ТОПОЛОГИЧЕСКАЯ ОПТИМИЗАЦИЯ ОБРАЗЦА ДЛЯ ИСПЫТАНИЙ НА ДВУХОСНОЕ РАСТЯЖЕНИЕ

Abstract

Applying the approaches of topology optimization, we consider the problem of substantiation of the configuration of the 2D test specimen, in the workspace of which the biaxial stress-strain state is realized. The original area occupied by the specimen is a square plate with a given side size made of an isotropic material. At the boundaries of the region, segments of fixed length are established on which boundary conditions are specified. The length of the segments is determined by the dimensions of the grippers of the testing machine. In the central part of the specimen is located the working area of the square form where the definition of displacements is carried out using measuring devices. The dimensions of the working area are selected taking into account the region of the used measuring devices. The test specimen is considered as a complex system consisting of working and auxiliary parts interacting with each other. The latter ensures the transfer of forces from the testing machine to the working part. The basic criterion determining the performance of this system is the criterion of accuracy of determining the deformations (displacements) in the working part. The implementation of the criterion is possible by ensuring the necessary stiffness of the overall system, i.e. the system's ability to carry the effect of external loads with allowable deformations that do not violate the performance of the system. The specimen design scheme for biaxial stretching used in the topological optimization process is reduced to the scheme of a two-dimensional plate of variable thickness which is in a plane stress state and occupies the initial region. The original search field is replaced by its finite element approximation. The objective function to be maximized is the stiffness of the system, and the design variables are the thicknesses of 2D finite elements. The specimen volume is set. A technique is proposed that allows determining the distribution of the material ensuring the achievement of the maximum integral stiffness of the system. The analysis of results of numerical simulation using the technique showed the need for holes on the specimen sleeves used in the experiments.