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Vol 212, No 2 (2016)
- Year: 2016
- Articles: 8
- URL: https://journals.rcsi.science/1072-3374/issue/view/14706
Article
Efficient Approach to the Evaluation of Dynamic Stresses in Layered Circular Plates Based on the Prudnikov Formula for the Inverse Laplace Transformation
Abstract
We propose an algorithm for the solution of axisymmetric dynamic problem of the theory of elasticity for a piecewise homogeneous ring, loaded by normal forces variable as functions of time. We perform the numerical analysis of stresses in plates with arbitrary numbers of layers on the basis of finding the Laplace transform by the modified Prudnikov formula for its inversion. We also establish the characteristic features of the distribution of dynamic stresses in homogeneous and piecewise homogeneous plates.
107-120
Mathematical Models for Estimating the Residual Life of Plates with Systems of Cracks Under the Action of Long-Term Static Loads, High Temperatures, and Hydrogen
Abstract
We formulate computational models used to determine the durability of plates with systems of cracks under the action of long-term static loads, high temperatures, and hydrogen-containing environments. These models are based on the first law of thermodynamics, i.e., on the balance of energy components and rates of their changes in metallic materials containing macrocracks and subjected to long-term tension, high-temperature field, and hydrogen-containing environments. We also consider specific cases of periodic and doubly periodic systems of cracks.
121-130
Conditions of Wave Propagation in a Two-Layer Liquid with Free Surface
Abstract
We analyze the roots of the dispersion equation for the problem of wave propagation in a two-layer liquid of finite depth with free surface for different values of the ratio of densities. It is shown that the roots obtained in the limiting cases are in good agreement with the previously known results. We prove the existence of two linearly independent solutions of the problem in the first approximation and study the shapes of the free and contact surfaces.
131-141
Discrete Mathematical Model of the Problem of Diffraction for E -Polarized Waves on Slots in the Impedance Plane
Abstract
We consider the problem of diffraction for E -polarized plane monochromatic waves on slots in the impedance plane. A discrete mathematical model of the boundary integral equations of this problem is constructed. We also perform a numerical experiment based on the use of the efficient numerical method of discrete singularities.
142-155
Mathematical Model of Scattering of Polarized Waves on Impedance Strips Located on a Screened Dielectric Layer
Abstract
The description of the processes of interaction of electromagnetic waves with imperfectly conducting gratings leads to the consideration of boundary-value problems for the Helmholtz equation with boundary conditions of the third kind. The original problem of scattering of polarized waves on the reflecting structures is reduced to a system of boundary integral equations. The procedure of derivation of the integral equations is based on the method of parametric representations of integral operators.
156-166
Effect of Heating on the Subsurface Inhomogeneity of the Electric and Mechanical Fields in Dielectrics
Abstract
The relations of the local gradient theory of dielectrics based on the analysis of the process of local displacements of masses are used for the investigation of the stress–strain state and polarization of a hollow sphere. The surfaces of the sphere are free of force loads and may have different temperatures. It is shown that the relations of this nonlocal theory enable one to estimate the effect of the temperature gradient on the subsurface inhomogeneity of the fields of stresses, polarization, and bound electric charges. These relations also describe the pyroelectric and thermopolarization effects.
167-181
Determination of the Natural Frequencies of an Elliptic Shell of Constant Thickness by the Finite-Element Method
Abstract
We study natural vibrations of a thin isotropic elliptic shell of constant thickness by the finite-element method realized with the use of the high-performance FEMAR software developed for the engineering analyses. The comparative analysis of the numerical results and experimental data is carried out.
182-192
Nonclassical Periodic Functions: Their Calculation and Applications
Abstract
A system of continuous T-periodic functions, which express the values of Cartesian coordinates of a moving point as functions of the traveled distance, is constructed on a one-parametric family of closed flat constraints with four axes of symmetry. We discover 2π -periodic functions that differ from the classical trigonometric functions by the sign of curvature at every point of their existence. The asymptotic 23 -periodic functions are computed and applied to the problem of motion of a material point along a closed flat-ribbed surface and to the modeling of kinematic perturbations of the bearing platforms of solid bodies.
193-211