Vol 8, No 4-4 (2014)

In the framework of the work the authors conducted a simulation of the behavior of porous materials of different densities under the influence of impact loading. Results of computational experiment were compared with the results obtained using the model of Deshpande-Fleck porous material.

The paper continues research of group of authors on flow of thin layer of plastically anisotropic material on the surface of elastic body. Previously obtained results are used to formulate the problem of elasticity theory and the study of stress-strain state of an elastic body (tool).

The paper discuses an efficient method for calculating network operators, which solve initial boundary value problems for the homogeneous heat conduction equation with constant coefficients in cylindrical domain with zero initial conditions and boundary conditions on the grounds and inhomogeneous boundary conditions on the lateral surface of the cylinder. The savings have been achieved through calculation of operators in the algebra of polynomials formed by power of spatial-temporal semigroup operator as well as the separation of calculations by spatial variables along element and base of cylinder. Along all the variables quadratic approximation is used. The convergence and stability of method are proved, approximation orders are obtained relatively digitalization of different variables.

The paper considers full group of one-dimensional or multidimensional potentials of stress and strain of rheological materials, which are described by linear and quasilinear integral ratios of Boltzmann-Kelvin type, containing one pair of temporary relaxation and creep functions, interconnected together with linear integral equations of Maxwell reciprocity. The built group of potentials as a function of integral pulse flows and forces satisfies Legendre-Eiler transformations and forms a chain of Gibbs-Helmholtz in generalized Bourne diagram. Variants of potential relations are shown.

The paper considers tensor-parametric version of endochronic theory of inelasticity for large deformations and rotations, taking into account the time effects. Stress relaxation process in material was numerically modeled. There was examined an impact of parameter included in the deformation gradient and parameter of hardening material to form curves "voltage~time" and their quantitative characteristics. The results of numerical experiments are shown.

Method of numerical simulation of shape of the Earth has shown that its real shape does not correspond to the central gravitational field. Two-mass analogue source of noncentral gravity field of the Earth in form of a nucleus and the equatorial ring is proposed. There were calculated two element masses model and radius of ring under which the estimated figure of the Earth and dependence gravitational acceleration on its surface on latitude correspond to experimental data and international agreements.