Thermal impact on a circular sandwich plate on an elastic foundation

Symmetric transverse vibrations of a circular metal-polymer sandwich plate under a thermal impact are studied. The plate is connected with an inertialess Winkler foundation. The facesheets are assumed to satisfy the Kirchhoff hypothesis and the deformed normal in the low-density core is rectilinear and incompressible across thickness. Analytical solutions are obtained and their numerical analysis is given.     

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

Resonant effects of local loads on circular sandwich plates on an elastic foundation

The axisymmetric forced vibrations of a circular sandwich plate on an elastic foundation are studied. The plate is subjected to axisymmetric surface and mechanical loads with frequency equal to one of the natural frequencies of the plate. The foundation reaction is described by the Winkler model. To describe the kinematics of an asymmetric sandwich, the hypothesis of broken normal is used. The core is assumed to be light. The analytical solution of the problem is obtained and numerical results are analyzed     

Elastoplastic bending of a sandwich bar on an elastic foundation

The elastoplastic bending of a sandwich bar with a stiff compressible core on an elastic foundation is studied. The kinematics of the bar, which is asymmetric across the thickness, is described adopting Bernoulli’s hypotheses for the face layers. The displacements of the core are assumed to vary linearly across the thickness. The foundation is described by the Winkler model. A system of equilibrium equations for displacements is derived and solved. Numerical results for a metal-polymer sandwich bar are presented __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 110–120, April 2007.     

Natural vibration of a sandwich beam on an elastic foundation

The natural vibration of an elastic sandwich beam on an elastic foundation is studied. Bernoulli’s hypotheses are used to describe the kinematics of the face layers. The core layer is assumed to be stiff and compressible. The foundation reaction is described by Winkler’s model. The system of equilibrium equations is derived, and its exact solution for displacements is found. Numerical results are presented for a sandwich beam on an elastic foundation of low, medium, or high stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 57–63, May 2006.     

弹性圆板下横观各向同性弹性地基的轴对称问题

将与板相关的各力学量展开为Fourier-Bessel级数,利用解析法对弹性圆板下横观各向同性弹性地基的轴对称问题进行了分析。这些级数中的待定系数由板的边界条件、板的控制方程、地基-板的相容条件加以确定。数值计算结果表明:横观各向同性地基的沉降比各向同性地基的沉降要小,而地基反力则变化不大,说明按各向同性地基进行分析偏于保守。该分析方法将原问题简化为求解代数方程组的问题,且该方法可以推广到板的一般弯曲及层状地基与板的相互作用问题。     

Bending of a circular plate on a nonuniform elastic foundation in partial contact with the plate

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 162–169, January–February, 1989.     

Unilateral contact between a plate and an elastic foundation

Summary The unilateral frictionless contact between a plate and an elastic subgrade is examined. The foundation is modeled as an elastic half-space or as a Winkler subgrade. The variational formulations more convenient to get approximate solutions are presented. Furthermore the results of a numerical investigation relative to an axisymmetric circular plate are given.

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Sommario Si analizza il problema di contatto unilaterale senza attrito tra una piastra e una fondazione elastica. Per la fondazione si esaminano i modelli di semispazio elastico e di suolo alla Winkler.Vengono presentate le formulazioni variazionali più convenienti ai fini dell'approssimazione delle soluzioni col metodo degli elementi finiti e si illustrano alcuni risultati di un'indagine numerica per il caso di piastra circolare con carico assialsimmetrico.

     

Thermoplastic strain of circular sandwich plates on an elastic base

We consider thermomechanical bending of an elastoplastic circular (solid or annular) light-filler sandwich plate resting on an elastic base. The hypotheses of broken normal are used to describe the kinematics of the plate stack nonsymmetric along the thickness. The base reaction is described by the Winkler model. We obtain the system of equilibrium equations and its exact solution in terms of displacements. We also present numerical results for a sandwich annular metal-polymer plate.     

Unbonded contact between a circular plate and an elastic half-space

The paper concerns the unbonded contact between a thin circular plate of finite radius, governed by Kirchhof or Reissner theory, pressed by means of rotationally symmetric distributed load and its own weight against the surface of an elastic half-space. The contact is assumed frictionless and unbonded. A Hankel transform solution is used for the half-space and the plate deflection is found by inverting the plate equation. The coefficients in a power expansion are obtained by equating plate and half-space deflections at a number of points in the contact region. The variation of contact radius with plate radius, the radius of the uniformly applied load, and the relative stiffness of plate and foundation, is displayed in a series of figures.     

On modes of buckling for a plate on an elastic foundation

We study flexural stability of a homogeneous plate compressed in its plane and lying on an elastic foundation. There is an elastic stratum between the plate and the foundation. In the case of homogeneous uniform compression, the linear approximation does not answer the question of the shape of buckling. A geometrically nonlinear approach leads to the conclusion that the buckling shape is of staggered character.     

Thermoelastic bending of a sandwich plate on a deformable foundation

The thermoelastic bending of a circular light-core sandwich plate on a deformable foundation is examined. To describe the kinematics of the plate with asymmetric thickness, the hypothesis of broken normal is adopted. The reaction of the foundation is described by Winkler’s model. The thermomechanical load is local and symmetric. The system of equilibrium equations is derived and solved exactly. Numerical results for three-layer metal-polymer plate are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 96–103, February 2006.     

The large deflection on problem of circular plate on elastic foundation and in conjunction with linear elastic structure

This paper deals with the axisymmetrical deformation of the circular plate in large deflection, which is on elastic foundation and in conjunction with a certain linear elastic structure. The governing integral equations are established by the method of mixed boundary condition 1 and the simplified form is given. The pertrubation method is used to obtain the solutions and an example of the composite structure made up of a circular plate and a cylindrical shell is presented.     

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

Based on the nonlocal elasticity theory, the vibra-tion behavior of circular double-layered graphene sheets (DLGSs) resting on the Winkler- and Pasternak-type elas-tic foundations in a thermal environment is investigated. The governing equation is derived on the basis of Eringen’s nonlocal elasticity and the classical plate theory (CLPT). The initial thermal loading is assumed to be due to a uniform temperature rise throughout the thickness direc-tion. Using the generalized differential quadrature (GDQ) method and periodic differential operators in radial and cir-cumferential directions, respectively, the governing equation is discretized. DLGSs with clamped and simply-supported boundary conditions are studied and the influence of van der Waals (vdW) interaction forces is taken into account. In the numerical results, the effects of various parameters such as elastic medium coefficients, radius-to-thickness ratio, thermal loading and nonlocal parameter are examined on both in-phase and anti-phase natural frequencies. The results show that the thermal load and elastic foundation respec-tively decreases and increases the fundamental frequencies of DLGSs.