Accurate linear analytical solutions for biaxial symmetry problems of rectangular thin plates using an innovative series expansion method

Abstract

This paper presents an innovative series expansion method for the accurate solution of biaxial symmetry problems of rectangular thin plates. This method surpasses traditional techniques such as the Navier and Lévy series solutions, the Timoshenko and Woinowsky-Krieger superposition method, and the symplectic geometry method, offering improved efficiency, easier implementation, and faster convergence. It effectively handles corner singularities arising from different boundary conditions and demonstrates superior accuracy. Key contributions include the application of particular closed-form solutions, the supplementation of corner conditions at intersections of free and clamped edges, the classification of corner singularities, and the selection of appropriate series expansions based on the inherent nature of the boundary conditions. The robustness of this method in dealing with complex boundary conditions and different loading scenarios is emphasized, providing deep insight and exceptional accuracy in structural analysis. Validation against peer results confirms its superiority and identifies potential problems in existing “exact” solutions, highlighting its practical value and potential for widespread adoption.