جستجوی مقالات مرتبط با کلیدواژه « تئوری تغییر شکل برشی مرتبه اول » در نشریات گروه « مکانیک »

Considering the increasing use of hybrid cylindrical shells in various industries, the free vibration analysis of these types of structures is very important. In this research, the free vibrations of the hybrid cylindrical shell under the influence of hydrostatic pressure have been analyzed and investigated. Investigating the hydrostatic pressure in hybrid shells is one of the important and required things for the optimal design of the structure, investigating the performance of the structure in different environmental conditions, bearing and resistance to pressure, etc. The boundary conditions for the cylindrical shell have been considered as fixed, free and simple, the equations governing the structure of the hybrid cylindrical shell are based on the displacement field and the stress and strain relations in matrix form using the first-order shear deformation theory of the shell and Hamilton's principle obtained and using generalized differential quadratic numerical method, the governing equations of the structure were solved and the effect of fiber angle, composite materials, hydrostatic pressure, composite to metal ratio, length to radius and thickness to radius of the cylinder on the natural frequency of the shell was investigated  and analyzed. Numerical results have been compared and validated with the results of the research. The results show that the hybrid shell with the distribution of composite materials and in a specific volume ratio shows better behavior against different hydrostatic pressure.

In this article, the thermal buckling and post-buckling of functionally graded plates with a matrix of isotropic polymer reinforced with graphene platelets (GPLs) have been investigated. In these multilayer plates, the thickness of all layers is the same, and by changing the weight fraction of reinforcing graphene platelets in each layer, the type of layer arrangement of nanocomposite plates changes. The plates are reinforced with three functional graded distributions: X and O and a uniform U distribution. The governing equations of the plate are obtained with the help of the first-order shear deformation theory (FSDT). The thermal buckling behavior of plates has been studied by the differential quadrature method. To find the effective Young's modulus, the Halpin-Tsai modified micromechanical model is used, and the law of mixing is used to obtain the equivalent properties of composites. The results show that the distribution of graphene platelets with an X arrangement improves the resistance of the plate against buckling. Also, the effect of parameters such as the weight fraction of graphene platelets, aspect ratio, and length-to-thickness ratio has been investigated.

In this paper, the finite element analysis of the free vibrations of functionally graded porous circular plate reinforced with graphene based on the first order shear deformation theory (FSDT) is presented for the first time. The governing equations are obtained using Hamilton's principle and the finite element method (FEM) is used to solve the governing equations of the sheet. The results of the present work were compared with previous studies and a good agreement between the results was observed. The effect of different parameters such as porosity distribution, porosity coefficient, different GPL patterns and weight percentage of graphene nanoparticles, types of boundary conditions and also the ratio of thickness to radius on the vibrations of the circular sheet was investigated. Next, while validating the analysis method, the results obtained from the numerical solution were compared and analyzed. In the results, it was found that the effect of weight percentage of graphene and different types of graphene patterns as well as support conditions in sheet vibrations is more than other cases.

In this research, the free vibration of rotating tapered Timoshenko beam with piezoelectric layer has been studied. It is assumed that the beam is made of Functionally Graded Materials (FGM) through the thickness direction and the boundary condition is a cantilever attached to the hub. The first-order shear deformation theory has been used to drive governing equations. At first, the total energy of the system such as potential and kinetic energies for the beam and piezoelectric layer has been derived, and then the natural frequencies of the beam have been determined by the Ritz approach based on minimizing the total system energy. After verifying the results by comparing them with other research, the effects of some parameters such as hub radius, rotational speed, taper ratios, rotary inertia, material gradient, piezoelectric voltage, and beam thickness on the natural frequencies of the tapered Timoshenko beam have been studied in detail. The results showed that with increasing the angular velocity of the beam, the natural frequency increases so that as the increasing velocity increases, the natural frequency increases with a steeper slope.

In this study, low velocity impact analysis of functionally graded carbon nanotube annular plate based of finite element method is presented for the first time. The governing equations are based on first shear deformation theory and Hamilton's principle. To model the contact force between annular plate and impactor, modified contact Hertz law has been used. Results of present study is compared with previous studies, and it shows good agreement. The effect of different parameters such as distribution and volume fraction of carbon nanotubes, and also, different mass and velocity of impactor on contact force and transverse displacemet of plate have been investigated. Results denotes that by increasing the volume fraction of carbon nanotube from 11 to 17 %, the contact force 32% is increased and the contact time is notably decreased. Also, results show that, the FGX distribution of nanotubes along the thickness of plate, has the highest contact force and the lowest contact time.

