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...     

含分层损伤复合材料层合板非线性动力稳定性

采用Reddy 的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型, 推导了考虑几何非线性和阻尼效应的Methieu 方程, 给出了该方程的解析解表达式; 研究了参数振动解的稳定性; 然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响; 研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响, 以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知, 随着复合材料层合板分层损伤的扩大, 其动力稳定性能逐渐减弱, 特别是损伤接近层合板的中面时, 分层损伤对其动力稳定性能的影响最大。      

采用分层理论计算层合板的固有频率和振型

采用有限元方法并结合分层理论对复合材料层合板的固有频率和振型进行理论计算,再用实验验证。通过分层有限元模型求解层合板的位移模式,对层合板固有频率进行计算。分析有限元网格数,铺设角度、铺设层数等对固有频率的影响,获得层合板自由振动的前九阶振型,采用实验进行了验证。结果表明,提出的方法可较精确计算层合板的固有频率和振型。     

含多分层损伤平面编织层合板的振动特性

基于层合板Mindlin一阶剪切变形理论,研究了多处分层损伤对复合材料层合板固有特性的影响规律。根据一般分层模型,并采用线性接触模型模拟分层区域上、下子板的相互作用,建立含多个椭圆内埋型分层损伤平面编织层合板自由振动分析有限元模型。通过典型算例分析,讨论了椭圆分层区域长轴与试件纵向夹角对平面编织层合板固有频率的影响。结果表明,对于内埋型分层损伤,表面分层与中间分层对固有频率的影响区别很小;分层区域的长轴与试件纵向夹角越大,损伤对固有频率的影响越大。     

短纤维层间增韧的三维有限元分析

层间短纤维强韧化是复合材料层合板层间增韧的有效途径之一。采用三维非线性有限元方法分析了层间短纤维强韧化复合材料层合板的分层扩展问题,探讨其影响因素。以混合模式下通用裂纹扩展的能量准则作为分层扩展判据,通过虚拟裂纹闭合技术计算分层尖端能量释放率。用节点双编号和单元生死技术模拟分层扩展。采用弹簧单元模拟层间短纤维作用,通过改变弹簧刚度修正短纤维桥联力。采用GAP元处理分层区的接触非线性问题。分析了分层区桥联力对层间应力场、位移场以及分层扩展的影响。研究结果表明,层间短纤维有效延缓了分层扩展,增韧效果明显。     

具有分层损伤复合材料加筋与无加筋层合板热-机械力屈曲性态

基于复合材料一维剪切理论——Mindlin 理论, 给出了材料性质与温度有关的含分层损伤复合材料加筋和无加筋层合板的线性和非线性热-机械力耦合情况下的屈曲问题有限元分析方法, 并研究了含分层损伤的加筋和无加筋层合板的两种不同类型的热- 机械力屈曲问题。通过典型算例分析, 讨论了热-机械力耦合效应和分层大小对含分层损伤结构的屈曲性态的影响关系。     

考虑多尺度界面力学特性的损伤复合材料层合板分岔屈曲性能的等代化

提出了一种等效理论来分析含损伤碳纤维增强树脂T300/QY8911复合材料层合板的分层屈曲。针对含贯穿脱层层合板产生面外弯曲后的受力特点,引入损伤界面的接触效应,根据精确模型所给出的多尺度变形失效机制,提出了一个基于刚度等效理论来分析损伤层合板结构失效的力学性能。通过将含脱层的区域等效成一个几何形状和铺设方式完全一致,但刚度相应折减的完善子板,运用三分区模型,根据板壳理论、复合材料力学等基本原理建立各子板的屈曲控制方程,同时结合边界条件和连续性条件求解。算例分析表明,本文所得的屈曲荷载与考虑接触效应精确模型所得的解析解及ABAQUS有限元结果高度吻合。该研究方法充分考虑了脱层带来的刚度降低以及由于分层界面处非线性抗穿透约束的影响,不仅大大简化了繁琐的推导过程和节省了计算量,而且揭示了深层次的力学机制,更为主要的是,该方法可以有效推广到含多分层损伤层合板的非线性力学性能的评估,为航空航天先进复合材料的结构设计和力学分析提供有力的技术支持。      

