热载荷作用下层合板瞬态响应分析

本文研究了层合板在热载作用下的瞬态响应,推导出考虑横向剪切变形影响的运动方程,以简支的正交铺层板为例,对横向剪切的影响作了分析.     

层板弯曲与振动的近似分析

横向剪切变形对复合材料层合板弯曲与振动的影响甚大。在本文的近似分析中,假定板在弯曲时横向位移沿整个板厚为常量。横向剪切应变沿各层厚度方向也分别为常量,但各层不同。文中以特殊正交各向异性层合板为例,采用两种不同的方法建立了各层剪切应变间的关系,推演了层合板横向弯曲与振动的微分方程组及边界条件。算例表明,即使层合板的跨——厚比很小,用本文两种分析方案计算位移、应力及固有频率,都仍具有较高的精度。      

土中浅埋层合扁球壳的非线性动力响应

本文建立了考虑横向剪切影响、纤维增强对称正交铺设层合扁球壳的非线性动力方程。应用一维波阻法分析了土与结构的相互作用,对冲击波作用下土中浅埋周边弹性支承层合扁球壳的非线性动力响应问题进行了探讨。数值计算中考虑了各种材料参数及横向剪切变形对动力响应的影响。      

反对称正交铺层剪切圆柱壳在外压下的屈曲和后屈曲

给出了反对称正交铺层剪切圆柱壳广义大挠度Donnell 型方程, 并运用位移型摄动技术构造出该圆柱壳在均匀外压作用下的后屈曲渐近级数解。考虑到边界效应对中短圆柱壳的影响及边值问题摄动解的一致性, 详细研究了该圆柱壳端部边界层方程和奇异摄动解, 以便与中部正则摄动解相匹配。文中同时给出一些典型例子并讨论了横向剪切变形、Batdo rf 数、弹性模量比和初始几何缺陷对圆柱壳屈曲与后屈曲性态的影响。比较显示, 横向剪切变形对圆柱壳的屈曲与后屈曲有重要影响。      

冲击荷载作用下轴向运动层合板非线性动力学响应

研究轴向运动层合板在冲击荷载作用下的非线性动力学响应。基于单层材料本构关系及大变形理论,考虑几何非线性得到冲击荷载作用下的轴向运动层合板非线性动力学控制方程;通过Galerkin法对控制方程进行离散得到模态方程组,用Runge-Kutta法对模态方程组求解,得到冲击荷载作用下轴向运动层合板的动态响应。讨论了轴向速度、冲击波峰值和相位持续时间对轴向运动层合板动力学响应的影响。     

机电耦合载荷下的压电层合板瞬态响应分析

针对压电层合板在机电耦合激振下的瞬态响应问题, 提出一种高效混合数值计算方法。经过位移场、 电势场在厚度方向的离散, 利用机电耦合理论和哈密顿原理, 推导出结构的运动方程。引入傅里叶变换, 得到波数域内运动控制方程。应用模态分析方法求解波数域内的位移场和电势场, 对结果进行傅里叶逆变换, 得到空间域内的瞬态响应。以PZT-5A/0° PVDF铺层两相材料复合压电层合板为算例, 分析了力、 电耦合线载荷激励下, 位移场和电势场的瞬态响应历程与分布规律, 计算结果给出了该结构的动力学基本特征。该方法结合了有限元法、 傅里叶变换和模态分析法, 计算高频载荷激振下的压电层合板瞬态响应较一般有限元法大幅减少了单元的划分。该方法可推广至分析任意机电载荷下的各类铺层材料压电层合板瞬态响应问题。      

径向冲击下复合材料层合圆柱壳的动力屈曲

采用Lagrange方程导出包含横向剪切变形和转动惯量的复合材料层合圆柱壳径向脉冲屈曲控制方程;用四阶Runge-Kuta方法对方程数值求解,寻找占优屈曲模态数及对应于允许初缺陷放大值时的临界冲击速度;通过计算碳/环氧材料角铺设层合圆柱壳,讨论了横向剪切变形、壳体几何尺寸、铺层角度等因素对层合圆柱壳动力屈曲的影响.     

