A three-dimensional nonlinear analysis of cross-ply rectangular composite plates

The results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropie composite plates are presented. Individual laminae are assumed to be homogeneous, orthotropic and linearly elastic. A fully three-dimensional isoparametric finite element with eight nodes (i.e. linear element) and 24 degrees of freedom (three displacement components per node) is used to model the laminated plate. The finite element results of the linear analysis are found to agree very well with the exact solutions of cross-ply laminated rectangular plates under sinusiodal loading. The finite element results of the three-dimensional, geometrically nonlinear analysis are compared with those obtained by using a shear deformable, geometrically nonlinear, plate theory. It is found that the deflections predicted by the shear deformable plate theory are in fair agreement with those predicted by three-dimensional elasticity theory; however stresses were found to be not in good agreement     

Vibration and damping analysis of composite plates using finite elements with layerwise in-plane displacements

Finite element analysis is performed to study the effects of layerwise in-plane displacements on fundamental frequencies and specific damping capacity for composite laminated plates. The cross-ply and angle-ply composite laminated plates with simply-supported boundary conditions are considered. The strain energies of each stress component are computed to quantify the amount of the transverse shear deformations for thin and thick plates. The results show that the length-to-thickness ratios, cross-ply ratios, and fiber orientations have a great influence on the in-plane displacement responses. It is also shown that the layerwise in-plane displacements should be taken into account for the dynamic analysis of thick composite plate.     

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.     

An efficient facet shell element for corotational nonlinear analysis of thin and moderately thick laminated composite structures

In the present work, an efficient facet shell element for the geometrically nonlinear analysis of laminated composite structures using the corotational approach is developed. The facet element is developed by combining the discrete Kirchhoff-Mindlin triangular bending element (DKMT), and the optimal membrane triangular element (OPT). The membrane-bending coupling effect of composite laminates is incorporated in the formulation, and inconsistent stress stiffness matrix is formulated. Using corotational formulation and the proposed facet element, some example laminated composite structures with geometric nonlinearity are analyzed, and the results are compared with those found using other facet elements.     

Optimal design of hybrid laminated composite plates with dynamic and static constraints

Optimization procedures are presented that consider the static and dynamic characteristic constraints for laminated composite plates and hybrid laminated composite plates subject to a concentrated load on the center of the plate. The design variables adopted are ply angle or ply thickness. Considered constraints are deflection, natural frequency and specific damping capacity. Using a recursive linear programming method, nonlinear optimization problems are solved, and by introducing the design scaling factor, the number of iterations is reduced significantly. Relating interactive optimization procedures with the finite element method analysis, various hybrid composite plates with arbitrary boundary conditions can be designed optimally. In the optimization procedure, verification of analysis and design of the laminated composite plates are compared with a previous paper. Various design results are presented on laminated composite plates and hybrid laminated composite plates.     

Geometrically non-linear free vibrations of clamped simply supported rectangular plates. Part I: the effects of large vibration amplitudes on the fundamental mode shape

The geometrically non-linear free vibrations of thin isotropic and laminated rectangular composite plates with fully clamped edges have been successfully investigated in previous series of works using a theoretical model based on Hamilton’s principle and spectral analysis. The objective of this work is the extension of the above model to the case of clamped clamped simply supported simply supported rectangular plates, denoted by CCSSSSRP, in order to determine their fundamental non-linear mode shape, and associated amplitude-dependent resonant frequencies, and flexural stress distribution. Numerical data are given for both linear and non-linear analysis, for various plate aspect ratios and vibration amplitudes. Good agreement was found with previous published results.     

Design of laminated composite plates for optimal dynamic characteristics using a constrained global optimization technique

The lamination arrangements of moderately thick laminated composite plates for optimal dynamic characteristics are studied via a constrained multi-start global optimization technique. In the optimization process, the dynamical analysis of laminated composite plates is accomplished by utilizing a shear deformable laminated composite finite element, in which the exact expressions for determining shear correction factors were adopted and the modal damping model constructed based on an energy concept. The optimal layups of laminated composite plates with maximum fundamental frequency or modal damping are then designed by maximizing the frequency or modal damping capacity of the plate via the multi-start global optimization technique. The effects of length-to-thickness ratio, aspect ratio and number of layer groups upon the optimum fiber orientations or layer group thicknesses are investigated by means of a number of examples of the design of symmetrically laminated composite plates.     

Application of the spline finite strip to the analysis of shear-deformable plates

A spline finite strip is proposed to analyse thick isotropic or laminated composite plates. The formulation is based upon the principle of virtual work and the third-order plate theory developed by Reddy. The variational functional requires the satisfaction of C₁,-continuity of the assumed vertical deflection variable which can be easily fulfilled by the present method. The proposed spline finite strip is a conforming element with a smaller number of unknowns at each node compared to other existing elements based on the third-order theory. For the analysis of thin isotropic or laminated plates, the present element shows no sign of shear locking. A number of computational examples are given to demonstrate the efficiency and the accuracy of the present method.     

