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1.
An accurate and efficient solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of thick laminated annular sector plates is presented. Plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. In order to accurately model the variation of material properties across the thickness, the layerwise theory is used to approximate the displacement components in this direction. Then, employing the Hamilton’s principle together with the modal analysis, through-the-thickness and circumferential discretized form of the equations of motion and the related boundary conditions are obtained. Finally, the differential quadrature method (DQM) as an efficient and accurate numerical method is applied to discretize the resulting variable coefficients differential equations in the radial direction. The fast rate of convergence of the method is demonstrated and to show its high accuracy, comparison studies with the available results in the literature are made. Finally, some new results are prepared, which can be used as benchmark solutions for future works. 相似文献
2.
Mainly, this paper deals with cylindrical laminated panels, axially compressed under the constraint of four simply-supported edges.By imposing uniform increasing end-shortening to the two opposite circular edges, characteristic equilibrium paths have been obtained in correspondence to numerical evaluations with finite element models subject to geometric non linearity. A peculiar link among different branches of the total path, each of which is connected to a proper deformed configuration, is pointed out in the axial load/end-shortening space.Convergence problems and mesh sensibility are also examined. 相似文献
3.
This research present the development of geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Geometric nonlinearity is accounted for in Von-Karman sense. A family of NURBS elements are constructed from refinement processes and validated using various examples. k-refined NURBS elements are developed to study thin plates. Isotropic, orthotropic and laminated composite plates are studied for various boundary conditions, length to thickness ratios and ply-angles. Computed center deflection is found to be in an excellent agreement with the literature. For thin plate analysis, linear and k-refined quadratic NURBS element is found to remedy the shear locking problem. k-refined quadratic NURBS element provide stabilized response to distorted, coarse meshes without increasing the order of the polynomial, owing to the increased smoothness of solution space. 相似文献
4.
Karan S. Surana 《International journal for numerical methods in engineering》1982,18(4):477-502
A geometrically nonlinear formulation using total Lagrangian approach is presented for the axisymmetric shell elements. The basic element is formulated using the co-ordinates of the mid-surface nodes and the mid-surface nodal point normals. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated. This is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the element behaviour and the accuracy. 相似文献
5.
A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration. 相似文献
6.
T. R. Mahapatra S. K. Panda V. R. Kar 《International Journal of Mechanics and Materials in Design》2016,12(2):153-171
In this article, nonlinear flexural behaviour of laminated composite doubly curved shell panel is investigated under hygro-thermo-mechanical loading by considering the degraded composite material properties through a micromechanical model. The laminated panel is modelled using higher order shear deformation mid-plane kinematics and Green–Lagrange geometric nonlinear strain displacement relations. In the present case, all the nonlinear higher order terms are included in the mathematical model to obtain the exact flexure of the structural panel. The nonlinear system governing equations are derived using variational method and discretised using the nonlinear finite element steps. Numerical results are computed through direct iterative method and validated by comparing with those published results available in open literature. Finally, wide variety of numerical examples are computed using the proposed model to address the effect of hygrothermal conditions, geometrical and material parameters and support conditions on the flexural behaviour of laminated composite doubly curved shell panel. 相似文献
7.
A new method is proposed for effective analysis of laminated plates incorporating accurate through-the-thickness distribution
of displacements, strains and stresses in the finite element formulation. It is a two-step analysis procedure. In the first
step, displacements are obtained using a post-processing procedure based on the three-dimensional stress equilibrium equations
and the thermoelasticity equations, from the results of FSDT finite element analysis. In the second step, the higher-order
through-the-thickness distribution of displacements are reflected on the subsequent finite element analysis. The effectiveness
of the present approach for the analysis of laminated plates is shown by numerical examples.
Received: 13 September 2001 / Accepted: 23 May 2002 相似文献
8.
Summary Based on the three-dimensional theory of elasticity, this paper presents the state space equation for axisymmetric deformation of a laminated transversely isotropic annular plate. The finite Hankel transform is then introduced and applied to the state space equation. Four exact solutions corresponding to four specified boundary conditions are obtained and expressions for displacements and stresses are presented. Numerical results are finally compared with those obtained by the classical plate theory, the Reissner plate theory and the finite element method. 相似文献
9.
Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: A comparative perspective 总被引:1,自引:0,他引:1
Significance of using higher-order shear deformation theory (HSDT) over the first-order shear deformation theory (FSDT) for analyzing laminated composite stiffened plates is brought out using the finite element method (FEM). For this purpose, a C0 HSDT, is extended for application to stiffened configurations, for linearly elastic static and natural vibration analysis. The spatial displacement fields of both the plate and the stiffener are derived as functions of reference plane variables using Taylor series expansion. The developed computational tool is employed for analyzing systems having varying configurations using the FSDT and two different HSDTs, and their comparative effects are systematically studied, demonstrating the need for using HSDT instead of FSDT, for obtaining accurate structural response of such stiffened configurations. 相似文献
10.
This study is concerned with bending of moderately thick rectangular laminated plates with clamped edges. The governing equations, based on Reissner first-order shear deformation plate theory; in terms of deflection and rotations of the plate include a system of three second-order, partial differential equations (PDEs). Application of extended Kantorovich method (EKM) to the system of partial differential equations reduces the governing equations to a double set of three second-order ordinary differential equations in the variables x and y. These sets of equations were then solved in an iterative manner until convergence was achieved. Normally three to four iterations are enough to get the final results with desired accuracy. It is demonstrated that, unlike other weighted residual methods, in the extended Kantorovich method initial guesses to start iterations are arbitrary and not even necessary to satisfy the boundary conditions. Results of this study also reveal that the convergence of the EKM is rapid and the method is an efficient way to solve system of PDEs of the same type. To compare the results of this study, the problem was also analyzed using commercial finite element software, ANSYS. Results show reasonably good agreement with the finite element analysis. 相似文献
11.
In this paper, an efficient method is presented for the geometrically nonlinear analysis of circulant structures. A structure is called regular if its model can be formed as the product of two subgraphs, and if one of the subgraphs is a cycle then it is termed circulant. In the present method, we deal with the eigensolution of circulant structures by simply finding the eigenvalues and eigenvectors of the blocks of the stiffness matrix rather than those of the entire structural matrix, leading to a considerable reduction in the computational time. The developed method utilizes concepts from product graphs and linear algebra for the nonlinear analysis of structures. Graph products are used to perform the eigensolution of circulant structures through those of its constituting subgraphs. Here, using the existing numerical methods, nonlinear static and dynamic analyses can be performed. In the presented method instead of solving the characteristic equation in each iteration of each step, the eigensolution of the structure is obtained using the eigensolution of the primary structure (the structure of the first iteration of the first step) together with some simple mathematical operations. In the present method instead of heavy matrix operations such as inverting a matrix and solution of the corresponding equations, one needs only to perform simple matrix multiplications and additions. The advantage of the presented method becomes more apparent when it is applied to the nonlinear analysis of a structure, where analysis should be performed many times. 相似文献
12.
《Engineering Analysis with Boundary Elements》2007,31(9):783-792
In this paper, the geometrically nonlinear analysis of cylindrical shells is carried out using the element-free kp-Ritz method. The first-order shear deformation shell theory, which can cater for both thin and relatively thick shells, is utilized in the present study. Meshfree kernel particle functions are employed to approximate the two-dimensional displacement field. The nonlinear equilibrium equations are formulated by applying the Ritz procedure to the energy functional of shells. The Newton–Raphson method and the arc length technique are used to determine the load–displacement path. To validate the accuracy and stability of this method, convergence studies based on the support size and number of nodes were performed. Comparisons were also made with the existing results available in the open literature, and good agreement is obtained. 相似文献
13.
