A study on the Radial Integration Method for elastoplastic analysis

Resumo

In the context of numerical analysis for structural engineering problems, the Boundary Element Method (BEM) offers a significant computational advantage by reducing problem dimensionality through boundary-only discretization. However, in elastoplastic problems, domain integrals arise, requiring special treatment. A widely adopted approach involves discretizing the domain into internal cells to evaluate these integrals, which, however, eliminates the primary advantage of dimensionality reduction. An alternative technique for handling domain integrals in nonlinear problems using BEM is the Radial Integration Method (RIM), which extinguish the need for domain discretization. In elastoplastic problems, the RIM transforms domain integrals into boundary integrals by approximating initial stress increments using Radial Basis Functions (RBFs) augmented with polynomial terms. In this study, the RIM is implemented within a BEM methodology to perform two and three-dimensional elastoplastic analysis. Numerical experiments demonstrate that this methodology  maintains a reduced-order formulation in terms of dimensionality and achieves good results for appropriate mesh refinements. However, for excessive (and unnecessary) mesh refinements, the RIM decreases in accuracy when compared to cells approach.