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.     

Sensor placement optimization applied to laminated composite plates under vibration

The location optimization of sensors is a essential problem in structural health monitoring systems. Taking the cost of sensors into account, it is uneconomical to install sensors on every part of a structure and moreover in aeronautical industry, the weight is a crucial factor. In this paper, a optimal placement optimization of sensor locations for structural health monitoring systems is studied. Several techniques of optimization of sensors are approached and applied in a shell structure. The structure, a laminate of carbon fiber, was modeled by the finite element method (FEM) and then subject to free vibration. Genetic algorithms (GAs) are then employed to locate the best sensor distribution to cover a specific number of low frequency modes. Numerical results have demonstrated the overall efficiency of sensor delivery methods. Specific problems occurred, especially regarding the method of effective independence, being less efficient and discrepant in relation to the other methods employed. In summary, the results obtained in this paper provide an optimal position for sensors in real SHM systems and experiments.     

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．     

Topology optimization of piezoelectric curved shell structures with active control for reducing random vibration

Structural and Multidisciplinary Optimization - This paper investigates topology optimization of the surface electrode coverage on piezoelectric sensor/actuator layers attached to a curved shell...     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A state space finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for the stress analysis of cross-ply laminated composite plates. The method is based on a mixed variational principle that includes the variations of both displacements and stresses. Finite element approximation is introduced only for the in-plane variations of displacements and stresses, while the through-thickness distributions of them are obtained by using the method of state equation. Numerical tests show that the results obtained approach the analytical three-dimensional solutions. Moreover, the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate. Compared with the traditional finite element method, the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces.     

Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm

In this paper, genetic algorithm and generalized pattern search algorithm are used for optimal stacking sequence of a composite panel, which is simply supported on four sides and is subject to biaxial in-plane compressive loads. The problem has several global optimum configurations in the vicinity of local optima. The composite plate under consideration is 64-ply laminate made of graphite/epoxy. The laminate is taken to be symmetric and balanced, comprised of two-ply stacks with discrete fiber angles of 0₂, ± 45, 90₂ in the laminate sequence. The critical buckling loads are maximized for several combinations of load case and plate aspect ratio, and are compared with published results. Performance of both algorithms is compared in terms of capability of identifying global optima. It is found that genetic algorithm is efficient for problems with global optima.     

Multilevel optimization of laminated composite structures

A two-stage optimization method aiming at the optimal design of shells and plates made of laminated composites has been developed. It is based on a mixture of sensitivity analysis, optimality criteria and mathematical programming techniques. The design variables are the optimality criteria and mathematical programming techniques. The design variables are the macro-element thicknesses and the layers' angles. Weight minimization with material efficiency maximization are the objectives with constraints on stresses and displacements. Maximization of the material efficiency is performed at one level using the conjugated method applied to the angles of the macro-element layers keeping the thicknesses constant. The other level is dedicated to weight reduction using optimality criteria and using as variables the macro-element thicknesses with the angles of the macro-element layers constant.     

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.     

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.     

Multi-pulse orbits dynamics of composite laminated piezoelectric rectangular plate

The multi-pulse orbits and chaotic dynamics of a simply supported laminated composite piezoelectric rectangular plate under combined parametric excitation and transverse excitation are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motion for the laminated composite piezoelectric rectangular plate are derived from von Karman-type equation and third-order shear deformation plate theory of Reddy...     

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.