Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections

For the stiffened composite laminated plates with interfacial imperfections, the problem of static response and sensitivity analysis was investigated in Hamilton system. Firstly, the meshfree formulation of Hamilton canonical equation for the composite laminated plate with interfacial imperfections was deduced by the linear spring-layer and the state-vector equation theory. And then, based on the equation of plates and stiffeners, governing equation of the composite stiffened laminated plate was assembled by using the spring-layer model again to ensure the compatibility of stresses and the discontinuity of displacements at the interface between plate and stiffeners. At last, a three-dimensional hybrid governing equation was developed for the static response analysis and sensitivity analysis.     

压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程。给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的。这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析。变分原理将有利于压电材料问题相应的半解析法或有限元法的推导。     

Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

A partial mixed finite element (FE)–state space method (SSM) semi-analytical approach is presented for the static analysis of piezoelectric smart laminate composite and functionally graded material (FGM) plates. Hence, using the Hamiltonian formalism, the three-dimensional piezoelectricity equations are first worked so that a partial mixed variational formulation, which retains the translational displacements, electric potential, transverse stresses, and transverse electric displacement as primary variables, is obtained; this allows, in particular, straightforward fulfillment of the electromechanical continuity constraints at the laminate interfaces. After an in-plane FE discretization only, the problem is first reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved using the symplectic approach; then, the multilayer solution is reached via the SSM propagator matrix. The proposed methodology is finally applied to the static analysis of piezoelectric-cross-ply hybrid laminated composite and FGM plates. In a comparison with open literature, available tabulated results show good agreements, thus validating the proposed approach.     

Development of a strength model for the cocured stepped lap joints under tensile loading

The cocured stepped lap joints for composite structures were manufactured and tested under static and fatigue tensile loads. From the tests, it was found that the joints were shear-failed at the joining interfaces. As the length of the stepped lap of the joint increased, the average static tensile strength of the joint increased, while the average static shear strength decreased in proportion to the length of the stepped lap of the joint. The fatigue endurance limit was found to be 30–40% of the static strength.

Also, the cocured stepped lap joints were manufactured by curing plies laid-up on the composite plates which had machined stepped laps. The static strength of the joints manufactured by the latter method was found to be 70–80% of the static strength of the joints manufactured without machining and the fatigue endurance limit was found to be about 25% of the static strength.     

四边简支压电层合板灵敏度分析的精确解

为了应用弹性力学中的Hamilton 正则方程研究压电材料的灵敏度系数问题,基于压电材料的H-R(Hellinger-Reissner) 变分原理,简要地导出Hamilton正则方程算子表达式,建立了四边简支板静力学控制方程。根据灵敏度定义,在静力学控制方程的基础上联立灵敏度控制方程,得到了增维的齐次压电材料静力响应和灵敏度系数混合控制方程。应用该方程可以同时求得压电层合板的力学、电学参量及其灵敏度。该算法过程简单、运算效率和稳定性好。数值算例结果与有限差分法的结果比较表明本文方法切实有效。      

Hamilton体系下含弱粘接复合材料层合板的无网格求解方法

该文结合径向基点插值函数、弹簧层模型和弹性材料修正后的H-R（Hellinger-Reissner）变分原理,推导了含弱粘接复合材料层合板控制方程的无网格列式。利用典型径向基函数Multiquadric（MQ）,计算了含弱粘接复合材料层合板的应力与位移。通过与精确法的对比,证明了控制方程无网格列式的正确性,并研究了弱粘...     

Hamilton体系下复合材料层合板特征值灵敏度分析研究

在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固支复合材料层合板前四阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明了该文所提出方法的可靠性。另外,该方法能够方便地拓展到复杂层合板壳结构以及智能材料层合板特征值灵敏度系数的求解问题中去。     

Nonlinear static response of laminated composite plates by discrete singular convolution method

In this paper, large deflection analysis of laminated composite plates is analysed. Nonlinear governing equation for bending based on first-order shear deformation theory (FSDT) in the von Karman sense is presented. These equations have been solved by the method of discrete singular convolution (DSC). Regularized Shannon’s delta (RSD) kernel and Lagrange delta sequence (LDS) kernel are selected as singular convolution to illustrate the present algorithm. The effects of plate aspect ratio, fiber orientation, boundary conditions, thickness-to-side ratio, and applied load on the nonlinear static response of the laminated plate are investigated.     

Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections

An exact three-dimensional (3D) piezothermoelasticity solution is presented for static, free vibration and steady state harmonic response of simply supported cross-ply piezoelectric (hybrid) laminated rectangular plates with interlaminar bonding imperfections. The bonding imperfection is modeled by considering the jump in the displacements, electric potential and temperature across the non-rigid interface proportional, respectively, to the associated tractions, transverse electric displacement and heat flux. The solution includes the case when electric potentials are prescribed at the interfaces for effective actuation. Numerical results are presented for hybrid composite and sandwich plates with varying imperfection compliance. The effect of location of imperfect bonding on the response is investigated for mechanical, electric potential and thermal load cases. The effect of weak bonding at elastic–piezoelectric interface on the actuation authority of the piezoelectric layer is also investigated. These results would serve as benchmark for assessing 2D plate theories incorporating interlaminar bonding imperfections.     

Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches

In this paper, nonlinear dynamic response of rectangular laminated composite plate resting on nonlinear Pasternak type elastic foundations is investigated. First-order shear deformation theory (FSDT) is used for modeling of moderately thick plates. The plate formulation is based on the von Karman nonlinear equation. The resulting nonlinear governing equations for transient analysis of laminated plates on elastic foundation are integrated using the discrete singular convolution-differential quadrature coupled approaches. The nonlinear governing equations of motion of plate are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the foundation parameters, boundary conditions and geometric parameters of plates on nonlinear dynamic response of laminated thick plates are investigated.     

压电作动器对热变形层合板形状修复研究

基于一阶剪切效应Mindlin板理论,建立了在热载下含分布式压电作动器的复合材料层合板有限元分析模型和控制方程,分别研究了该板在内外表面存在温差的情况下的热变形,以及使用压电作动器对热变形区域进行形状修复的问题;在分析中考虑了压电作动器与复合材料层合板间含有胶接层的影响。由典型算例结果讨论,得到如下结论:1)使用压电作动器可以有效地对复合材料层合板的表面热变形形状进行修复;2)压电作动器的分布位置对修复效果影响很大;3)在电压达到一定数值后,继续增加电压值对修复效果贡献很小。     

Analysis of tapered (in steps) laminated plates under uniform inplane load

A quasi three-dimensional isoparametric finite element has been developed for the linear elastic static stress analysis of variable thickness (stepped) laminated plates of infinite width subjected to a uniform inplane load. Numerical results are given for a single step plate with various arrangements for the ply fibre directions. Very high peak stresses are predicted in the corner region of the step, but these are reduced when a resin fillet is included in the theoretical model for the stepped region.     

Transverse vibration of symmetrically laminated rectangular composite plates

A general numerical method for estimation of the vibrational response of symmetrically laminated rectangular composite plates is presented. This is based on the Rayleigh-Ritz method using the admissible 2-D orthogonal polynomials to derive the governing eigenvalue equation. The natural frequencies and mode shapes for the laminated plates are obtained by solving this governing eigenvalue equation. Several test problems are solved to demonstrate the accuracy and flexibility of the proposed method. The present results, where possible, are verified with those available values from the literature. The effects of the material, number of layers and fibre orientation upon the frequencies and mode shapes are discussed. This study may provide valuable information for researchers and engineers in design applications.     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。     

Non-linear bending analysis of laminated sector plates using Generalized Differential Quadrature

Non-linear static analysis of laminated sector plates with any combination of clamped, simply supported and free edges is presented using Generalized Differential Quadrature (GDQ) method. Particular interest of this study is large deformation of asymmetric sector plates with free edges. Based on the first-order shear deformation theory and von Kármán type non-linearity, the governing system of equations include a system of 13 partial differential equations (PDEs) in terms of unknown displacements, forces and moments. Successive application of the GDQ technique to the governing equations resulted in a system of non-linear algebraic equations. The Newton–Raphson iterative scheme is then employed to solve the system of non-linear equations. Illustrative examples are presented to demonstrate accuracy and rapid convergences of the method with small number of grid points. Predictions of the presented method show very good agreement with other numerical studies available in the literature. Further results for asymmetric laminated sector plates with free edges are also presented for future references.     

Impact analysis of laminated composite plates and shells by super finite elements

A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.     

A semi-analytical finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for laminated composite plates. The method is based on a mixed variational principle that involves both displacements and stresses. Finite element meshes are only used in the plane of plate, while the through thickness distributions of displacements and stresses are obtained using the method of state equations. Numerical results show that the rate of convergence of the new method is fast and the solutions can be very close to corresponding exact three-dimensional ones. The use of a recursive formulation of the state equations leads to an algebra equation system, from which solution are sought, whose dimension is independent of the numbers of layers of the plate considered.     

Nonlinear static analysis of composite laminated plates with evolving damage

Considering geometric nonlinearity and damage evolution, the static response characteristics of laminated composite plates subjected to uniformly distributed loading are investigated using finite element approach based on the first-order shear deformation theory. The damage evolution is modeled employing generalized macroscopic continuum theory within the framework of irreversible thermodynamics. The governing nonlinear equations are solved using Newton–Raphson iterative technique. The resulting finite element-based continuum damage model enables to predict the progressive damage and failure load. A detailed parametric study is carried out to investigate the influences of damage evolution, boundary conditions, span-to-thickness ratio, and lamination scheme on the static response of laminated plates undergoing moderately large deformation. It is revealed that the in-plane stretching forces owing to geometric nonlinearity significantly influence the failure load, damage, and stress distribution for immovable thin laminates.     

Nonlinear flexural analysis of laminated composite plates using RBF based meshless method

The paper presents the nonlinear flexural response of laminated composite plates. The mathematical formulation of the actual physical problem of the laminated composite plate subjected to mechanical loading is presented utilizing higher order shear deformation theory and von-Karman nonlinear kinematics. These nonlinear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. A meshfree technique based on multiquadric RBFs is used for analysis of the problems. Isotropic, orthotropic and laminated composite plates with immovable simply supported and clamped edges are analyzed.     

Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory

A consistent formulation for the bending of cross-ply laminated composite plates that possess non-homogeneous elastic properties is presented. Based on a third-order shear deformation plate theory, the governing equations are obtained using the principle of virtual work. With the help of the small parameter method, a wide variety of results are presented for the symmetric and antisymmetric analysis of non-homogeneous rectangular laminated plates. The influence of non-homogeneity, lamination schemes, aspect ratio and material anisotropy on the deflections and stresses is investigated. The new results for non-homogeneous response of composite plates should serve as bench marks for future comparisons.