Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, one-dimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.     

Free vibration of laminated plates using a high-order element

Free vibration analysis of laminated composite plates using the finite element method has been presented. A high-order quadratic isoparametric element has been employed in the analysis. Both the eight-node serendipity and the nine-node Lagrangian shape functions have been used and their performances have been compared. Various schemes for the generation of the mass matrix have been discussed and a comparative study of these schemes has been presented. The results from the present method have been compared with the closed form solutions and experimental observations of the previous investigators.     

Transverse shear effect on vibration of laminated plate using higher-order plate element

An approach using a higher-order plate element to include the effect of transverse shear deformation on free vibration of laminated plate is presented. The total displacement of the element is expressed as the sum of the displacement due to bending and that due to shear deformation. The double-sized stiffness and mass matrices due to the separation of bending and shear displacements are then reduced to the size as if only the total deflection was considered. Numerical results for natural frequencies for a range of different isotropic and anisotropic plates with various thickness-to-length ratios are obtained and compared with solutions available in the literature. The effect of transverse shear deformation on natural frequencies of higher modes of laminated plates is also discussed.     

Free vibration analysis of plates using least-square-based finite difference method

In this paper, we apply the two-dimensional least-square-based finite difference (LSFD) method for solving free vibration problems of isotropic, thin, arbitrarily shaped plates with simply supported and clamped edges. Using the chain rule, we show how the fourth-order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation. By analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results, we clearly demonstrate the effectiveness of LSFD as a mesh-free method for computing vibration frequencies of generally shaped plates accurately.     

Stability analysis of anisotropic laminated composite plates by finite strip method

The finite strip method has been applied to the stability analysis of rectangular shear-deformable composite laminates. However, for the plates with two opposite simply supported sides, the existing analysis was restricted to the symmetrical cross-ply laminates under compression loading.In the present study, by selecting proper displacement functions and including the coupling between different series terms, the finite strip method is extended to the stability analysis of any anisotropic laminated plates under arbitrary in-plane loading. Furthermore, a number of numerical results are presented to show the effects of thickness, fibre orientation and stacking sequence on the buckling loads.     

Post-buckling of thick symmetric laminated plates under end-shortening and normal pressure using semi-energy finite strip method

The application of the semi-energy CLPT-FSM for the non-linear analysis of symmetric laminates is extended to include the effects of normal pressure loading in addition to the end-shortening. Moreover, a new semi-energy FSM is developed based on the concept of FSDT theory in order to attempt the large deflection solution for relatively thick laminates. It is noted that for a given level of accuracy, the developed semi-energy FSM requires a markedly lower number of degrees of freedom compared to those of FEM analysis. Hence, the semi-energy FSM is more computationally efficient than the conventional energy based schemes.     

Buckling of initially stressed mindlin plates using a finite strip method

The buckling of initially stressed Mindlin plates is considered using a thick finite strip method. The method is compared with a wide variety of published results and for both thin and moderately thick plates excellent accuracy is obtained. Some further results are obtained for initially stressed rectangular plates with two opposite edges simply supported and various support conditions on the remaining sides. In general, it is found that for moderately thick plates, Mindlin's plate theory gives lower buckling loads than those obtained using classical thin plate theory.     

Free vibrations of laminated composite plates using second-order shear deformation theory

A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.     

Analysis of plates by finite strip method

New finite strips are developed for the analysis of plates. Based on Reissner's plate theory, the effect of shear deformation is included in the formulation. To eliminate artificial hardening, the shape functions for the strips are so chosen that there is no mismatched term along the interpolation functions for the interpolation parameters. Numerical examples are reported to demonstrate that the strips can work equally well in thick as well as thin plates.     

基于修正变分法开孔板和加强板结构的自由振动分析

为研究船舶开孔板和加强板结构的振动特性,用1阶剪切变形板理论描述各向同性板的位移场,并采用修正变分原理和区域分解方法建立板的离散动力学模型.每一块子域板的位移和转角分量通过第一类切比雪夫正交多项式展开.针对加强板模型,将该方法获得的结果与已经发表的文献和有限元商用软件计算结果进行对比,验证该方法的收敛性和正确性.基于修正变分法探讨多种开孔和加强板模型的自由振动特性,充分说明该数理模型和半解析方法是一种适合处理复杂板结构问题的数值工具.     

Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method

A general finite strip method of analysis is presented for the geometrically nonlinear analysis of laterally loaded, rectangular, isotropic plates. The analysis is based on the use of Mindlin plate theory and therefore includes the effects of transverse shear deformation. The nonlinearity is introduced via the strain-displacement equations and correspondingly the analysis pertains to problems involving moderate displacements but small rotations. The principle of minimum potential energy is used in the development of the strip and the complete plate stiffness equations and the latter equations are solved using the Newton-Raphson method. In numerical applications a particular type of finite strip is used in which all five reference quantities (three displacements and two rotations) are represented by cubic polynomial interpolation across the strip whilst the ends of the strip are simply supported for bending/shearing behaviour and immovable for membrane behaviour. These applications are concerned with uniformly loaded plates of both thin and moderately-thick geometry and detailed presentation is given of both displacement- and force-type quantities.     

