A local mesh free method for linear elasticity and fracture mechanics

The paper presents recent developments on mesh free numerical methods, implemented at the Department of Civil Engineering and Environment of the University of Brasilia. The concern is a local mesh free numerical model developed to solve two-dimensional problems in elasticity and linear elastic fracture mechanics. The model formulation is based in the work theorem of the theory of structures, kinematically formulated with a simple rigid-body displacement. The discretization considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration which improves the model accuracy. Both regular and irregular nodal distributions can be considered, which makes it a reliable model. The arbitrary discretization parameters, which determine the accuracy and efficiency of local mesh free methods, can be generated automatically, in a multi objective optimization environment, with genetic algorithms (GA), which makes it a robust model. Applications of linear elastic fracture mechanics implement the singularity subtraction technique (SST) to regularize the elastic field, before the numerical solution, introducing the stress intensity factors (SIF) as additional unknowns of the problem. These features make it an efficient model. Benchmark problems were solved for an assessment of the accuracy and efficiency of these techniques.