A layer-wise triangle for analysis of laminated composite plates and shells

The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of different laminate plate and shell structures.     

Free vibrations and stability analysis of laminated composite plates and shells with hybrid/mixed formulation

Modern theory for applications of laminated plates and shells calls for detailed study of the effect of large spatial rotations on the geometric stiffness for stability analysis as well as inertia operators for vibrations. These two issues are carefully examined here in conjunction with the recently developed mixed finite element formulation for plates and shells with low-order displacement/strain interpolations. An extensive set of stability and vibration problems has been solved to demonstrate the effectiveness and general utilities of the formulation described for laminated plate and shells with arbitrary geometry.     

A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates

In view of the increasing interest in using composite materials for aerospace structures, the analysis of laminated composite plates becomes essential. A three-dimensional eight-node hybrid stress finite element method is developed for the analysis of laminated plates. The hybrid stress model is based on the modified complementary energy principle and takes into account the transverse shear deformation effects. The displacement field is interpolated through shape functions and nodal displacements. All three displacement components are assumed to vary linearly through the thickness of each lamina. The stress field is interpolated through assumed stress polynomials with 55 stress parameters for each lamina. All six stresses are included and satisfy the homogeneous equilibrium equations. The validity of the hybrid stress finite element model is determined by comparing the predicted numerical results with the existing three-dimensional elasticity solutions. Excellent accuracy and fast convergence are observed in the numerical results.     

复合材料悬臂外伸板的非线性动力学建模及数值研究

研究了横向气动载荷和参数激励联合作用下复合材料悬臂外伸矩形板在伸出过程中的非线性动力学问题.根据Reddy的高阶剪切层合板理论,应用Hamilton原理建立了外伸板在横向气动力和参数激励作用下的非线性动力学方程,其中横向气动力采用一阶活塞气动力.然后应用Galerkin方法对系统偏微分形式的非线性方程进行离散,得到了一组时变系数的非线性动力学方程.在此方程的基础上,对复合材料悬臂外伸板进行了数值模拟分析,讨论了外伸速度对悬臂外伸板非线性动力学特性的影响.     

压电纤维复合材料层合壳的非线性动力学研究

本文对横向激励作用下的1-3型压电纤维复合材料层合壳进行了非线性动力学分析,并研究了压电特性对结构振动响应的影响.首先建立了压电纤维复合材料层合壳的非线性动力学方程,并且在已知的几何结构和材料特性基础上考虑了电场属性.然后根据位移边界条件,选择合适的振型函数,通过Galerkin方法将运动控制方程转化成两自由度的非线性常微分方程.通过数值模拟方法分析了横向激励和压电系数对压电纤维复合材料层合壳非线性振动特性的影响.通过波形图、三维相图、庞加莱图和分叉图等来研究壳体不同类型的周期和混沌运动.结果表明,外激励作用下结构存在复杂的非线性振动响应,同时压电参数对层合壳结构振动响应具有很强的调节作用.     

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．     

Free material optimization for laminated plates and shells

Free Material Optimization (FMO) is a powerful approach for conceptual optimal design of composite structures. The design variable in FMO is the entire elastic material tensor which is allowed to vary almost freely over the design domain. The imposed requirements on the tensor are that it is symmetric and positive semidefinite. Most of today’s studies on FMO focus on models for two- and three-dimensional structures. The objective of this article is to extend existing FMO models and methods to laminated plate and shell structures, which are used in many engineering applications. In FMO, the resulting optimization problem is generally a non convex semidefinite program with many matrix inequalities which requires special-purpose optimization methods. The FMO problems are efficiently solved by a primal-dual interior point method developed and implemented by the authors. The quality of the proposed FMO models and the method are supported by several large-scale numerical experiments.     

A boundary element analysis of symmetric laminated composite shallow shells

This paper presents a boundary element formulation for the analysis of symmetric laminated composite shallow shells where only the boundary is discretized. Classical plate bending and plane elasticity formulations are coupled and effects of curvature are treated as body forces. Fundamental solutions for elastostatic formulations are used and body forces are written as a sum of approximation functions multiplied by unknown coefficients. Two approximation functions are used. Domain integrals which arise in the formulation are transformed into boundary integrals by the radial integration method. Results for the approximation functions are compared and the accuracy of the proposed formulation is assessed by results from literature. It was shown that results obtained with the approximation function called augmented thin plate spline present very good agreement with literature even for shells that are not so shallow.     

Bending analysis of composite laminated plates using a partially hybrid stress element with interlaminar continuity

A partially hybrid stress element for modelling composite laminated plates is developed based on the state space in which only the displacement components and the transverse stress components are assumed to be independent. This formulation satisfies exactly the interlaminar continuity requirements and the surface traction free conditions. It also combines the advantages of both the conventional displacement elements and the fully hybrid stress elements. Numerical examples are illustrated to investigate the accuracy, convergence and shear locking sensitivity of the present method. The nonlinear distributions of the normal and transverse stresses along the thickness direction are also especially studied.     