横向剪切及伸缩变形对层合板振动特性的影响分析

针对层合板振动特性问题,基于广义谱方法和微分求积法建立了一种适用一般边界条件和铺层方式的三维解法。验证结果表明该方法具有良好的收敛速度和计算精度。系统分析了不同边界条件和铺层方式下横向剪切及伸缩变形对层合板振动特性的影响。分析结果表明:①横向剪切变形对层合板固有频率的影响非常显著,且随厚度比增加而加剧;②横向伸缩变形对各铺层材料参数相同的层合板的固有频率影响不大,而对于各铺层材料性质差异明显的层合板,其影响非常显著,且随厚度比增加而加剧。     

基于共旋三角形厚薄通用壳元的几何非线性分析

基于共旋列式方法发展了一种用于复合材料层合板结构几何非线性分析的简单高效的三结点三角形平板壳元。该壳元由具有面内转动自由度的广义协调膜元GT9与假设剪切应变场和假设单元转角场的广义协调厚薄通用板元TMT组合而成。为避免薄膜闭锁而采用单点积分计算与薄膜应变有关的项, 同时增加一个稳定化矩阵以消除单点积分导致的零能模式。基于层合板一阶剪切变形理论, 给出了考虑层合板具体铺层顺序的修正的横向剪切刚度, 使该壳元可用于中厚层合板结构的分析。由于共旋列式大转动小应变的假设, 共旋列式内核的几何线性的单元刚阵可仅计算一次而保存下来用于整个几何非线性求解的过程以提高计算效率。数值算例表明提出的壳元进行包括复合材料层合板结构的厚薄壳结构的几何非线性分析的精度高且效率高。     

基础激励下带金属外层的多黏弹性层纤维增强层合板的动力学模型

以包含三层黏弹性材料、二层纤维增强材料和金属外层的多黏弹性层纤维增强(MVFLM)层合板为例,建立其在基础激励作用下的动力学模型.将坐标系设置在层合板结构的中心层,使用高阶剪切变形理论(考虑多个黏弹性层的剪切应变影响)和经典层合板理论分别对纤维层和金属层进行建模,进而获得MVFLM层合板的位移场函数;将基础激励等效成均...     

Accurate calculation of transverse shear stresses for soft-core sandwich laminates

Accurate evaluation of transverse stresses in soft-core sandwich laminates using the existing 2D finite element (FE) models involves cumbersome post-processing techniques. In this paper, a simple and robust method is proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in soft-core sandwich laminates by using a displacement-based C⁰ continuous 2D FE model derived from refined higher-order shear deformation theory (RHSDT) and a least square error (LSE) method. In this refined higher-order shear deformation theory (RHSDT), the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly early varying displacement field. The transverse displacement is assumed to have a quadratic variation within the core, and it remains constant in the faces beyond the core. The proposed C⁰ FE model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C¹ continuity requirement of the transverse displacements associated with the RHSDT. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus, the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for the calculation of transverse stresses in a sandwich laminates. The accuracy of the proposed method is demonstrated in the numerical examples through the comparison of the present results with those obtained from different models based on HSDT and 3D elasticity solutions.     

复合材料层合板非线性热屈曲分析

本文基于高阶变形理论和修正型Hahn-Tsai非线性本构模型,提出一种复合材料层合板非线性热屈曲分析方法.针对四边简支反对称角铺设复合材料层合板,导出了非线性热屈曲临界温度封闭解.数值结果表明:材料非线性能显著降低层合板临界温度.      

Postbuckling analysis of stiffened laminated composite panels,using a higher-order shear deformation theory

The investigation aims at: (i) constructing a modified higher-order shear deformation theory in which Kirchhoff's hypotheses are relaxed, to allow for shear deformations; (ii) validating the present 5-parameter-smeared-laminate theory by comparing the results with exact solutions; and (iii) applying the theory to a specific problem of the postbuckling behavior of a flat stiffened fiber-reinforced laminated composite plate under compression.The first part of this paper is devoted mainly to the derivation of the pertinent displacement field which obviates the need for shear correction factors. The present displacement field compares satisfactorily with the exact solutions for three layered cross-ply laminates. The distinctive feature of the present smeared laminate theory is that the through-the-thickness transverse shear stresses are calculated directly from the constitutive equations without involving any integration of the equilibrium equations.The second part of this paper demonstrates the applicability of the present modified higher-order shear deformation theory to the post-buckling analysis of stiffened laminated panels under compression. to accomplish this, the finite strip method is employed. A C ²-continuity requirement in the displacement field necessitates a modification of the conventional finite strip element technique by introducing higher-order polynomials in the direction normal to that of the stiffener axes. The finite strip formulation is validated by comparing the numerical solutions for buckling problems of the stiffened panels with some typical experimental results.     

Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading

A two-dimensional global higher-order deformation theory is presented for the free vibration and stability problems of angle-ply laminated composite and sandwich plates subjected to thermal loading. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through Hamilton’s principle. Several sets of truncated Mth order approximate theories are applied to solve the eigenvalue problems of a simply supported angle-ply multilayered plate. Natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading are obtained. Critical temperatures are obtained by increasing the temperature until the natural frequency vanishes. The effects of prebuckling displacements on the natural frequencies and critical temperatures are taken into account. Modal displacement distributions through the transverse direction of the laminates are plotted for the specific temperature parameter. Numerical results are compared with those of the published existing theories. The present global higher-order approximate theories can predict the natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading accurately within small number of unknowns.     

Curvature effects in the buckling of symmetrically-laminated rectangular plates with transverse shear deformation

It is shown that the effect of stress discontinuities from ply-to-ply must be taken into account when curvature terms are included along with shear deformation in the buckling analysis of rectangular, symmetrically-laminated plates. Such ply-stress discontinuities lead to curvature terms in the governing equations which differ considerably from those derived for homogeneous plates. Critical buckling loads are determined for orthotropic laminates subjected to biaxial inplane loading and for cylindrical bending of anisotropic plates subjected to uniaxial compression loading. Simply-supported boundary conditions are considered in conjunction with the rectangular, orthotropic laminate, while simply-supported and clamped boundaries are considered for the case of cylindrical bending of anisotropic plates. Numerical results indicate that the curvature terms have little effect on critical buckling loads for the laminates investigated. The effect of transverse shear deformation is shown to depend on the degree of boundary constraint, laminate stacking geometry, and inplane load ratio.     

冲击荷载下一端简支一端固支高桥墩的动力屈曲

考虑剪切变形和大位移的影响,建立一端简支一端固支高桥墩在冲击荷载作用下的非线性动力学基本方程式;通过位移形函数假设,采用伽辽金积分方法得到了时间变率的动力学控制方程;利用四阶Runge-Kutta法进行数值求解,得到冲击荷载作用下高桥墩的临界荷载、位移响应曲线以及各种荷载和几何参数对临界荷载的影响规律。通过数值算例比较了三角形冲击荷载和矩形冲击荷载作用下的荷载-位移幅值响应曲线;给出了矩形冲击荷载作用下,不同峰值的位移响应曲线、临界荷载随高桥墩柔度的变化曲线、不同冲击持续时间对临界荷载的影响     

Higher order shear deformation effects on analysis of laminates with piezoelectric fibre reinforced composite actuators

A complete analytical solution for cross-ply composite laminates integrated with piezoelectric fiber-reinforced composite (PFRC) actuators under bi-directional bending is presented in this paper. A higher order shear and normal deformation theory (HOSNT12) is used to analyze such hybrid or smart laminates subjected to electromechanical loading. The displacement function of the present model is approximated by employing Taylor’s series in the thickness coordinate, while the electro-static potential is assumed to be layer wise (LW) linear through the thickness of PFRC. The equations of equilibrium are obtained using principle of minimum potential energy and solution is by Navier’s technique. Transverse shear stresses are presented at the interface of PFRC actuator and laminate under the action of electrostatic potentials. Results are compared with first order shear deformation theory (FOST) and exact solution.     

Hygrothermal analysis of antisymmetric cross-ply laminates using a refined plate theory

The effect of hygrothermal conditions on the antisymmetric cross-ply laminates has been investigated using a unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions do not involve the undesirable implications of the transverse shear correction factors. The differential equations of laminated plates whose deformations are governed by either the shear deformation theories or the classical one are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. A wide variety of results is presented for the static response of simply supported rectangular plates under non-uniform sinusoidal hygrothermal/thermal loadings. The influence of material anisotropy, aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the hygrothermally induced response is studied.     

径向载荷作用下复合材料圆柱壳的非线性动力屈曲

采用半解析法求解径向阶跃载荷作用下复合材料圆柱壳的非线性动力屈曲。基于一阶剪切变形理论，由Hamilton原理推导出包含横向剪切变形以及几何初缺陷的圆柱壳的非线性动力方程，位移及载荷沿周向采用级数展开，由Galerkin方法得到微分方程组，通过有限差分法求解；根据响应情况，由B—R准则判定屈曲，确定屈曲临界载荷。     

Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.