Regular boundary element method for composite shear deformable plate and shell

This paper presents a fundamental solution for a double-curvature simply supported shell, incorporating three concentrated forces and two bending moments. It introduces the reference domain concept and formulates fictitious load boundary integral equations using both constant and linear elements. These equations are developed in the Laplace transform domain for both static and dynamic problems. The key contribution of this study is the development of the Regular Boundary Element Method (RBEM) based on the new fundamental solution. The reference domain includes the real structure’s configuration, and a system of linear equations is established with fictitious forces and moments as unknowns. These equations are derived from traction and displacement boundary conditions. To obtain all physical values in the time domain, the Durbin’s Laplace inverse technique is applied. The accuracy and reliability of the proposed method are evaluated through four numerical examples, with results compared against exact solutions or the finite element method.