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

Abstract

One of the approaches to the construction of graphic images of the stress state for the force vector applied to a point is considered in this work. Has been proposed a geometric model for a continuous medium, formed by a bunch of projection planes for each point of the examined object’s space. This permits to obtain a model for a volume vector in the form of a distributed decomposition into stress components at each point specified by a bunch of projection planes. The building a model for a volume vector, defined as a set of specified laws of direction and length, in the context of modeling stress from an applied force vector to a selected point, is based on strength of materials’ classical laws for calculation the stress state values at an inclined section. Such approach allows use a voxel graphic structure for computer representation of the simulated stress, rather than a finite element mesh. In such a case, there is no obtained result’s error dependence on the spatial position of the mesh nodal points, which is often a problem in FEM calculations. The resulting functional-voxel computer model of the volume stress vector is a structural unit for modeling the distributed load on areas of complex configuration. In this case, the elementary summation of such vectors allows any uneven distribution of the load relative to each point on the specified area. The considered approach works well with geometric models initially represented analytically in the form of a function space (for example, models obtained by the R-functional modelling – RFM-method), and reduced to functional-voxel computer models. A method for deformation modeling based on obtained stresses by means of local transformations of the function space, describing the investigated geometric object, is demonstrated.