Bezsíťové metody ve strukturální mechanice

Abstract

The thesis deals with the description of a meshfree or numerical method that does not use element discretization but an array of nodes. First, the properties and assumptions of the meshfree method, the formulation itself and the types of interpolation functions are described. Next, the paper discusses in more detail the advantages and interpolation using the point interpolation method (PIM) and then the radial point interpolation method (RPIM). For the numerical method LSD - FEM, which is used in IDEA StatiCa, a new 2D polygonal element has been developed which produces a polyhedral cell. RPIM interpolation is used for this element, on which a sensitivity parametric study of the influence of parameters on the behavior of the radial multi-quadric basis function itself has been performed. A spectrum of parameters was found and tested on benchmark examples for 2D plane stress. The study of the parameters was carried out on the examples of a cantilever beam and a Cook's membrane. Solutions with different parameter levels were verified using FEM software ANSYS, where the relative error and convergence rate were compared against LSD – FEM and RPIM interpolation.