Considerations on higher-order finite elements for multilayered plates based on a Unified Formulation

In this work, a numerical assessment of a series of multilayered finite plate elements is proposed. The finite elements are derived within the “Unified Formulation”, a technique developed by Carrera for an accurate modeling of laminates. The Unified Formulation affords an implementation-friendly possibility to derive a large number of two-dimensional, axiomatic models for plates and shells. An accurate model for multilayered components naturally involves transverse shear and normal stresses, as well as higher-order displacement assumptions in thickness direction. The aim of this work is to give a first insight of the numerical properties of finite elements relying on these formulations. Some considerations concerning the numerical difficulties associated to thickness locking phenomena are presented. A detailed numerical analysis is performed to study the shear locking phenomenon. For the selected case study, once the latter spurious stiffening effect is suppressed with classical or advanced numerical techniques, the resulting elements are shown to behave robustly and accurately.     

Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

     

采用MFC压电作动器对复合材料悬臂板振动主动控制

针对复合材料层合悬臂板,在其上表面铺设压电纤维复合材料MFC作为作动器,同时在下表面对称铺设压电薄膜(PVDF)作为传感器,应用速度反馈控制方法研究其主动振动控制.运用Hamilton原理和假设模态法推导含多个MFC作动器的复合材料层合板的力电耦合结构运动方程,其中考虑了MFC作动器作为悬臂板附加质量及刚度的影响.基于模态控制力/力矩最大化的原则,将多对MFC作动器/PVDF传感器铺设在层合悬臂板前几个低阶模态应变最大的区域,通过算例得出结构受控前后的时域和频域响应以及各MFC作动器所需的控制电压曲线.讨论复合材料层合板纤维铺设角度不同情况下,作动器MFC铺设位置及压电纤维铺设方向的相应变化.     

The free vibration of skew plates using the hierarchical finite element method

The hierarchical finite element method is used to determine the natural frequencies and modes of flat, isotropic skew plates. A number of such plates with different boundary conditions—including free edges and point supports—are considered in this paper. The dependence of frequency on skew angle, aspect ratio and Poisson's ratio is investigated, though succinctness prohibits a complete study exploring the full interrelation of these parameters. Extensive results are presented in diagrammatic, graphical, and tabular format; these are shown to be in very good agreement with the work of other investigators, and should prove a valuable source of data for use by engineers and scientists.     

Analysis of piezolaminated plates by the spline finite strip method

This paper deals with the development of a family of higher order B-spline finite strip models applied to the static and free vibration analysis of laminated plates, with arbitrary shape and lay-ups, loading and boundary conditions. The lamination scheme can be such that the embedded and/or surface bonded piezoelectric actuating and sensing layers are included. The structure is discretised in a specified number of strips, and the geometry and displacement components of each strip are represented by interpolating functions that are products of linear or cubic B-spline, and linear or quadratic Lagrange functions along the y and x orthonormal directions. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed and alternative models.     

Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method

The Natural Neighbour Radial Point Interpolation Method (NNRPIM), an improved meshless method, is used in the numerical implementation of an Unconstrained Third-Order Plate Theory applied to laminates. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoï tessellation and to the Delaunay triangulation. Within NNRPIM the obtained interpolation functions, constructed with the Radial Point Interpolators, pass through all nodes inside the influence-cell providing the interpolation functions with the delta Kronecker property. In order to prove the high accuracy and convergence rate of the proposed meshless method several well-known benchmark static and dynamic laminate examples are solved. The numerical results obtained with the NNRPIM are compared with the Unconstrained Third-Order Plate Theory exact solution, when available, and with exact solutions of other plate deformation theories.     

Three-dimensional finite strip analysis of laminated panels

In this paper, a combined finite strip and state space approach is introduced to obtain three-dimensional solutions of laminated composite plates with simply supported ends. The finite strip method is used to present in-plane displacement and stress components, while the through-thickness components are obtained by using the method of state equation. The method can replace the traditional three-dimensional finite element solutions for structures that have regular geometric plans and simple boundary conditions, where a full three-dimensional finite element analysis is very often both extravagant and unnecessary. The new method provides results that show good agreement with available benchmark problems having different material compositions, thickness and boundary conditions. The new method provides a three-dimensional solution for laminated plates, while the advantages of using the traditional finite strip method are fully taken. This solution also yields a continuous transverse stress field across material interfaces that normally is not achievable by other numerical modelling of laminates, such as the traditional finite element method.     

Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions

In this paper, we use the first-order shear deformation theory in the multiquadric radial basis function (MQRBF) procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates. The transverse deflection and two rotations of the laminate are independently approximated with the MQRBF approximation. The natural frequencies of vibration are computed for various laminated plates and compared with some available published results. Through numerical experiments, the capability and efficiency of the MQRBF method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.