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This paper aims to present a nonclassical circular plate model subjected to hydrostatic pressure and electrostatic actuations by considering the modified couple stress theory and the surface elasticity theory. The pull-in phenomenon and nonlinear behavior of circular nanoplate are investigated.

The hybrid differential transformation method (DTM) and finite difference method (FDM) are used to approach the model. The DTM was first applied to the equation with respect to the time, and then the FDM was applied with respect to the radius.

The numerical results were in agreement with the numerical data in the previous literature. The effects of the length scale parameters, surface parameters, thermal stress, residual stress, hydrostatic pressure and electrostatic actuations of the nonclassical circular plate on the pull-in instability are investigated. The parametric study demonstrated that the pull-in behavior of the circular nanoplate was size dependent.

In this study, the results provide a suitable method in a nonclassical circular plate model. The length scale parameter had an obvious effect on the nonlinear behavior of the circular nanoplate.

It has been revealed that application of the differential form of Eringen’s nonlocal elasticity theory to some cases (e.g. cantilevers) leads to paradoxical results, and recourse must be made to the integral version of Eringen’s nonlocal model. The purpose of this paper, within the framework of integral form of Eringen’s nonlocal theory, is to study the bending behavior of nanoscale plates with various boundary conditions using the isogeometric analysis (IGA).

The shear deformation effect is taken into account according to the Mindlin plate theory, and the minimum total potential energy principle is utilized in order to derive the governing equations. The relations are obtained in the matrix-vector form which can be easily employed in IGA or finite element analysis. For the comparison purpose, the governing equations are also derived based on the differential nonlocal model and are then solved via IGA. Comparisons are made between the predictions of integral nonlocal model, differential nonlocal model and local (classical) model.

The bending analysis of nanoplates under some kinds of edge supports indicates that using the differential model leads to paradoxical results (decreasing the maximum deflection with increasing the nonlocal parameter), whereas the results of integral model are consistent.

A new nonlocal formulation is developed for the IGA of Mindlin nanoplates. The nonlocal effects are captured based on the integral model of nonlocal elasticity. The formulation is developed in matrix-vector form which can be readily used in finite element method. Comparisons are made between the results of differential and integral models for the bending problem. The proposed integral model is capable of resolving the paradox appeared in the results of differential model.

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a nonlocal porous thermoelastic medium.

In this study normal mode analysis is used to obtain analytical expressions of the physical quantities. The numerical results are given and presented graphically when mechanical force is applied.

The model is illustrated in the context of the Green-Naghdi theory of types II, III and the three-phase lags model. Expressions for the physical quantities are solved by using the normal mode analysis and represented graphically.

Comparisons are made with the results predicted in the absence and presence of the rotation as well as a nonlocal parameter. Also, the comparisons are made with the results of the 3PHL model for different values of time delay.

Hoping to uncover the physical principles of the vibration of the functionally graded material (FGM) microplate, by which the authors can make contributions to the design and manufacturing process in factories like micro-electro-mechanical system (MEMS) and other industries.

The authors design a method by establishing a reasonable mathematical model of the physical microplate composed of a porous FGM.

The authors discover that the porosity, the distributions of porosity, the power law of the FGM and the length-to-thickness ratio all affect the natural frequency of the vibration of the microplate, but in different ways.

Originally proposed a model of the micro FGM plate considering the different distributions of the porosity and scale effect and analyzed the vibration frequency of it.

The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded).

The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification.

Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments.

A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

This paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.

The governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.

The results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.

The results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

This paper attempts to evaluate the transverse stresses that are generated within the interface between two layers of laminated composite and sandwich laminates by using Cℴ finite element formulation of higher‐order theories. These theories do not require the use of a fictitious shear correction coefficient which is usually associated with the first‐order Reissner‐Mindlin theory. The in‐plane stresses are evaluated by using constitutive relations. The transverse stresses are evaluated through the use of equilibrium equations. The integration of the equilibrium equations is attempted through forward and central direct finite difference techniques and a new approach, named as, an exact surface fitting method. Sixteen and nine‐noded quadrilateral Lagrangian elements are used. The numerical results obtained by the present approaches in general and the exact surface fitting method in particular, show excellent agreement with available elasticity solutions. New results for symmetric sandwich laminates are also presented for future comparisons.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The theory of generalized thermoelasticity, based on the Lord‐Shulman theory (LS) with one relaxation time and the Green‐Naghdi theory (GN) (of type II) without energy dissipation, as well as the classical dynamical coupled theory (CD), is used to study the electromagneto‐thermoelastic interactions in a semi‐infinite perfectly conducting solid subjected to a thermal shock on its surface. The entire elastic medium is rotating with a uniform angular velocity. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock, the rotation and due to the application of the magnetic field. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the variables considered are represented graphically for two different cases. From the distributions, the wave type heat propagation in the medium can be found. This indicates that the generalized heat conduction mechanism is completely different in essence from the classic Fourier’s law. Comparisons are made with the results predicted by the three theories in the presence and absence of rotation and a magnetic field.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.