Plates made of laminated composite materials with variable stiffness can have wide applications in various branches of engineering due to such advantages as high strength /stiffness to weight ratio. In these composites, curved fibers are used to reinforce each lamina instead of the straight fibers. In this paper, the application of finite strip method for the buckling analysis of moderately thick composite plates with variable stiffness is investigated. For buckling analysis, a semi-analytical finite strip method based on the first-order shear deformation theory is employed. In this method, all displacements are presumed by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The minimum potential energy method has been used to develop the stability formulations. This analysis examines the effect of using curved fibers instead of straight fibers on the laminate composites. The critical loads obtained from this analysis are compared with those of other researchers and the efficiency and accuracy of the developed finite strip method are confirmed. Comparison of the analysis results of these plates shows that changing the slope of the fibers can lead to a significant change in the buckling response. Also, increasing the number of the terms of shape functions in the longitudinal direction has a significant effect on the convergence to the desired results.

Delamination is one of the common flaws in the composite plates, which may be created during manufacturing, boring or loading in the composite plate. This flaw has an impact on the flexibility, strength and performance of composite plates and structures and reduces them, which may even result in a layer fracture or complete fracture in the composite plate. In this study, a circular composite plate with the circular delamination under buckling load is considered. Given that the delamination grows and the delamination boundary is movable, the equilibrium equations governing the circular plate with circular delamination is produced by using Calculus of Variations method with moving boundary. The theory used in this paper for finding equilibrium equations governing the mentioned plate is the third order shear deformation theory. Ultimately, for isotropic and orthotropic materials, the critical buckling load is determined by using spectral homotopy analysis method and the results of the present paper is compared with the results of other studies. The results produced shows a good conformity with the other reference results.

In this paper, free vibration of the joined sandwich conical-conical shell is investigated by using differential quadrature method (DQM). It is assumed that the conical shell is truncated. The core of sandwich conical-conical shell is made from the four different types of materials such as Polyether ether ketone (PEEK), Polycarbonate (PC), Solid polypropylene (SPP) and high density polyimide foam (HDPF), and Aluminum is supposed for material of inner and outer skin layers. The first-order shear deformation shell theory (FSDT) is adopted to formulate the theoretical model and governing equations of motion are derivated by Hamilton’s principle. The governing equations of motion, the boundary conditions of the two ends of the shell and the continuity conditions at the interface section of shell segments, are discretized by means of the DQM. Then, eigenvalue problem, and, consequently natural frequencies are achieved. The effects of thickness, length of the shell, cone angle, material of the core and boundary conditions on natural frequencies are investigated. To verify the accuracy of this method, comparisons of the present results with results available in the open literature and Abaqus software are performed.

The most important application of functionally graded materials (FGM) is in the aerospace industry, these materials at high temperatures are very resistant to stresses especially residual stresses. In this study, a numerical solution for a circular branch made of FGM material with simple supports on radial edges, under transverse load along the thickness line, is presented. For this purpose, based on the first-order shear deformation theory and the principle of minimum energy, the potential of the entire equations of equilibrium is obtained. These equations are not independent. It is formulated for ease in solving, re-formulation, and for a circular sector with simple supports in radial edges and are solved numerically for the various boundary conditions in the periphery edges of the sector. In fact, this study aims to singularity of stress in a near-zero radius with calculations that indicate this stress is infinite in the near-zero radius, so failure will not occur.

