复合材料层合圆柱壳的动力响应与层间应力

采用分层壳理论和厚度方向的二次插值函数推导出正交铺设层合圆柱壳的动力响应方程,并得出简支层合圆柱壳自由振动问题的解。对于给定算例,计算出的自振频率与三维分析的结果吻合良好,说明所推导的二维解具有足够精度。计算了前四阶模态对应的壳中应力。计算结果说明,对于高阶模态,层间应力相对于面内应力的比值远高于低阶模态的对应比值,高的层间正应力是高阶模态导致脱层破坏的主要原因。     

复合材料层合厚圆柱壳高阶理论的改进及其应用

建立了一个改进的LCW型的精化高阶理论,以分析厚圆柱壳的振动。提出u,v为三次多项式、w为二次多项式的位移模式,并利用上、下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,将三阶剪切变形理论的未知数缩减为7个,在此基础上建立了相应的有限元列式。通过一个典型算例,与Soldatos和Lam的高阶剪切变形理论的解析解作了比较,说明笔者的精化高阶理论是可行的,而且具有较高的精确性,比LCW高阶理论更具有实用性。还通过频率参数随长度半径比L/R的变化,说明由于考虑了法向应力和法向应变,本文方法更适用于长度半径比较小的结构。     

轴向极化的层合压电圆柱壳的自由振动

从轴向极化的三维圆柱型正交各向异性压电弹性力学基本方程出发,建立了状态方程。采用细分近似方法,得到了状态变量解。分析了两端简支的层合压电圆柱壳的自由振动问题,给出了频率方程的精确形式,并作了具体计算。     

充液压电阻尼圆柱壳的有限元建模

基于Mindlin板理论、压电理论、粘弹性理论和理想流体方程，对充液圆柱壳主动约束阻尼结构在流固耦合条件下的建模进行了研究。利用拉格朗日方法得到结构的动力学方程，利用GHM方法描述粘弹性阻尼的本构关系，结合流体方程建立主动约束阻尼结构在流固耦合条件下的动力学方程。建立从压电材料的电压到流固耦合边界下的圆柱壳结构振动的频响函数，利用实验结果对理论计算加以验证，结果表明该建模方法是可行的。     

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.     

基于广义混合有限元的压电复合材料层合板的数值分析

将纯弹性体的广义混合有限元法引入到压电材料的静力学分析中。由于采用了8节点六面体非协调实体单元对整体结构进行离散求解,摒弃了板壳理论中的诸多人为假设。非协调项的加入使该方法比同类协调元显示出更好的数值性能。本文方法将应力边界条件和位移边界条件同时考虑,并且求解过程中将层间应力和平面内应力分开处理,按每层的本构关系求解平面内应力,这样求得的层间应力和平面内应力都更加接近精确解。通过几个有代表性的层合板的数值算例说明了本文方法的精度,相较于传统的解析法和数值法,本文方法在适用性和有效性方面都具有优势。     

基于三维有限元法的层合圆柱壳应力分析

针对空间结构中常见的蜂窝夹芯壳体提出了一种32节点相对自由度三层壳元,以及一种精确计算层间应力的后处理方案。这种32节点壳元可以更好地反映结构固有的特性,易与三维实体单元相连接,使变厚度、带有补强的蜂窝夹芯复合材料壳体等复杂结构问题得以正确建模。本文作者的后处理方案克服了位移有限元层间应力不连续的缺点,保证了应力精确满足边界条件。综合运用以上方法的典型算例表明:计算精度是令人满意的。     

基于混合分层理论的粘弹层合圆柱壳的阻尼振动和层间应力研究

应用混合分层理论,并在壳厚方向采用位移和应力插值函数推导出粘弹层合圆柱壳的动力学方程。计算了两层粘弹层合圆柱壳的振动频率和结构损耗因子,与Okazaki A的结果吻合良好。针对不同模量和厚度的粘弹性材料,计算出层合圆柱壳的层间横向应力的幅值。结果表明:过大的层间法向正应力是导致自由阻尼层合壳脱层破坏的主要因素,采用环向加强的粘弹性材料将有效地降低层间法向正应力的幅值。     

