Object-oriented data structure for adaptive FEM-SPIM coupling in physically nonlinear analysis

Resumo

This paper presents the data structure developed for a coupled adaptive refinement strategy using Finite Element Method (FEM) and Smoothed Point Interpolation Methods (SPIMs) in physically nonlinear analysis. The solution of elastic degradation constitutive models adopted for this type of problem requires highly refined meshes that, when applied to the entire model, may lead to high computational cost. To overcome this, in the proposed approach, the domain starts with a coarse mesh of FEM and is only refined with a SPIM method in regions that can be automatically detected by different parameters. These regions generally exhibit higher stress concentrations and crack propagation. The implementations were carried out in the INSANE (INteractive Structural ANalysis Environment) system, an open-source software developed by the Department of Structural Engineering at the Federal University of Minas Gerais. The software follows the Object-Oriented Programming (OOP) paradigm using the Java language. The data structure is presented through UML diagrams and flowcharts describing the solution of the problem and the adaptive strategy. The phase-field constitutive model was considered, along with different refinement criteria.