinate transformation BEM (SCT-BEM), which converts domain integrals into equivalent boundary integrals, thereby improving numerical accuracy and stability. Furthermore, to tackle the challenges inherent in thin-body structures, a nonlinear coordinate transformation is introduced to effectively remove the near-singular behavior of the integrals. The proposed method offers several advantages, including greater flexibility in managing transient terms, lower computational costs, and improved stability for thin-body problems.