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First time, an analytical three-dimensional elasticity solution is proposed for bending analysis of composite laminated cylindrical shell panels having arbitrarily end-support conditions which were unavailable hitherto. Governing partial differential equations are obtained in terms of displacements and stresses by employing Ressiner mixed variational principle in the cylindrical coordinate system. Further employing extended Kantorovich method, governing partial differential equations are reduced to sets of non–homogeneous first order ordinary differential equations (ODEs). The set of ODEs with variable coefficients (along radial direction) is ingeniously solved through a new modified power series method whereas the set with constant coefficients (along circumferential direction) is solved using Pagano’s approach. After thorough validation, some new benchmark results are presented for single layer and multilayered laminated composites under various boundary conditions. This development will help to revisit/develop solutions for many classical problems of arbitrarily supported shell structures.

A three-dimensional analytical solution is developed for a longitudinally functionally graded plate subjected to Levy-type boundary conditions. A linear variation of material compliances is taken along the x-direction. The recently developed mixed-field multiterm extended Kantorovich method is applied to solve the governing equations in mixed form. A set of non-homogeneous ordinary differential equations (ODEs) with varying coefficients are obtained along the x-direction, which is solved by using the recently developed modified power series method. Another set of ODEs with constant coefficient is obtained along the z-direction, which is solved analytically. For the first time, numerical results for a two layered plate having a different in-plane material variation in each layer are presented along with single layer plate results. Benchmark results are presented which can be used to validate approximate two-dimensional solutions and 3D numerical results.

A coupled three-dimensional piezoelasticity solution for rectangular piezoelectric laminated plates with Levy-type boundary conditions is presented using the mixed-field multi-term extended Kantorovich method (EKM) and Fourier series expansion. The solution considers two-way electromechanical coupling, and satisfies all the essential and natural boundary conditions as well as the continuity conditions at the interface exactly at all points. The objective is to accurately characterize the edge effects in finite dimensional piezolaminated plates under mechanical and actuation potential loading, and also to provide a benchmark for assessing the accuracy of the two-dimensional laminate theories. The interlaminar shear stress is also accompanied by a singular stress field of the transverse normal (peel) stress near the edge. The numerical study is conducted for both single layer PZT plates for sensory applications and hybrid sandwich plates for smart structural applications. It is shown that the EKM solution predicts the displacement, stress, electric potential and electric displacement fields very accurately including the sharp variations of stresses near the edge, under the potential loading with just two/three terms in the trial function.

This is the first time, a three-dimensional (3D) analytical solution of arbitrarily supported cross-ply cylindrical panel with weak interfaces is developed using multi-term extended Kantorovich method (EKM). A generalized variational based mathematical model is developed by considering the Reissner-type mixed variational principle in conjunction with weak interface model. A linear spring layer model is implemented for depicting the behaviour of weak interfaces. Recently developed EKM is applied to obtain two sets of non-homogeneous ordinary differential equations (ODEs) along radial and circumferential directions, respectively. A suitable solution algorithm is developed for the present case. The accuracy of the presently developed solution is verified by comparing with 3D finite element model using ABAQUS. The multi-term EKM solution is efficient as just two terms yield the accurate results. Further, displacement and stress variations in a laminate at the edges are obtained and some new benchmark results are also presented for arbitrarily supported cylindrical panels with weak interfaces. Effect of the weak interface parameter and other characteristic parameters are investigated to reflect their design aspect. This development may help the researchers to develop analytical models for viscoelastic cases.

An accurate three dimensional elasticity solution for rectangular laminated plates subjected to Levy-type boundary conditions is presented using the recently developed mixed-field multi-term extended Kantorovich method (EKM) in conjunction with Fourier series. Such a solution accurately characterizes the edge effects in finite laminated plates under general bending, which can be used as a benchmark for assessing two-dimensional (2D) laminate theories for predicting of edge effects. The variables are expanded in Fourier series along the direction intersecting the simply-supported edges, and the 3D EKM is applied for the inplane and thickness directions. Using the Reissner-type variational principle, the governing partial differential equations are converted into two sets of 9n algebraic-ordinary differential equations for each Fourier term. The boundary conditions are satisfied exactly at all points on the boundaries. It is shown that similar to the case of cylindrical bending of infinite panels, the present solution for the general bending of finite plate also converges within two or three terms in the trial function. The numerical results are presented for composite and sandwich plates with four different boundary conditions. The effect of aspect ratio and width to length ratio on the boundary layer effect in the in-plane and interlaminar stresses are investigated.

A benchmark three-dimensional (3D) exact piezoelasticity solution is presented for free vibration and steady state forced response of simply supported smart cross-ply circular cylindrical shells of revolutions and panels integrated with surface-bonded or embedded monolithic piezoelectric or piezoelectric fiber reinforced composite (PFRC) layers. The effective properties of PFRC laminas for the 3D case are obtained based on a fully coupled iso-field model. The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends. These equations with variable coefficients are solved using the modified Frobenius method, wherein the solution is constructed as a product of an exponential function and a power series. The unknown constants of the general solution are finally obtained by employing the transfer matrix method across the layers. Results for natural frequencies and the forced response are presented for single layer piezoelectric and multilayered hybrid composite and sandwich shells of revolution and shell panels integrated with monolithic piezoelectric and PFRC actuator/sensor layers. The present benchmark solution would help assess 2D shell theories for dynamic response of hybrid cylindrical shells.

A recently developed improved third order theory (ITOT) for angle-ply hybrid piezoelectric plates in cylindrical bending is extended to include geometric non-linearity in the Von Karman sense. The transverse deflection is approximated non-uniformly to explicitly account for the transverse strain due to temperature and electric potential. The coupled non-linear equations of motion and the boundary conditions are derived using the extended Hamilton’s principle. The non-linear theory is used to obtain the buckling and free vibration response of symmetrically laminated hybrid angle-ply panels under inplane electro-thermomechanical loading. This theory and the third order zigzag theory with additional layerwise terms for inplane displacements are assessed in direct comparison with the exact 2D piezothermoelasticity solutions for forced harmonic response, buckling and free vibration response under initial inplane electro-thermomechanical loading. The comparison establishes the accuracy of the results of the zigzag theory and its superiority over the ITOT for the dynamic and buckling response of angle-ply hybrid panels.

A new improved third order theory (ITOT) is presented for hybrid piezoelectric angle-ply flat panels under thermal loading. The transverse deflection is approximated nonuniformly to explicitly account for the transverse strain due to temperature and electric potential which are approximated as piecewise linear. The governing equations are derived using Hamilton’s principle. The ITOT and an existing efficient zigzag theory are assessed for simply-supported angle-ply flat hybrid panels for static loads and for natural frequencies by comparison with 2D solutions. The comparisons for test, composite and sandwich panels establish that for most cases the zigzag theory is very accurate and ITOT is an improvement over the third order theory (TOT) based on uniform approximation of deflection across the thickness.