基于一阶剪切变形理论的新型复合材料层合板单元

基于一阶剪切变形理论(FSDT),本文构造一种新型的20自由度(每结点5个自由度),四边形复合材料层合板单元,适合于任意铺设情形的层合板的计算。它是按如下方式构造的:(1) 单元每边的转角和剪应变由Timoshenko层合厚梁理论来确定;(2) 对单元域内的转角场和剪应变场进行合理的插值;(3) 引入平面内双线性位移场来体现层合板面内与弯曲的耦合作用。本文单元,记为TMQ20,不存在剪切闭锁现象,在计算单层的各向同性板时可以退化为文[1]中优质的中厚板单元TMQ。在文[2]中将给出本文单元对于层合板问题的详细数值算例。     

MT300/KH420碳纤维/聚酰亚胺树脂复合材料层合圆柱壳高温承载性能

基于Donnell-Mushtali近似理论及热弹性理论,考虑结构热变形和材料高温性能衰减等温度影响因素,对MT300/KH420碳纤维/聚酰亚胺树脂复合材料圆柱壳在常温、420℃及周向210～420℃不均匀温度场等热载工况下的承载性能进行了理论分析.并引入一阶屈曲模态缺陷作为几何初始扰动,利用ABAQUS,采用非线性...     

Finite element buckling analysis of rotationally periodic laminated composite shells

A finite element (FE) buckling analysis of rotationally periodic laminated composite shells is performed in this paper. Because the buckling mode of such structures is characterized as rotationally periodic, a corresponding FE buckling analysis scheme is proposed to reduce the computational expenses. Moreover, a new kind of relative degrees‐of‐freedom element is developed, which can be connected to other solid elements with ease and can yield satisfactory results with a relatively coarse FE mesh. Numerical results of two laminated cylindrical shells subjected to lateral pressure are compared with theoretical ones. The good agreement of them shows the validity of this new computational strategy. Finally, a practical structure is analysed to demonstrate the advantage of this method. Copyright © 2001 John Wiley & Sons, Ltd.     

A four‐noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory

A new bilinear four‐noded quadrilateral element (called quadrilateral linear refined zigzag) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20‐noded hexahedral elements. Copyright © 2013 John Wiley & Sons, Ltd.     

Non-linear coupled multi-field mechanics and finite element for active multi-stable thermal piezoelectric shells

In this paper, a coupled multi-field mechanics framework is presented for analyzing the non-linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations in thermal environments. The mechanics incorporate coupling between mechanical, electric and thermal fields and encompass geometric non-linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear coordinates and are combined with the kinematic assumptions of a mixed-field shear-layerwise shell laminate theory. A finite element methodology and an eight-node coupled non-linear shell element are developed. The discrete coupled non-linear equations of motion are linearized and solved, using an extended cylindrical arc-length method together with a Newton–Raphson technique, to enable robust numerical predictions of non-linear active shells transitioning between multiple stable equilibrium paths. Validation and evaluation cases on laminated cylindrical strips and cylindrical panels demonstrate the accuracy of the method and its robust capability to predict non-linear response under thermal and piezoelectric actuator loads. Moreover, the results illustrate the capability of the method to model piezoelectric shells undergoing large shape changes by actively jumping between stable equilibrium states and quantify the strong relationship between shell curvature, applied electric potential, applied temperature differential and induced shape change. Copyright © 2008 John Wiley & Sons, Ltd.     