含压电片复合材料层合板的高阶计算模型

给出了一种分析含任意内埋压电片复合材料层合板的高阶耦合模型, 板的位移场采用三阶剪切理论, 并提出了压电片中电势场在厚度方向的三次分布模式, 可以更精确地描述力、电耦合作用下电场的非均匀分布。在平面应力的假设下给出了简化的压电材料本构方程, 推导了基于该模型的压电层合板有限元计算公式, 并对双压电片梁的弯曲和层合板的变形控制进行了计算, 压电梁的弯曲计算结果与解析结果吻合良好, 表明本文的模型和公式是精确有效的。     

绝对节点坐标法中压电层合板的大变形研究

压电层合板可以通过对作动器施加电压变形为各种形态,在智能可折叠结构领域具有潜在的应用前景。理解这种结构的大变形作动机理是软体智能结构设计的基础。利用等效单层模型,基于绝对节点坐标法（ANCF）,建立了一种柔性压电层合薄板单元。引入了压电材料的本构方程来推导弹性力和压电力,建立了压电层合薄板单元的动力学方程,并对比了在大变形范围内三种曲率表达形式的收敛效果。通过与ABAQUS有限元软件求得的结果进行比较,验证了压电层合薄板单元的正确性,并给出了一些大变形算例。结果表明,在压电材料全覆盖、部分覆盖、多段覆盖等情形下,该单元均能得到较为稳定的结果,表明此单元可以与单层线弹性单元进行耦合。此外还研究了压电层合板受集中力状态下的动态响应。该研究有助于理解受智能压电材料驱动的柔性或软体结构的复杂耦合非线性力学行为。     

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。     

Analysis of delamination fatigue growth for delaminated piezoelectric elasto-plastic laminated beams under hygrothermal conditions

A nonlinear analysis model of fatigue delamination growth for piezoelectric elasto-plastic laminated beams under hygrothermal conditions is presented. Based on the incremental elasto-plastic constitutive equations, the incremental nonlinear governing equations of the piezoelectric elasto-plastic laminated beams with delamination are derived when taking into account the hygrothermal environments, transverse shear deformation, geometrical nonlinearity and piezoelectric effect. According to the elasto-plastic fracture dynamics and J-integral theory, the energy-release-rate along the delamination is obtained. Then, applying the Paris law, the delamination growth rate is obtained and the delamination growth lengths along the delamination fronts under cyclic loads are finally determined by using the cyclic skip method. The equations are solved by the finite difference method and iterative method as a whole. Effects of voltages, variation of temperature and humidity, delamination length and depth on the energy-release-rate and delamination growth length for the piezoelectric elasto-plastic laminated beams are discussed in numerical examples.     

Active constrained layer damping of geometrically nonlinear vibrations of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of sandwich plate with orthotropic laminated composite faces separated by a flexible core. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. The Golla?CHughes?CMcTavish method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory and the Von Kármán type nonlinear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element model of smart laminated composite sandwich plate integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of the plates. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the sandwich plates with laminated cross-ply and angle-ply facings for suppressing their geometrically nonlinear vibrations. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Behavior of laminated sandwich plates having interfacial imperfections by a new refined element

The static response of laminated sandwich plates having imperfections at the layer interfaces is investigated by a refined plate theory. The plate theory represents parabolic through thickness variation of transverse shear stresses, which are continuous at the layer interfaces and become zero at the plate top and bottom surfaces. In this plate model the interfacial imperfection is represented by a linear spring-layer. Moreover, with all these features of an accurate modeling, it involves unknowns only at the reference plane of the plate. To have generality in the analysis, finite element method is adopted. But any existing plate element cannot be used, as the plate theory demands certain inter-elemental continuity. Thus an attempt has also been made to develop a new triangular element. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and ordinary laminated plate with inter-laminar imperfection are used for validation.     

