板壳分析与应用

板壳分析是现代固体力学的一个重要分支。这门学科几乎与一切工程设计都有关联,对航天、航空、航海、机械、石化、建筑、水利、动力、仪表、交通等工程设计,尤其具有指导意义。现今,经典的薄板壳线性 理论已较成熟,并在各种工程设计中起着指导作用。然而,在薄板壳非线性领域和厚板壳线性领域,还有许多问题未被解决。章在介绍这门学科发展历史的基础上,概述了作近四十年结合工程实际对波纹板壳、单层板壳、双层金属旋转扁壳、网格扁壳、夹层板壳和复合材料层合板壳等六类薄板壳的非线性弯曲、稳定和振动问题以及厚、薄板壳弯曲问题进行理论探索的情况。     

橡胶隔振器大变形有限元分析

以橡胶隔振器为研究对象,基于超弹性本构模型,对拉伸、压缩、剪切状态下分别进行有限元计算,探讨橡胶等不可压缩材料大变形有限元建模技术;重点研究橡胶结构不同受载方式下变形模式及有限元分析所需要的材料试验数据。经与试验结果对比分析,得到隔振器三种状态下,填充超弹本构模型最优的材料数据类型,为橡胶结构件的数值模拟提供有益参考。     

Static and Dynamic Analysis of Laminated Thick and Thin Plates and Shells by a Very Simple Displacement-based 3-D Hexahedral Element with Over-Integration

A very simple displacement-based hexahedral 32-node element (denoted as DPH32), with over-integration in the thickness direction, is developed in this paper for static and dynamic analyses of laminated composite plates and shells. In contrast to higher-order or layer-wise higher-order plate and shell theories which are widely popularized in the current literature, the proposed method does not develop specific theories of plates and shells with postulated kinematic assumptions, but simply uses the theory of 3-D solid mechanics and the widely-available solid elements. Over-integration is used to evaluate the element stiffness matrices of laminated structures with an arbitrary number of laminae, while only one element is used in the thickness direction without increasing the number of degrees of freedom. A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity. Comprehensive numerical results are presented for static, free vibration, and transient analyses of different laminated plates and shells, which agree well with existing solutions in the published literature, or solutions of very-expensive 3D models by commercial FEM codes. It is clearly shown that the proposed methodology can accurately and efficiently predict the structural and dynamical behavior of laminated composite plates and shells in a very simple and cost-effective manner.     

基于三维等效弹性模量的复合材料中厚层合板稳定性分析

通过对复合材料层合板刚度矩阵的转换,将中厚板等效为3D各向异性板,并将得到的等效弹性模量运用到有限元模型中,对轴压载荷作用下的中厚层合板进行稳定性分析。结果表明：有限元模拟得到的屈曲载荷与工程经验公式得到的屈曲载荷相差很小,简支情况下相差5.86%,固支情况下相差6.47%。证明这种等效方法是可行的,且可以提高复合材料中厚板的三维建模效率。     

A review of meshless methods for laminated and functionally graded plates and shells

This review focuses mainly on the developments of element-free or meshless methods and their applications in the analysis of composite structures. This review is organized as follows: a brief introduction to shear deformation plate and shell theories for composite structures, covering the first-order and higher-order theories, is given in Section 2. A review of meshless methods is provided in Section 3, with main emphasis on the element-free Galerkin method and reproducing kernel particle method. The applications of meshless methods in the analysis of composite structures are discussed in Section 4, including static and dynamic analysis, free vibration, buckling, and non-linear analysis. Finally, the problems and difficulties in meshless methods and possible future research directions are addressed in Section 5.     

