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A numerical method is presented in this paper for the free vibration analysis of circular and elliptical first order shear deformable plates. In this method, the ellipse is mapped into a circle and then the circular geometry of the plate is mapped using parabolic interpolation function of natural coordinates and eight nodal points of prescribed coordinates. The displacement fields are defined by a set of relatively very high order interpolation functions and for the displacement degrees of freedom a set of nodal points are defined separate from those of the geometric interpolation. Numerical results for the fully clamped elliptical plate are obtained and compared with the available data from the literature. Additional results for the simply 1‐supported complete elliptical plate and the annular elliptical plates subjected to various boundary conditions are presented and discussed.

This paper describes the development and the numerical analysis of an electrochemical model for the analysis of a novel polymer/metal composite actuator. A general continuum model describing the transport and deformation processes of these actuators is briefly presented, along with a detailed description of the simulation scheme used to predict deformation, current, and mass transport. The predictions of the model are compared with experimental data, indicating a significant role of water transport in the large‐scale deformation. Comparison of the simulations and experimental data showed good agreement confirming the central role of water transport in the deformation process. For the sake of completeness the fabrication process and testing apparatus are also described.

The purpose of this paper is to study the wave propagation in a homogeneous isotropic, thermo‐elastic plate of arbitrary cross‐sections using the two‐dimensional theory of thermo‐elasticity.

A mathematical model is developed to study the wave propagation in an arbitrary cross‐sectional thermo‐elastic plate by using two‐dimensional theory of thermo‐elasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the boundary conditions prevailing at the arbitrary cross‐sectional surface of the plate for symmetric and antisymmetrical modes in completely separate forms using Fourier expansion collocation method. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

The computed non‐dimensional frequencies are compared with those results available in the literature in the case of elliptic cross‐sectional solid plate with clamped edges without thermal field and this result is coincide with the results of Nagaya. The computed non‐dimensional frequencies are plotted in the form of dispersion curves for longitudinal and flexural (symmetric and antisymmetric) modes of vibrations for the material copper.

The wave propagation in a plate of arbitrary cross‐sections with the stress free (unclamped) and rigidly fixed (clamped) edges are analyzed with and without thermal field.

This study aims to construct a mathematical model to study the dispersion analysis of magneto-electro elastic plate of arbitrary cross sections immersed in fluid by using the Fourier expansion collocation method (FECM).

The analytical formulation of the problem is designed and developed using three-dimensional linear elasticity theories. As the inner and outer boundaries of the arbitrary cross-sectional plate are irregular, the frequency equations are obtained from the arbitrary cross-sectional boundary conditions by using FECM. The roots of the frequency equation are obtained using the secant method, which is applicable for complex solutions.

The computed physical quantities such as radial stress, hoop strain, non-dimensional frequency, magnetic potential and electric potential are plotted in the form of dispersion curves, and their characteristics are discussed. To study the convergence, the non-dimensional wave numbers of longitudinal modes of arbitrary (elliptic and cardioid) cross-sectional plates are obtained using FECM and finite element method and are presented in a tabular form. This result can be applied for optimum design of composite plates with arbitrary cross sections.

This paper contributes the analytical model for the role of arbitrary cross-sectional boundary conditions and impact of fluid loading on the dispersion analysis of magneto-electro elastic plate. From the graphical patterns of the structure, the effects of stress, strain, magnetic, electric potential and the surrounding fluid on the various considered wave characteristics are more significant and dominant in the cardioid cross sections. Also, the aspect ratio (a/b) and the geometry parameters of elliptic and cardioids cross sections are significant to the industry or other fields that require more flexibility in design of materials with arbitrary cross sections.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading.

Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematically, a general mathematical model is developed for laminated shell geometries. The responses are evaluated numerically using a finite element model-based computer code developed in MATLAB environment. Subsequently, a simulation model has been developed in ANSYS using ANSYS parametric design language code to evaluate the responses.

Vibration and thermal buckling responses of laminated composite curved panels have been obtained based on proposed model through a customised computer code in MATLAB environment and ANSYS simulation model using ANSYS parametric design language code. The convergence behaviour are tested and compared with those available in published literature and ANSYS results. Finally, the investigation has been extended to examine the effect of different parameters (thickness ratios, curvature ratios, modular ratios, number of layers and support conditions) on the free vibration and thermal buckling responses of laminated curved structures.

