In this paper the influence of objects’ thermal processes on their correspondence to a given geometry has been considered, and an alternative apparatus for geometric modeling of bodies’ temperature stress and thermal expansion after effect of a heat source, based on a functional-voxel approach, has been proposed as well. A discrete geometric model of temperature stress at a point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, allowing simulate a single action of a heat source to obtain local geometric characteristics of thermal stress in the body. This approach, unlike traditional approaches based on the FEM, allows apply the temperature load at the object’s point taken by itself. A discrete geometric model for expansion at the point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, which allows simulate the change of an object’s local geometric characteristics during the process of material expansion from a single effect of a heat source to obtain a value upon the body volume changing. This approach, unlike traditional approaches based on the FEM, allows simulate a change in the body’s surface geometry from thermal expansion at a point taken by itself without errors arising from calculations using a mesh. Have been proposed algorithms for functional-voxel modeling of temperature stress and expansion under distributed thermal loading. These algorithms allow construct a loading region of complex configuration based on the spatial distribution and scaling of the temperature stress’s geometric model for a single point of thermal loading, uniformly form a contour (surface) after material expansion, and obtain information about the change in products’ length (volume) based on information about each point of functional space. Has been presented an example of using the proposed approach for solving a processing tool’s correction problem based on the temperature in the cutting zone and material thermal reaction. The geometric model can be used to the automated design of a processing tool path for parts cutting on CNC machines.
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.
The paper proposes a method of functional voxel modeling (FVM) of stresses arising under the influence of a force or heat load in an isotropic body. We consider the principles of modeling the unit stress in a volume vector a geometric object, set by analogy with the normal vector with two parameters: the function of the value and the function of the angle of direction.The principles of constructing a functional-voxel model are demonstrated that allows a computer to graphically represent a three-dimensional vector as a set of M-images displaying local geometric characteristics of the obtained functional area.The possibilities of constructing stress fields from distributed loads by means of sequential addition of a single stress distributed in space are considered. The principles of constructing a single thermal stress and constructing distributed fields based on it are considered separately. Existing approaches are used to model the shape of thermal expansion of the body. The obtained visual images of stresses and strains are compared with the simulated results in the existing computational modules based on FEM. The advantages of visualizing the results obtained from the standpoint of accuracy and clarity of representation are demonstrated. The prospects of such an approach to modeling visual physical quantities in relation to the visual diagnostics of the part geometry are considered.
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.
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