Nonlinear flexural vibrations of laminated orthotropic plates

Large amplitude free flexural vibrations of laminated orthotropic plates are studied using C⁰ shear flexible QUAD-8 plate element. The nonlinear governing equations are solved using the direct iteration technique. Numerical results are obtained for isotropic, orthotropic and cross-ply laminated plates with simply-supported boundary conditions on immovable edges. It is observed that hardening behaviour is increased for thick plates and orthotropic plates.     

Optimization formulations for the maximum nonlinear buckling load of composite structures

This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization.     

Finite element buckling analysis of stiffened plates

An isoparametric stiffened plate bending element for the buckling analysis of stiffened plates has been presented. In the present approach, the stiffener can be positioned anywhere within the plate element and need not necessarily be placed on the nodal lines. The element, being isoparametric quadratic, can readily accommodate curved boundaries, laminated materials and transverse shear deformation. The formulation is applicable to thin as well as thick plates. The buckling loads for various rectangular and skew stiffened plates with varying skew angles and stiffness parameters have been indicated. The results show good agreement with those published.     

A modified ACM element for thick plate analysis

A modified version of the ACM thin plate bending element is presented for the analysis of thick plates. The shape functions used are homogeneous solutions of Mindlin's equations plus a particular solution associated with the applied load on the element. The approximation is consistent for both thick and thin plates, enabling the element to be developed in a straightforward manner without any special techniques. The examples demonstrate the good accuracy that is achieved by the element for both static and dynamic problems.     

Nonlinear transient responses of initially stressed composite plates

The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.     

Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

Summary This paper presents a state of the art review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements. These shell elements are built up from flat triangular membranes and plates. We propose an element comprised of the constant strain triangle (CST) membrane element and the discrete Kirchhoff (DKT) plate element and describe its formulation while stressing two main issues: the derivation of the geometric stiffness matrix and the isolation of the rigid body motion from the total deformations. We further use it to solve a broad class of problems from the literature to validate its use.     

An equivalent layer sandwich panel model

An equivalent layer method for modeling sandwich panels with thin laminated composite facings and honeycomb cores is presented. It avoids the need for separate face sheet and core representations. The equivalent layer is given Mindlin plate behavior and it reproduces the face sheet midsurface strains and displacements, while matching the strain energy and work of external loads. The equivalent layer also matches the eight resultants of stress in the sandwich panel. This article starts with a derivation of the sandwich panel strain energy and the inherent bending, stretching, and transverse shearing stiffnesses. It is then shown that the available equivalent layer stiffness parameters can be used for exact matching if the sandwich has a special neutral surface. Therefore, the equivalent layer can be used for linear or geometrically nonlinear analyses for in-plane and out-of-plane loads. Examples are given illustrating two general types of sandwich panels for which exact equivalence is possible. Included are equivalent layer linear response calculations using finite element computer code ADINA.     

From periodic to chaotic oscillations in composite laminated plates

The geometrically non-linear, linear elastic, oscillations of composite laminated plates are studied in the time domain by direct numeric integration of the equations of motion. A p-version finite element, where first-order shear deformation is followed and that was recently proposed for moderately thick plates, is employed to define the mathematical model. By applying transverse harmonic forces, the variation of the oscillations with the angle of the fibres is investigated. With this kind of excitation, only periodic motions with a period equal to the one of the excitation are found. However, introducing in-plane forces, m-periodic or quasi-periodic oscillations, as well as chaotic oscillations are computed. The existence of chaos is confirmed by calculating the largest Lyapunov exponent.     

A comparison of the linear,quadratic and cubic mindlin strip elements for the analysis of thick and thin plates

The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques are used to ensure the good behaviour of the elements when dealing with thin plates. Numerical results showing the convergence and accuracy of the elements for the analysis of plates of a wide range of thicknesses are given. The general performance of the three elements is discussed in detail. In particular, the linear element with a single integration point seems to be the best value strip element for practical purposes.     

复合材料层合板非线性热振动分析

采用有限元方法研究复合材料层合板结构在线性温度场作用下非线性热振动特性．采用特征值屈曲分析方法,判断了结构在线性温度场作用下的临界屈曲分歧点,计算了结构的一阶弯曲固有频率,分析了铺层角度及铺层层数对结构临界屈曲温度分布和结构固有频率的影响,总结了其对复合材料层合板结构热振动特性影响的一般规律．这些结论对复合材料结构设计、抗热设计有一定的指导意义．