Region-by-region modeling of laminated composite plates

Several plate models have been proposed in the literature for the analysis of laminated plates. These are based either on an equivalent through-thickness formulation or a layerwise formulation. It is shown in the literature that while the equivalent models are economical, the layerwise models are expensive but are also more accurate, especially with respect to the transverse stresses. Generally, the same model is used throughout the domain. The current study addresses the issue of economical and accurate computation of local stresses, strains and displacements (as well as global quantities) using combinations of layerwise, equivalent or intermediate models in various regions of the domain. A region-by-region modeling strategy is presented for a chosen general family of equivalent, intermediate and layerwise models. The proposed strategy allows the user to put any model (of any order in the thickness direction) in any desired region of interest. The effectiveness of the strategy is demonstrated through numerical examples. It is shown that this approach can significantly reduce computational cost and can also lead to good resolution of the local stress and displacement fields for domains with unsymmetric laminae, cut-outs, local damage, corner edges, sudden transition of boundary conditions and material.     

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigen mode of the panel.In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths.The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.     

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.     

Dynamic stability of rectangular laminated composite plates

The dynamic stability of rectangular layered plates due to periodic in-plane load is studied in this paper. Using the finite strip method, the problem is reduced to that of one with finite degrees of freedom. Then following Bolotin's procedure, the regions of parametric instability have been determined. The influence of plate configuration, aspect ratio and static in-plane force have been studied.     

Optimum weight design of composite laminated plates

Optimum designs for the minimum weight of composite laminated plates subjected to size, displacement, buckling and natural frequency constraints are investigated by a technique of combining finite element method and mathematical programming, in which the structural analysis is based on the YNS theory. The recurrence relation based on the feasible direction method (FDM) and the scaling step is used to modify the design variables (ply-thicknesses and ply-orientations) during the iterative procedure. Grouping technique is engaged in the procedure in order that the number of design variables can be greatly reduced to make the problem more practical. Illustrative examples are given to show that the present technique is quite efficient and reliable.     

Interlaminar stress analysis for laminated plates containing a curvilinear hole

This study presents a variational-perturbation approach for the three-dimensional stress analysis around a curvilinear cutout in composite laminates. The solution is based on a composite expansion and assumed stress finite element methods. Stress field solutions for angleply and cross-ply laminates containing an elliptical hole have been presented. The effects of the ellipse aspect ratio and the fiber orientation on the interlaminar shear stress magnitude have been investigated. A failure criterion based on the interlaminar distortional energy function has been suggested. According to this criterion, it was found that, for angle-ply laminates containing an elliptical hole, a delamination failure initiation occurs at a point along the perpendicular to the direction of loading.     

Hybrid-interface element for thick laminated composite plates

A novel 27-node three-dimensional hexahedral hybrid-interface finite element (FE) model has been presented to analyze laminated composite plates and sandwich plates using the minimum potential energy principle. Fundamental elasticity relationship between components of stress, strain and displacement fields are maintained throughout the elastic continuum as the transverse stress components have been invoked as nodal degrees of freedom. Continuity of the transverse stresses at lamina interface has been maintained. Each lamina is modeled by using hybrid-interface elements at the top and the bottom interfaces and conventional displacement based elements sandwiched between these interfaces. Results obtained from the present formulation have found to be in excellent agreement with the elasticity solutions for thin and thick composite cross-ply, angle-ply laminates, as well as sandwich plates. Additional results have also been presented on the variation of the transverse strains to highlight magnitude of discontinuity in these quantities due to difference in properties of face and core materials of sandwich plates. Present formulation can be used effectively to interface hybrid formulation that uses transverse stresses and displacements as degrees of freedom with conventional purely displacement based formulation for realistic estimates of the transverse stresses.     

Mixed isoparametric finite element models of laminated composite shells

Mixed shear-flexible isoparametric elements are presented for the stress and free vibration analysis of laminated composite shallow shells. Both triangular and quadrilateral elements are considered. The “generalized” element stiffness, consistent mass, and consistent load coefficients are obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Group-theoretic techniques are used in conjunction with computerized symbolic integration to obtain analytic expressions for the stiffness, mass and load coefficients. A procedure is outlined for efficiently handling the resulting system of algebraic equations.The accuracy of the mixed isoparametric elements developed is demonstrated by means of numerical examples, and their advantages over commonly used displacement elements are discussed.     

Application of natural approach to non-linear analysis of sandwich and composite plates and shells

The natural approach is used to construct a curved triangular shell element for analysis of sandwich and composite shells. The shells can be either symmetric or unsymmetric and the in-plane shear relation can be linear or non-linear. The attention is centered on the transverse shear treatment, the local rigid movement representation and the development of the geometrical stiffness matrix.     

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.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.