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The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank-Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.

This paper presents an analysis of the possibility of increasing the ultimate elongation and penetration capability of metallic shaped-charge jets in the presence of an axial magnetic field in the shaped-charge liner by the heating and thermal softening of the jet material due to a sharp increase in the magnetic-field induction in the jet formation region upon liner collapse. This process is studied by numerical simulation in a quasi-two-dimensional formulation taking into account the inertial extension of the conductive rigid-plastic rod in the presence of a longitudinal magnetic field in it.

The processes of elastic strain of thin films under mechanical load are considered. The film is simulated by a longitudinally compressed plate placed on an elastic foundation. The computer model of the buckling of the narrow thin plate with a detachment portion, placed on an elastic foundation is constructed. The supercritical behavior of the plate - substrate system is studied. The experiments on the axial compression of the metal strip adhered to the rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. The possibility of progressive detachment of the metal plate from the foundation in excess of the critical load is shown. It is found that the use of the proposed approach, which, in contrast to other approaches, takes into account the elastic strain of the substrate, causes the dependence of critical bending stresses on the stiffness of the foundation.

This paper presents the results of calculations and experiments on the torsion of plates made of isotropic and transversely isotropic BT-20 and 1163T alloys with reduced resistance to creep strain in the direction perpendicular to the median surface. The numerical modeling results for plates of different thickness that belong to the class of rigid and flexible plates made with the use of the pure bending theory and the finite element method are compared. It is established that during the deformation of the plate of anisotropic material into an alternating saddle-shaped surface, the curvature values are smaller than in the case of a plate of a isotropic material. The calculation carried out ccording to the pure bending theory yields an upper estimate of the curvature ifference during the strain of the plates of transversely isotropic and sotropic materials.

This paper describes an experimental work on a 1:100 scaled model of a miniature sea-star tension leg platform (TLP) in a wave flume. Two different numerical models are developed: finite element model (FEM) based on the Morison equation and boundary element model (BEM) based on a 3D diffraction/radiation theory. The developed codes are used to calculate hydrodynamic forces and related coefficients. The nonlinear hull/tendon coupled dynamic equation of a mini sea-star TLP is solved by using a modified Euler method (MEM). The results of numerical modeling of the motion response behavior of the platform in different degrees of freedom are compared with experimental data. This comparison shows good agreement between the results. Furthermore, this modeling reveals that the first-order diffraction method and quasi-static tendon modeling are sufficient in general for the hydrodynamic analysis of the sea-star TLP.

Instability of a thin-walled stainless steel tube with a crack-shaped defect under combined loading is studied in this paper. Furthermore, the effects of the tube length, crack orientation, and crack length on the buckling behavior of tubes are investigated. The behavior of tubes subjected to combined is analyzed by using the finite element method (by Abaqus software). For cracked tubes with a fixed thickness, the buckling load decreases as the tube length and the ratio of the tube length to its diameter increase. Moreover, the buckling load of cracked tubes under combined loading also decreased with increasing crack length.

A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.

The thermoelastic problem of laser effect on metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally.

Numerical and analytical studies of the natural and quasi-natural flexural-gravitational vibrations of an elastic plate floating on a liquid surface are performed based on shallow-water long-wave theory. Dependences of natural and quasi-natural frequencies on the geometrical parameters of the vibration region are studied for the cases of bounded and unbounded reservoirs. The effect of bottom irregularities in the form of a circular cylinder or a circular truncated cone on the natural and quasi-natural frequencies and functions is studied.

This paper describes the effect of thermal exposition (high temperature soak) (T=675^oC) on the relaxation of residual creep stresses in the surface reinforced solid cylindrical sample of a ZhS6UVI alloy. The analysis is performed with the use of experimental data for the residual stresses after reinforcement by microspheres and after high-temperature soaks T=675^oC for 50, 150, and 300 h. The paper describes the solution technique for the boundary-value problem of creep of the reinforced cylindrical sample with the initial stress-strain state in thermal exposition. The uniaxial experimental creep curves obtained at constant stresses of 500, 530, 570, and 600 MPa to construct models describing the first and second stages of creep. The calculated and experimental data for the longitudinal (axial) component of the residual stress tensor are compared, and it is found that they are in satisfactory agreement