Numerical calculation of the stress-strain state of composite materials taking into account physical and geometric nonlinearity
DOI:
https://doi.org/10.18372/0370-2197.3(96).16839Keywords:
composite materials, stress-strain state, theory of elasticity, physical and geometric nonlinearity, numerical methods, iterative algorithms, multi-core processors, parallelization of calculationsAbstract
The article introduces specialists developing composite materials with The article introduces specialists developing composite materials with predetermined physical and mechanical properties, as well as specialists from related industries, with the problem of studying the stress-strain state of objects, taking into account their physical and geometric nonlinearity. The main ways of ensuring strength are noted: empirical, experimental and calculated, in which, due to the corresponding theoretical apparatus, the empirical component is minimized, as a result of which, its role increases with the development of science and technology. It is noted that when calculating the strength, it is necessary to solve three problems consistently and in mutual compliance: the problem of external forces (normalization of loads); the problem of internal forces (determining mechanical stresses) and the problem of allowable stresses (rationing strength). Mutual correspondence means that the final accuracy of calculations is determined mainly by the lowest accuracy when these problems are solved sequentially, and a local increase in accuracy for one or two of them does not provide a significant increase in the overall accuracy. This development is devoted to the problem of calculating the stress-strain state of composites by methods of the theory of elasticity, which in its classical formulation, due to the progress of computers and the development of numerical methods for solving problems of mathematical physics, has now been completed to a certain extent, which cannot be said about nonlinear problems. On the example of a two-dimensional linear problem, the general approaches to obtaining the resolving equations of the linear theory of elasticity for an orthotropic body in stresses and displacements are analyzed. The difficulties and cumbersomeness of writing their analogues for nonlinear problems are noted. A method is proposed for direct integration of all groups of equations of the nonlinear theory of elasticity in an expanded form by numerical methods, when each of the groups of unknowns is determined by iterations in combination with parallelization of calculations on a multi-core processor, which makes it possible to more fully use the capabilities of modern computers in relation to nonlinear problems of mechanics of materials. This algorithm has been tested and tested based on the results of a well-known solution in the displacement of the problem for the "polymer coating - steel base" system. The replacement of geometric and (or) physical relations by their nonlinear analogs does not cause any fundamental difficulties.
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