Fourier analysis of thick cross-ply Levy type clamped doubly-curved panels

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick doubly-curved panel of rectangular plan-form, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the C4-type simply supported boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of the deflection and moment of a cross-ply spherical panel, and also by comparison with the available FSDT (first-order shear deformation theory) based analytical solution. Additionally, numerical results pertaining to flat symmetric and antisymmetric cross-ply plates with the same boundary conditions have also been reproduced. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry (cylindrical and spherical), lamination, lamina material property, and thickness effects, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick singly- and doubly-curved cross-ply panels.     

Fourier solution to a thick cross-ply Levy type clamped plate problem

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick rectangular plate, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated plate analysis, with the C4-type clamped boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a square cross-ply plate. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, lamina material property, and thickness-to-length ratio, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick cross-ply plates.     

Boundary discontinuous Fourier analysis of thick cross-ply clamped plates

A new analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick rectangular plate, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach, is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated plate analysis, with the C3-type clamped boundary condition prescribed at all four edges. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a cross-ply plate. The primary focus of the present study is to investigate the effect of end clamping on the response of a thick laminated plate, while keeping the in-plane end constraints unaltered. Important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, material property, thickness effects and end clamping as well as their interactions.     

Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation

The static, dynamic, and free vibration analysis of a functionally graded material (FGM) doubly curved panel are investigated analytically in the present paper. The FGM Panel is originated from a rectangular planform and its principle curvatures are considered to be constant. All mechanical properties of the FGM panel are assumed to vary continuously through the thickness according to a power law formulation except Poisson’s ratio, which is kept constant. A Pasternak-type elastic foundation containing damping effects is considered to be in contact with the panel during deformation. The elastic foundation reacts in both compression and tension. Equations of motion are established based on the first order shear deformation and the modified Sanders shell theories. Following the Navier type solution, the established equations are reduced to time-dependent ordinary differential equations. Using the Laplace transform, the time-dependency of the problem is eliminated. The solutions are obtained analytically in the Laplace domain and then are inverted to the time domain following an analytical procedure. Finally, the analytical results are verified with those reported in the literature.