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Based on the von Kármán geometric nonlinear plate theory, the displacement-type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2-point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer-thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness-radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate’s critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. [ABSTRACT FROM AUTHOR]

In the paper the influence function and the method of partial discretization in free axisymmetric vibration analysis of multilayered circular plates of constant and linearly variable thickness were presented. The effects of shear deformation and rotary inertia for the core as well as the facings were neglected. An analytical investigation based on the classical plate theory was made for the multilayered plate which satisfies Sokołowski’s condition. Discretization of mass and replacing stiffness of a fixed circular plate were presented. Formulas of influence matrix and Bernstein-Kieropian’s estimators for different steps of discretization were defined. The influence of variable distribution of parameters on the value of double estimators of natural basic and higher frequency of a sandwich circular plate was investigated.

Abstract The study is devoted to thin-walled clamped symmetrical three-layer circular plate. The sandwich plate consists of two facings, and a metal foam core. The mechanical properties of the core plate vary along its radius, remaining constant in the facings. The main goal of the study is to elaborate a mathematical model of the compressed circular plate in its middle plane, analytical description and solution of the global buckling problem. The nonlinear hypothesis of deformation of the normal to the middle plane of the plate is formulated. The equations of equilibrium are derived based on the principle of stationary total potential energy. The proposed mathematical model of the displacements considers the shear effect. The analytical model is verified numerically with the use of Finite Element Analysis. [ABSTRACT FROM AUTHOR]

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, BaTiO3/Al/BaTiO3 and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length. [ABSTRACT FROM AUTHOR]

This paper is devoted to analytical and numerical studies of global buckling of a sandwich circular plate. The mechanical properties of the plate core vary along its thickness, remaining constant in the facings. The middle surface of the plate is its symmetrical plane. The mathematical model of the plate is presented. The field of displacements is formulated using the proposed nonlinear hypothesis that generalizes the classical hypotheses. The equations of equilibrium are formulated based on the principle of stationary total potential energy. The proposed mathematical model of the displacements considers the shear effect. The numerical model of the plate is also formulated with a view to verify the analytical one. Numerical calculations are carried out for the chosen family of plates. The values of the critical load obtained by the analytical and numerical methods are compared. The effects of the material properties of the core and the change of the plate radius on the critical load intensity are presented. [ABSTRACT FROM AUTHOR]

This study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature load are investigated. In this paper, the stability of the plate is compared through saturated and unsaturated porous layers, and the effect of the fluid's thermal expansion coefficient on the stability of the plate is investigated. [ABSTRACT FROM AUTHOR]

The axisymmetric dynamic stability of sandwich circular plates with a constrained damping layer treatment subjected to a periodic uniform radial loading along the outer edge of the host plate is studied by the discrete layer annular finite element method. The viscoelastic material with frequency dependent properties in the damping layer is assumed to be incompressible, and the extensional and shear moduli are described by complex quantities. The regions of dynamic instability are determined by Bolotin’s method while two eigenvalue problem systems with frequency dependent parameters are formed. The modified complex eigensolution method is employed to solve the eigenvalue problems. Numerical results are shown that the constrained damping layer attached to circular plates tends to stabilize the circular plate system. The effects of various parameters, such as types of viscoelastic material response, treatment thickness and area, on dynamic stability are also investigated. [Copyright &y& Elsevier]