This study aims to investigate the transverse vibration of single- and double-layered graphene sheets embedded in an elastic medium based on the third-order shear deformation theory considering the axial force effect within the framework of Eringen’s nonlocal elasticity theory, where the governing equations of motion are obtained using Hamilton’s principle. The superiority of the studied non-local continuum model to its local counterpart is to consider the effect of size on the mechanical behavior of the structure. The results from a natural frequency analysis are obtained for different conditions such as the effect of size and aspect ratio, axial force, nonlocal coefficient, and change in the stiffness properties of the surrounding elastic medium by using the Navier-type solution for simply supported boundary conditions. Given that in a double-layered graphene sheet, the system has an in-phase vibrational mode and anti-phase vibrational mode with 180-degrees phase difference, the effect of van der Waals force on both vibrational modes is attempted to be investigated and it is shown that the van der Waals force has no effect on in-phase vibrational mode and by increasing it, the anti-phase frequency increases. It is also demonstrated that the nonlocal parameter is not a constant parameter but its value depends on the size and atomic structure, like chiral and zigzag configurations, and even on the type of boundary conditions.

In this study, based on the third-order shear deformation theory the equations of motion are obtained to analyses the deformation of a long and slender composite beam. The beam has initial geometric imperfection and subjected to impact load. The impact procedures are applied by rigid body with a specific speed, off-center and at a certain distance from the beam's surface. Hamilton’s principle and the von-Karman nonlinear strain-displacement relationship are used to obtain the equations of motion that they are based on displacement and in a set of coupled nonlinear partial differential equations in dynamic mode. The generalized differential quadrature Method (GDQM) is used to discretize the obtained equations and convert them into a set of ordinary differential equations. Newton-Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Then, by solving the equations of the system, the effects of initial geometric imperfection on the beam’s deflection have been studied. Also the effects of mass and the initial velocity of the impactor on the beam’s deformation are investigated. The results of this research show that an increase in the amount of the initial velocity and mass of the impactor entail an increase in the beam deformation.

The main purpose of this study is to investigate the nonlinear bending and buckling analysis of radially functionally graded sector plates subjected to uniform in-plane compressive loads. The mechanical properties of plates assumed to vary continuously along the radial direction by the Mori–Tanaka distribution. The incremental form of nonlinear formulations are derived based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Also, due to the lack of similar research for the buckling of functionally graded sector plates with material variation in the radial direction, some results are compared with the ones reported by the ABAQUS finite element software. The achieved good agreements between the results indicate the accuracy of the present numerical method. Finally, numerical results for the maximum displacement and critical buckling load for various boundary conditions, effects of grading index, thickness-to-radius ratio, sector angle and inner radius-to-outer radius ratio are presented.

In this study, free vibration analysis of isotropic sector plates coupled with piezoelectric layers based on first-order shear deformation theory has been analyzed. Governing differential equations of the dynamic behavior of free vibration of isotropic sector plates coupled with piezoelectric layers are derived using Hamilton's principle and the electrostatic Maxwell equations. The Coupled governing differential equations of the vibrating composite plate are solved by applying the method of separation of variables and auxiliary potential functions. The presented analytical exact solution in this paper is validated with available data in the literature. Using numerical results the effect of opening angle of sector plate , the host thickness to radius ratios , inner to outer radius ratios , the ratio of thickness of the piezoelectric layer respect to thickness of the host plate and different boundary conditions on the natural frequencies of the vibrating sector plates coupled with piezoelectric layers are obtained. Also impact, manner and conditions of each parameter on the natural frequencies areconsidered and discussed.

The objective of this paper is representation an analytical solution to calculate sound transmission loss (TL) of infinite thick transverse-isotropic cylindrical shell immersed in a fluid medium with an uniform external airflow and contains internal fluids where external sidewall of the shell excited by an oblique plane wave. In order to derive the governing equations the third-order shear deformation theory (TSDT) is used. Also، equation of motion of shell is obtained using Hamilton''s principle. With solving shell vibration equations and acoustic wave equations simultaneously، the exact solution for TL is obtained. Transmission loss resultant from this solution is compared with those of other authors. The results also indicate that TSDT is more powerful than FSDT and CST، especially in high frequency and less R/h.

In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.

In the present research, the elastic buckling of composite cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on shear deformation theory and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately accounted for in the formulation in local coordinate system. The contributions of the work done by applied load are also incorporated. The obtained governing equations by the principle of minimum potential energy is solved through eigenvalue approach. The influence of elliptical cross-sectional parameters on the critical buckling loads of elliptical cylindrical shells is examined .Results show that changes in the elliptical cross-sectional parameters significantly change critical buckling loads of the elliptical cylindrical shells.