روش مربعات دیفرانسیلی تعمیم یافته

Orthotropic plates used in composite structures are subject to local buckling, including compressive buckling. In the process of designing and building most large structures or instruments with complex geometry, joints in the structure are unavoidable. Today, adhesive joints are widely used in connecting composite structures due to some advantages over mechanical joints. In this article, the buckling phenomenon of orthotropic rectangular multilayer plates connected with glue has been investigated, and the force effects of the glue layer under buckling loading conditions have been studied. In order to obtain the critical buckling loads under different boundary conditions, the generalized differential quadrature method (GDQM) has been used. Buckling analysis is presented based on first-order shear deformation theory (FSDT) for carbon/epoxy, glass/epoxy and Kevlar/epoxy composite materials with different porcelain layers. The effect of thickness and type of the adhesive as a bonding layer has been investigated. In plates made of a type of porcelain layer, two-way carbon epoxy plates show higher buckling strength, and in general, the higher the ratio of length to width of the plates is, the higher the buckling strength will be. In the connections, the obtained results have been compared with the results from the finite element analysis in ABAQUS commercial software.

In this research, the free vibration of the joint of two hybrid cylindrical-conical shells have been studied, considering the continuity conditions in the joint of the two shells, based on the first order shear deformation shell theory. The equations of the joint of two shells have been extracted using the Hamilton’s principle, and solved by applying the generalized differential quadrature method under different boundary conditions. Also, hybrid shells are composed of composite layers in the core and two layers of aluminum metal at the top and bottom of the shells. In this study, the Carbon- Epoxy, Glass- Epoxy and Aramid-Epoxy composite materials are used. The results obtained in this research are compared with previous studies, and there is a very good agreement between the results. Also, the effects of cone angle of the conical shell, boundary conditions, volume fraction, circumferential mode, composite materials, variation of length to shell radius and variation of thickness to shell radius, on the natural frequency have been investigated. The results have shown that, with the increase of the cone angle of the conical shell, the dimensionless natural frequency of the joint of two cylindrical- conical shells increased. Also, with increase of the circumferential mode, the non-dimensional frequency of the structure of two joined hybrid shells, first decreased and then increased.

In this paper, static buckling of homogeneous beams coated by a functionally graded porous layer with different boundary conditions is investigated based on the Timoshenko beam theory. The principle of virtual work has been used to obtain the governing equations. Two different methods, namely analyticalsolution and numerical solution are used to solve the governing equations and extract the buckling force. The governing equations are coupled as a series of ordinary differential equations. In the analytical solution, these equations are first uncoupled using a series of mathematical operations, and are then solved. The obtained solution has a series of parameters and unknown constants. Using the boundary conditions at the boundaries of the beam, a homogeneous system of equations is extracted, from which the axial buckling force is obtained. In the numerical solution, the generalized differential quadrature method is used to solve the static equations. Finally, the numerical results are presented and the effects of various parameters such as thickness to beam length ratio, porous layer thickness, porosity parameter, etc. on the buckling of the beam are investigated. Comparison of the results obtained from the two analytical and numerical solution methods confirms the accuracy and validity of both methods.

This article aims at studying the free and forced vibrations of shape memory alloy beam ‎actuators. The constitutive equations are derived based on a three dimensional ‎phenomenological model which accounts for pseudoelastically and shape memory effect by ‎considering phase transformation strains in the formulation. In the present study, the ‎pseudoelastic deformations are studied. Assuming Timoshenko beam model for the structures ‎with moderate thickness, equations of motion are derived through Hamilton principle, and the ‎obtained partial differential equations are discretized by applying the Generalized Differential ‎Quadrature approach and then are solved incrementally using Newmark integration method. ‎The return mapping algorithm, considering Newton-Raphson iteration procedure, is employed ‎to update phase transformation strains and any related parameters during solution in each time ‎steps. Results show that energy dissipation occurs due to hysteric behavior of SMA beams ‎during vibrations for both free and forced cases. In most cases, the reduction in amplitudes ‎continues till the material behaves like the elastic solids within austenite phase where no ‎dissipation is appeared. Also, it can be observed from the results that the amplitude of ‎damped vibrations is constant for SMA structure. Therefore, it exhibits more stable behavior ‎in comparison with elastic beam with similar harmonic actuations. Consequently, it is ‎concluded that the SMA materials can be applicable to adjust response frequency in addition ‎to their various applications such as in dampers.

In this paper thermal buckling of a thin cylindrical panel made of piezo-magnetic two dimensional functionally graded materials (2D-PFGM) subjected to magnetic field have been investigated. The material properties of structure assumed varying by exponential functions of volume fraction in longitudinal and circumferential directions. In order to solving the problem at the first, the equilibrium equations have been derived by the first order shear deformation theory by concerning the nonlinear terms from the strain-displacement relations. In the next step, by giving the incremental changes on the displacement components and calculating the resultant forces and moments, using Lagrang,s equations on the second functional of potential energy the stability equations have been derived. After solution the mentioned equations by generalized differential quadrature method based on the simply supported boundary conditions the critical buckling temperature has been determined. By solving the numerical example in special cases and comparing the obtained results we confident from the method of analysis. At the end, effect of geometrical features, applied voltage on the external surface of panel, and changing the material properties on the critical buckling load have been investigated.

Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results.

In this paper, buckling of orthotropic rectangular plates under different loadings was investigated. For this reason, governing buckling equations for an isotropic plate were modified by applying constitutive equations of orthotropic materials. After obtaining the equations of orthotropic plates, Generalized Differential Quadrature method (GDQM) was applied on buckling equations and thus a set of Eigen value equations resulted. In order to solve this Eigen value problem, a computer program was developed using MATLAB software in a way that the influence of different parameters such as length to width ratio (aspect ratio), the number of layers, the angle of layers arrangement, material of layers, kind of loading and boundary conditions were included. A buckling load factor was calculated for simply supported and clamped supported plates. The results of GDQ method were compared with reported results from Rayleigh – Ritz method and with results from solving the Finite element using ANSYS 8.0 software. The comparison showed the accuracy of obtained result clearly.