Geometric Modeling of Stress Visualization Based on the Functional-Voxel Method

Abstract

The visualization of the parameters of the stress state of a solid remains one of the parameters influencing the adoption of engineering decisions. For example, methods for determining finite elements (FEM), which make it possible to determine and visualize stress in the selected regions of the model. Applying element methods to analytically constructed models to localize the search for stress to its values at a point, however, will not lead to successful results. The paper discusses the principles of visualization of local stresses based on the functional-voxel method. The concept of a volume vector as a unit of volume distribution of a force vector in a solid isotropic medium is introduced. Geometrical foundations are proposed for computer representation of the stress unit in an isomorphic body based on a raster image. Geometric models of the stress tensor are constructed for the main site, the inclined platform. The principles of applying the functional-voxel model in the tasks of constructing complex objects are proposed. The application of the functional voxel method for discrete modeling of the deformation of a geometric object is illustrated by the example of a function that describes a rectangular plate.