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Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present a novel formulation in the framework of assumed stress quasi-conforming method for the static and free vibration analysis of anisotropic and symmetric laminated plates.

Firstly, an initial stress approximation ruled by 17 parameters, which satisfies the equilibrium equations is derived to improve the performance of the constructed element. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions for strain integration.

Several numerical examples are presented to show the performance of the new element, and the results obtained are compared with other available ones. Numerical results have proved that the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

This paper proposes a new QC element for the static and free vibration analysis of anisotropic and symmetric laminated plates. In contrast with the complicated analytical solutions of the equilibrium equations, an initial stress approximation ruled by 17 parameters is adopted here. The Timoshenkos laminated composite beam functions are introduced as boundary string-net functions for strain integration. Numerical results demonstrate the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

To predict the occurrence of the combination resonances in parametrically excited, simply supported laminated composite plates in contrast to the simple resonances by using first‐order shear deformation lamination theory considering the effects of shear deformation and rotary inertia.

Finite element technique is applied to obtain the equilibrium equation of a plate. Modal transformation is applied to transform the equilibrium equation into a suitable form for the application of the method of multiple scales (MMS). The MMS is applied to obtain the boundaries of the simple and combination resonances.

The combination resonance zones contribute a considerable amount to the local instability region and the widths of combination resonance zones are comparable to those of the simple resonance zones for the loading of the small bandwidth at one end or for the concentrated edge loading.

Aircrafts, spacecrafts and many other structures such as ships, bridges, vehicles and offshore structures use the plate type elements, which are susceptible to dynamic instability.

It will assist the researchers of stability behavior of elastic systems.

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 prediction of accurate failure strength and a composite laminate failure load is of paramount importance for reliable design. The progressive failure analysis helps to predict the ultimate failure strength of the laminate, which is more than the first ply failure (FPF) strength. The presence of a hole in the laminate plate results in stress concentration, which affects the failure strength. The purpose of the current work is to analyze the stress variation and progressive failure of a symmetric laminated plate containing elliptical cutouts under in-plane tensile loading. The effect of various parameters on FPF and last ply failure (LPF) strength is studied.

The ply-by-ply stresses around elliptical cutouts are obtained analytically using Muskhelishvili's complex variable formulation. To predict the progressive failure, Tsai–Hill (T-H) and Tsai–Wu (T-W) failure criteria are used, and depending on the mode of failure, lamina modulus is degraded.

The study has revealed that fiber orientation and stacking sequence for given loading have the most significant effect on the laminate's failure strength.

Complex variable method and conformal mapping are simple and proficient for studying failure analysis of a laminated plate with elliptical cutout.

A formulation has been developed for thermo‐elastoviscoplastic finite element analyses of continuous fibre‐reinforced composite plates subject to bending loading using a generalized continuum mechanics approach. Such an approach is used to model the non‐homogeneity in a composite, which is constituted by fibres embedded in a matrix material. The present formulation computes the respective stresses occurring in each constituent so that the respective yield criterion and flow rule of each constituent may be used if there is a material yielding in any constituent. Thermo‐elastic deformation of fibre and thermo‐elastoviscoplastic deformation of matrix are considered in the present study because the yield strength of fibre is substantially higher than that of matrix in many cases. Both constituents are assumed to be isotropic so that the von‐Mises yield criterion may be used for viscoplastic yielding of matrix. As numerical examples, a parametric study is performed for thermo‐elastoviscoplastic deformations of laminated composite plates subject to thermal bending loads.

This study aims to demonstrate the numerical application of differential quadrature (DQ) methods and show the experimental application of free vibration analysis of fiber-metal laminated composite (FML) plates with various boundary conditions.

The FMLs are hybrid structures consisting of fiber-reinforced polymer matrix composites such as carbon, glass, aramid and different metal sheets, and are currently widely used in the automobile, aircraft and aerospace industries. Thus, free vibration analysis of these hybrid materials is necessary for the design process. The governing equations of motion are derived based on the classical plate theory. The DQ, generalized DQ (GDQ) and harmonic DQ (HDQ) differential quadrature methods have been used to solve the governing equations of an FML composite plate numerically. The accuracy and convergence of the numerical model have been verified by comparing the results available in the published literature with the results obtained from these methods. Moreover, an experimental procedure has been performed in order to compare the results against those of the numerical methods.

