A MESHLESS ANALYSIS FOR BIHARMONIC SHELL BENDING USING THE MIXED FRAGILE POINTS METHOD (MIXED-FPM)

Abstract

Shell bending analysis plays a vital role in the structural design of engineering systems such as bridge decks, aircraft wings, and thin-walled pressure vessels. While element-based numerical methods like the Finite Element Method (FEM) are widely used for these problems, they suffer from limitations including mesh dependency, mesh distortion under large deformations, and high computational cost—especially when dealing with this fourth-order partial differential equations (PDEs) and crack propagationd. Meshfree methods such as the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) address some of these issues but introduce their own complexities in numerical integration due to the use of rational trial functions. This study introduces an efficient alternative: the Fragile Points Method (FPM), which uses simple, piecewise polynomial trial and test functions, enabling straightforward numerical integration with only one integration point per subdomain. The FPM is formulated to solve the biharmonic equation governing plate and shell bending. Continuity across subdomains is enforced through numerical flux corrections using a penalty parameter. This approach enables C1-continuity analysis without complex basis functions or excessive degrees of freedom. The method is applied to a square shell under self-weight, demonstrating its accuracy and sensitivity to penalty parameters and boundary condition enforcement, while avoiding the drawbacks of element-based methods.

Publication Title

ASME International Mechanical Engineering Congress and Exposition Proceedings Imece

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