Одновісний розтяг пружно-пластичних пластин з квадратним отвором різної орієнтації

Abstract

На основі числового розв’язування крайових задач теорії малих пружно-пластичних деформацій для лінійно зміцнюваного матеріалу з урахуванням розвантаження з’ясовано вплив орієнтації квадратного отвору в пластині на її напружено-деформований стан за одновісного розтягу.

Effective numerical methods for solving 2D problems related to the theories of elasticity and plasticity have been worked out. The variation-difference method of building finite difference schemes is extended to domains with curvilinear boundaries and disconnected domains. The application of the variation-difference method for solving problems of the theory of small elasto- plastic deformations relatively the plates with a hole, taking into account the linear strengthening of the material and unloading, has been developed. For solving the resultant systems of nonlinear and linear equation, the Newton-Kantorovich method and combined iterative method (gradient and cyclic Chebyshev’s one) were proposed to be used. The choice of iteration parameters of the methods for solving the obtained systems of linear and nonlinear algebraic equations was made. The elaborated software ensures solving the problems with different boundary conditions, medium and domain parameters. A variety of problems concerning one-axis stretching of the plates with the square hole of different orientation relatively the axis of stretching is numerically solved. The zones of evolution of plastic deformations for step enlarging of the loading are constructed, the remaining deformations and the limit loads are obtained. The influence of the orientation of square hole in the plate onto the stress magnitude was found. The orientation of the hole does not make essential influence onto the shape of zones of generation and development of residual deformations, but it essentially impacts onto magnitudes of the components of the stress tensor and its intensity, and therefore the moment of the beginning of plastic deformation. That is, in a plate with rotated square hole the initial plastic deformations appear under the tension 45% less than in a non-rotated one.