A coupled FEM-MFS method for the vibro-acoustic simulation of laminated poro-elastic shells

A new simulation method for the vibro-acoustic simulation of poro-elastic shells is presented. The proposed methods can be used to investigate arbitrary curved layered panels, as well as their interaction with the surrounding air. We employ a high-order finite element method (FEM) for the discretization of the shell structure. We assume that the shell geometry is given parametrically or implicitly. For both cases the exact geometry is used in the simulation. In order to discretize the fluid surrounding the structure, a variational variant of the method of fundamental solutions (MFS) is developed. Thus, the meshing of the fluid domain can be avoided and in the case of unbounded domains the Sommerfeld radiation condition is fulfilled. In order to simulate coupled fluid-structure interaction problems, the FEM and the MFS are combined to a coupled method. The implementation of the uncoupled FEM for the shell and the uncoupled MFS is verified against numerical examples based on the method of manufactured solutions. For the verification of the coupled method an example with a known exact solution is considered. In order to show the potential of the method sound transmission from cavities to exterior half-spaces is simulated.     

A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells

In this study a higher‐order shell theory is proposed for arbitrary shell geometries which allows the cross‐section to rotate with respect to the middle surface and to warp into a non‐planar surface. This new kinematic assumption satisfies the shear‐free surface boundary condition (BC) automatically. A new internal force expression is obtained based on this kinematic assumption. A new functional for arbitrary shell geometries is obtained employing Gâteaux differential method. During this variational process the BC is constructed and introduced to the functional in a systematic way. Two different mixed elements PRSH52 and CRSH52 are derived for parabolic and circular cylindrical shells, respectively, using the new functional. The element does not suffer from shear locking. The excellent performance of the new elements is verified by applying the method to some test problems. Copyright © 2000 John Wiley & Sons, Ltd.     

含裂纹压电材料的Cell-Based光滑扩展有限元法

为精确而有效地求解机电耦合作用下含裂纹压电材料的断裂参数,首先,通过将复势函数法、扩展有限元法和光滑梯度技术引入到含裂纹压电材料的断裂机理问题中,提出了含裂纹压电材料的Cell-Based光滑扩展有限元法;然后,对含中心裂纹的压电材料强度因子进行了模拟,并将模拟结果与扩展有限元法和有限元法的计算结果进行了对比。数值算例结果表明:Cell-Based光滑扩展有限元法兼具扩展有限元法和光滑有限元法的特点,不仅单元网格与裂纹面相互独立,且裂尖处单元不需精密划分,与此同时,Cell-Based光滑扩展有限元法还具有形函数简单且不需求导、对网格质量要求低且求解精度高等优点。所得结论表明Cell-Based光滑扩展有限元法是压电材料断裂分析的有效数值方法。      

A nine-node assumed strain finite element for large-deformation analysis of laminated shells

An application of the element-based Lagrangian formulation is described for large-deformation analysis of both single-layered and laminated shells. Natural co-ordinate-based stresses, strains and constitutive equations are used throughout the formulation of the present shell element which offers significant implementation advantages compared with the traditional Lagrangian formulation. In order to avoid locking phenomena, an assumed strain method has been employed with judicious selection of the sampling points. Three strictly successive finite rotations are used to represent the current orientation of the shell normal. The equivalent natural constitutive equation is derived using an explicit transformation scheme to consider the multi-layer effect of laminated structures. The arc-length control method is used to trace complex load-displacement paths. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. © 1998 John Wiley & Sons, Ltd.     

Non‐linear random response of laminated composite shallow shells using finite element modal method

This paper investigates the large‐amplitude multi‐mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non‐linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees‐of‐freedom (DOF) are transformed into modal co‐ordinates, and the non‐linear stiffness matrices are transformed into non‐linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap‐through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap‐through between the two BEPs, and (iii) non‐linear large‐amplitude random vibration over the two BEPs, can be predicted. Copyright © 2006 John Wiley & Sons, Ltd.     

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in‐plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one‐dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in‐plane matrix cracks combined with the extend FEM. Copyright © 2014 John Wiley & Sons, Ltd.