The dynamic response of thick laminated annular sector plates with simply supported radial edges subjected to a radially distributed line load, which moves along the circumferential direction, is studied. A three-dimensional hybrid method composed of series solution, the layerwise theory and the differential quadrature method in conjunction with the finite difference method is employed. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. Additionally, as a limit case, the out-of-plane dynamic responses of circular curved beams is obtained and compared with those of an unconstrained higher order shear deformation curved beam theory, which is formulated here. Then, the effects of different parameters such as the sector angle, thickness-to-outer radius ratio, ply lay out and the load velocity on the out-of-plane response of the symmetric and antisymmetric cross-ply laminated sector plates are investigated. The results can be used as benchmark solutions for future works. 相似文献
14.
In this paper, the nonlinear behavior of symmetric and antisymmetric cross ply, thin to moderately thick, elastic rectangular laminated plates resting on nonlinear elastic foundations are studied using differential quadrature method (DQM). The first-order shear deformation theory (FSDT) in conjunction with the Green’s strain and von Karman hypothesis are assumed for modeling the nonlinear behavior. Elastic foundation is modeled as shear deformable with cubic nonlinearity. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton–Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Comparisons are made and the convergence studies are performed to show the accuracy of the results even with a few number of grid points. The effects of thickness-to-length ratio, aspect ratio, number of plies, fiber orientation and staking sequence on the nonlinear behavior of cross ply laminated plates with different boundary conditions resting on elastic foundations are studied. 相似文献
15.
Abstract A mixed finite element scheme based on assumed local high‐order displacements is proposed for the free vibration of thick laminated plates. The effects of transverse shear deformation, transverse normal stress and rotary inertia are considered in the formulation. Cross‐ply laminates with simple supports and angle‐ply laminates with clamped edges are presented as examples. The three dimensional elasticity solutions of cross‐ply laminates with simple supports are used to assess the accuracy of the present scheme. The effects of the span‐to‐thickness, aspect and material anisotropy ratio on the fundamental natural frequency are investigated. The present results are compared with the results in the published literature, and agree closely with the 3‐D elasticity solutions. 相似文献
16.
《Composites Part B》2007,38(4):437-447
Nonlinear partial differential equations of motion for a laminated plate in a general state of non-uniform initial stress are presented in various plate theories. This study uses Lo’s displacement field to derive the governing equations. The higher-order terms in Lo’s theory can be disregarded, to obtain the equations of simpler forms and even other theories for laminated plate. These nonlinear partial equations are transformed to ordinary nonlinear differential equations using the Galerkin method. The Runge–Kutta method is used to obtain the ratio of nonlinear frequency to linear frequency. The numerical solutions of an initially stressed laminate plate based on various plate theories obtained by the Galerkin and Runge–Kutta method are presented herein. Using these equations with various theories, the nonlinear vibration behavior of laminated plate is studied. The results show that apparent discrepancies exist among the various displacement fields, which indicates the transverse shear strain, normal strain and initial stress state have great effect on the vibration behavior of laminate plate under nonlinear vibration. 相似文献
17.
Abderrahim Houmat 《Acta Mechanica》2009,208(3-4):281-297
The nonlinear free vibration of a laminated composite annular elliptical plate with elliptically orthotropic plies is investigated. The effects of out-of-plane shear deformations, rotatory inertia and geometrical nonlinearity are taken into account. The problem is solved numerically using a new polynomially enriched sector elliptic p-element. The nonlinear equations of free motion are obtained using the harmonic balance method and solved iteratively by the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained. Comparison is made with published results for a polar orthotropic annular plate and shows very good agreement. The minor semi-axis ratio, thickness ratio, moduli ratio, number of plies, layup sequence, and boundary conditions are shown to influence the hardening behavior. 相似文献
18.
《Composites》1986,17(1):42-48
A computationally efficient finite element model that can provide accurate numerical solutions to the problem of rotating laminated composite annular discs is presented. Numerical results showing the effects of composite material properties and laminate designs on the stress field and deformed shape of the disc are also presented and discussed. 相似文献
19.
An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results. 相似文献
20.
Hajlaoui A. Chebbi E. Wali M. Dammak F. 《International Journal of Mechanics and Materials in Design》2020,16(2):351-366
International Journal of Mechanics and Materials in Design - This paper presents a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution... 相似文献