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.     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.     

Optimal design in vibration control of adaptive structures using a simulated annealing algorithm

Advanced reinforced composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the development of smart structures. These structures offer potential benefits in a wide range of engineering applications such as vibration and noise suppression, shape control and precision positioning. This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as sensors and actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one additional electrical potential degree of freedom for each surface bonded piezoelectric element layer or patch. The control is initialized through a previous optimization of the core of the laminated structure, in order to minimize the vibration amplitude and maximize the first natural frequency. Also the optimization of the patches position is performed to maximize the piezoelectric actuators efficiency. The simulated annealing algorithm is used for these purposes. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers or patches, and to calculate the dynamic response of the laminated structures the Newmark method is considered. The model is applied in the optimization of an illustrative adaptive laminated plate case. The influence of the position and number of piezoelectric patches, as well as the control gain, are investigated and the results are presented and discussed.     

Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a laminated composite piezoelectric rectangular plate

The global bifurcations and multi-pulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations are investigated in this paper for the first time. The formulas of the laminated composite piezoelectric rectangular plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The extended Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that multi-pulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the laminated composite piezoelectric rectangular thin plate.     

基体损伤对分层复合材料加筋板动力特性的影响研究

基于Mindlin假定的复合材料层合板单元和层合梁单元,推导了复合材料加筋板的刚度阵和质量阵;采用Adams应变能法与Rayleigh阻尼模型相结合的方法,构造了相应的阻尼阵列式;建立了分层损伤特征的三板模型和表征基体微裂纹损伤的基体损伤模型;并推导了一种基于Hertz型非线性接触法则的虚拟联接单元模型,以避免在振动分析过程中在低阶模态中分层处出现的上、下子板间不合理的嵌入现象;在上述模型和理论基础上,采用精细积分法求解含损伤结构的动力响应。对典型数例进行参数讨论,表明在动载荷作用下,嵌入分层损伤以及在振动过程中诱发的基体微裂纹损伤的演化将明显地影响加筋层合板的动力特性。     

考虑静水压力的压电弹性层合圆柱壳动力响应的控制模型

基于经典的层合板理论和Navier解法,对静水压作用下压电弹性层合圆柱壳的动力问题的主动控制进行了研究。首先由Hamilton原理导出压电弹性层合壳的非线性动力基本方程。利用压电材料的正、逆压电效应,通过闭环方式,采用速度反馈控制方法得到了任意形式动载作用下带压电感测层/激励层的简支层合圆柱壳动力响应的主动控制模型。数值算例中对于三种不同的外载条件下该控制模型对圆柱壳的动力响应的控制效果进行了研究。结果表明本文中提出的控制模型能够有效抑制动载作用下结构的振动。     

Finite element modeling of delamination by layerwise shell element allowing for interlaminar displacements

This paper presents a novel approach of modeling the delamination phenomenon experienced by laminated composite plate and shell structures by using a previously developed layerwise shell finite element in conjunction with some transformations. This layerwise element is formulated by stacking some single-layered shell elements through a transformation of displacements of the mid-surface of a layer to those on the mid-surface of the laminated composite shell structure. It can accurately model the overall displacements and interlaminar stresses of a laminated composite shell structures whose layers are perfectly (rigidly) bonded. The novelty of the present approach, however, lies in the fact that two different transformations are used so that interlaminar displacements as well as interlaminar stresses can be represented in the finite element model. The transformations allow for displacement mismatches across the normal direction of the layer interfaces (the normal mode of delamination) and between layers (the shear mode). As a result, the proposed methodology can be used to model the open and shear modes of delamination. A two-layered simply supported composite beam and a two-layered simply supported cross-ply square plate are then chosen for numerical studies. These examples demonstrate how the present approach can be applied to accurately model delamination phenomena such as shear slip and normal separation. The paper concludes with suggestions for future work.