A large element computation for polygonal plates, shallow shells and cylindrical shells with the Fourier series and state-variable methods

The significance of a large element computation is that it drastically improves the computational efficiency by minimizing the work of mesh generation for modeling a physical problem. In this study, a large polygonal-shaped element was developed to compute problems involving the statics and dynamics of plates and shallow shells. A Fourier series method and a state-variable method were combined to solve the statics and dynamics of the polygonal-shaped plates or shallow shells with any admissible boundary conditions for isotropic and anisotropic materials. With the state-variable method, the anisotropic material properties and the initial curvature can be easily incorporated into the formulation and be solved.;A large cylindrical element was also developed for estimating the plastic area of a circumferential through crack on a cylindrical shell. The Fourier series method combined with the Fourier expansion-contraction technique effectively estimated the plastic area for a small or large crack in either a thin or a thick elastic perfectly-plastic cylindrical shell.;It is convenient to use these elements because the procedure for improving the solution accuracy involves no mesh generation or the increment of boundary points. This large polygonal element is more powerful in treating the boundary geometry than several other large element methods, such as the differential quadrature method and the hierarchic finite element method. The effectiveness and accuracy of this method was demonstrated by many examples such as the plate and shallow shell bending and vibration which were compared with the exact solutions and finite element solutions.