It is noteworthy that a high degree of similarity and accuracy was observed between the numerical results obtained by the DQ methods and the experimental results. Thus, the present study validates the applicability of the DQ methods for designing the FML composite plates.

In this study, the advantages of the DQ methods have been demonstrated differently from previous studies on the vibration analysis of the FML plates.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.

Effects of moisture and temperature on the behaviour of composite T‐joints made of carbon fibre composite (CFC) materials are investigated. T‐joints may be exposed to moisture and temperature during their service life. Under such circumstances moisture and temperature diffuse into T‐joints. As a consequence, the stiffness and strength properties of the laminates are degraded. Moreover, since the laminae in the laminate cannot deform freely, residual stresses are introduced. The analysis is carried out by the finite element method using a modified thick shell element that takes into account the hygrothermal effects. The analysis also accounts for the lamina material properties at elevated moisture concentration and temperature. Deflections are presented in the form of contours, and maximum stresses developed in the Redux layer are presented in tabular forms. Two stacking sequences with clamped boundary conditions are considered for each variation in moisture and temperature

A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic rectangular thin plates (ORTPs) and nano-rectangular plates, is established by using the symplectic superposition method (SSM).

The original fourth-order partial differential equation is first rewritten into Hamiltonian system. The class of boundary value problems of the original equation is decomposed into three subproblems, and each subproblem is given the corresponding symplectic eigenvalues and symplectic eigenvectors by using the separation variable method in Hamiltonian system. The symplectic orthogonality and completeness of symplectic eigen-vectors are proved. Then, the symplectic eigenvector expansion method is applied to solve the each subproblem. Then, the symplectic superposition solution of the boundary value problem of the original fourth-order partial differential equation is given through superposing analytical solutions of three foundation plates.

The bending, vibration and buckling problems of the rectangular nano-plate/isotropic rectangular thin plate/orthotropic rectangular thin plate with FFFF can be solved by the unified symplectic superposition solution respectively.

The symplectic superposition solution obtained is a reference solution to verify the feasibility of other methods. At the same time, it can be used for parameter analysis to deeply understand the mechanical behavior of related RTPs. The advantages of this method are as follows: (1) It provides a systematic framework for solving the boundary value problem of a class of fourth-order partial differential equations. It is expected to solve more complicated boundary value problems of partial differential equations. (2) SSM uses series expansion of symplectic eigenvectors to accurately describe the solution. Moreover, symplectic eigenvectors are orthogonal and directly reflect the orthogonal relationship of vibration modes. (3) The SSM can be carried to bending, buckling and free vibration problems of the same plate with other boundary conditions.

The purpose of this study is to investigate Thermo-mechanical limit elastic speed analysis of functionally graded (FG) rotating disks with the temperature-dependent material properties. Three different material models i.e. power law, sigmoid law and exponential law, along with varying disk profiles, namely, uniform thickness, tapered and exponential disk was considered.

The methodology adopted was variational principle wherein the solution was obtained by Galerkin’s error minimization principle. The Young’s modulus, coefficient of thermal expansion and yield stress variation were considered temperature-dependent.

The study shows a substantial increase in limit speed as disk profiles change from uniform thickness to exponentially varying thickness. At any radius in a disk, the difference in von Mises stress and yield strength shows the remaining stress-bearing capacity of material at that location.

Rotating disks are irreplaceable components in machinery and are used widely from power transmission assemblies (for example, gas turbine disks in an aircraft) to energy storage devices. During operations, these structures are mainly subjected to a combination of mechanical and thermal loadings.

The findings of the present study illustrate the best material models and their grading index, desired for the fabrication of uniform, as well as varying FG disks. Finite element analysis has been performed to validate the present study and good agreement between both the methods is seen.