The present paper intends to give sufficient amount of numerical experimentation, which may lead to help in designing of finished product made up of laminated composites. Most of the aerospace, space research and defence organisation intend to develop low cost and high durable products for real hazard conditions by taking combined loading and environmental conditions. Further, case studies might lead to a lighter design of the laminated composite panels used in high-performance systems, where the weight reduction is the major parameter, such as aerospace, space craft and missile structures.

In this analysis, the geometrical distortion due to temperature is being introduced through Green–Lagrange sense in the framework of higher-order shear deformation theory for different types of laminated shells (cylindrical/spherical/hyperboloid/elliptical). A simulation-based model is developed using ANSYS parametric design language in ANSYS environment for different geometries and loading condition and compared with the numerical model.

The purpose of this paper is to develop a general mathematical model for the evaluation of the bending and vibration responses of the skew sandwich composite plate using higher-order shear deformation theory. The sandwich structural components are highly preferable in modern engineering application because of their desirable structural advantages despite the manufacturing and analysis complexities. The present model is developed to solve the bending and vibration problem of the skew sandwich composite plate with adequate accuracy numerically in the absence of the experimental analysis.

The skew sandwich composite plate structure is modelled in the present analysis by considering laminated face sheet in conjunction with isotropic and/or orthotropic core numerically with the help of the higher-order mathematical model. Further, the responses are computed numerically with the help of in-house computer code developed in matrix laboratory (MATLAB) environment in conjunction with finite element (FE) steps. The system governing equations are derived via variational technique for the computation of the static and the frequency responses.

The skew sandwich composite plate is investigated using the higher-order kinematic model where the transverse displacement through the thickness is considered to be linear. The convergence and the validation study of the bending and the frequency values of the sandwich structure indicate the necessary accuracy. Further, the current model has been used to highlight the applicability of the higher-order kinematics for the evaluation of the sandwich structural responses (frequency and static deflections) for different design parameters.

In the present paper, the bending and the vibration responses of the skew sandwich composite plate are analysed numerically using the equivalent single-layer higher-order kinematic theory for the isotropic and the orthotropic core numerically with the help of isoparametric FE steps. Finally, it is understood that the present model is capable of solving the sandwich structural responses with less computation cost and adequate accuracy.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The main objective of this study is to develop a numerical model based on Isogeometric Analysis to study the dynamic behavior of multi-directional functionally graded plates with variable thickness.

A numerical study was conducted on the dynamic behavior of multi-directional functionally graded plates. Rectangular and circular plates with variable thickness are taken into investigation. The third-order shear deformation plate theory of Reddy is used to describe the displacement field, while the equation of motion is developed based on the Hamilton's principle. Isogeometric Analysis approach is employed as a discretization tool to develop the system equation, where NURBS basis functions are used. The famous Newmark method is used to solve time-dependent problems.

The results obtained from this study indicated that the thickness gradation has a more considerable effect than in-plane variation of materials in MFGM plates. Additionally, the influence of the damping factor is observed to affect the vibration amplitude of the plate. The results obtained from this study could be used for future investigations, where the viscous elasticity and other dynamic factors are considered.

Although there have been a number of studies in the literature devoted to analyzing the linear static bending and free vibration of FGM and MFGM plates with variable thickness, the study on dynamic response of FGM and MFGM plate is still limited. Therefore, this study is dedicated to the investigation of the dynamic behavior of multi-directional functionally graded plates.

The purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of order p to obtain high order approximations. To numerically demonstrate the features of the enriched approximation some examples on the mechanical elastic response and free‐vibration of axisymmetric plates and shells are carried out.

The global approximation is based on a particular family of weight function, which is defined on the parametric domain of the element, ξ∈[−1,1], resulting in shape functions with compact support, which have regularity C₀^k,k=0,2,4… in the global domain Σ. The PU shape functions are enriched by a set of monomials of order p to obtain high order approximation spaces.

Based on the numerical results of elastic axisymmetric plates and shells, it is demonstrated that the proposed methodology produces satisfactory results in terms of keeping the ill‐conditioning of the system of equations under accepted levels. Comparisons are established between linear and Hermitian shape functions showing similar results. The observed results for the free‐vibration problem of plates and shells show the potential of the proposed approximation space.

In this paper the formulation is limited to the modeling of axisymmetric plate and shell problems. However, it can be applied to model other problems where the high regularity of the approximation is required.

The paper presents an alternative approach to construct partition of unity shape functions based on a particular family of weight function.