An Elementarily Simple Galerkin Meshless Method: the Fragile Points Method (FPM) Using Point Stiffness Matrices, for 2D Elasticity Problems in Complex Domains
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The Fragile Points Method (FPM) is a stable and elementarily simple, meshless Galerkin weak-form method, employing simple, local, polynomial, Point-based, discontinuous and identical trial and test functions which are derived from the Generalized Finite Difference method. Numerical Flux Corrections are introduced in the FPM to resolve the inconsistency caused by the discontinuous trial functions. Given the simple polynomial characteristic of trial and test functions, integrals in the Galerkin weak form can be calculated in the FPM without much effort. With the global matrix being sparse, symmetric and positive definitive, the FPM is suitable for large-scale simulations. Additionally, because of the inherent discontinuity of trial and test functions, we can easily cut off the interaction between Points and introduce cracks, rupture, fragmentation based on physical criteria. In this paper, we have studied the applications of the FPM to linear elastic mechanics and several numerical examples of 2D linear elasticity are computed. The results suggest the FPM is accurate, robust, consistent and convergent. Volume locking does not occur in the FPM for nearly incompressible materials. Besides, a new, simple and efficient approach to tackle pre-existing cracks in the FPM is also illustrated in this paper and applied to mode-I crack problems.
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