The geometric stiffness of thick shell triangular finite elements for large rotations

This paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is ‘upgraded’ to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

复合材料厚壁连杆的RTM工艺模拟研究

采用数值模拟方法研究了一种复合材料厚壁连杆结构的RTM工艺过程,对比了其2D,2.5D,3D模型RTM树脂流动过程。结果表明3D模型模拟结果较为直观,能较准确地体现T接头处树脂三维流动的细节。对于本文所示的厚壁连杆结构,应采用3D模型来进行数值模拟,从而确定RTM成型的注胶口、出胶口位置及其他工艺参数。     

一种分析两相材料塑性响应的唯象模型

提出了一种分析两相材料塑性响应的模型。该模型由两个简单模型组成，它可以方便地预测不同体积比的两相材料的弹性模量，应力－应变响应。本文还提出了一种求解两相材料中“相”应力－应变响应的方法，并初步得到了试验的验证。     

圆板轴对称自由振动的微分容积解法

本文用一种新型的数值方法——微分容积法求解任意边界条件下圆形中厚板的轴对称自由振动问题。通过微分容积法将中厚板轴对称自由振动的控制微分方程和边界条件离散成为一组关于各配点位移的齐次的线性代数方程，这是一典型的特征值问题，求解该特征值问题便可求得板的自振频率和振型。文中用一些数值算例研究了该方法的收敛性和数值精度，展示了该方法的可行性和有效性。     

A note on finite element implementation of sandwich shell homogenization

A finite element (FE) implementation for sandwich shell through‐thickness homogenization is presented. The homogenization is performed within the analysis constitutive procedure and is suitable for the FE analysis of sandwich shells using explicit time‐integration scheme. Copyright © 2000 John Wiley & Sons, Ltd.     

MLPG Analysis of Layered Composites with Piezoelectric and Piezomagnetic Phases

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve static and dynamic problems of two-layered magnetoelectroelastic composites with specific properties. One layer has pure piezoelectric properties and the second one is a pure piezomagnetic material. It is shown that the electric potential in the piezoelectric layer is induced by the magnetic potential in the piezomagnetic layer. The magnetoelectric effect is dependent on the ratio of the layer thicknesses. Functionally graded material properties of the piezoelectric layer and homogeneous properties of the piezomagnetic layer are considered too. The magnetoelectric composites are analyzed under a pure magnetic or combined magneto-mechanical load. Various boundary conditions and geometric parameters are considered to analyze their influence on the value of the electromagnetic parameter.     

A shell element for the prediction of residual load-carrying capacities due to delamination

This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed.     

铝基复合材料应力传递的有限元分析

本文使用大型有限元分析软件Ansys建立了短纤维增强铝基复合材料的有限元模型,模拟复合材料界面上的应力应变分布,进一步详细分析了纤维的不同参数对纤维使用效率的影响,以及不同纤维弹性模量的匹配对应力传递的影响。     

用于壳体自由振动分析的广义协调元

本文采用基于解析试函数的广义协调四边形膜单元和中厚板单元构造了平板型4节点壳体单元,并将其用于壳体振动分析。该壳体单元具有列式简单,易于编程的优点,通过数值算例表明,该单元计算精度高,非常适合工程计算     

基于有限元不同大塑性变形应变特征对比研究及组织分析

目的 探究往复挤压工艺(CEC)与往复挤扭镦工艺(SETE)的变形特点,并研究单道次变形后的金属流动行为和应变分布特征。方法 以低活化钢为材料,对CEC和SETE等2种工艺下的变形过程进行有限元模拟分析,获得3个道次变形后的CLAM钢等效应变云图,同时,开展相关试验以验证有限元模拟的准确性。结果 往复挤压工艺(CEC)与往复挤扭镦工艺(SETE)均能实现多道次累积应变,其中SETE下的单道次累积应变量更大,其各道次等效应变分别比CEC下的等效应变高2.47、5.06、7.84。0.5道次变形后,SETE下的平均硬度值比CEC下的高6.1HV。结论 在CEC与SETE下进行各道次变形后,边缘等效应变都高于心部等效应变,且1道次变形后应变均匀性相差不大,但随着道次的增加,SETE下的应变分布更加均匀。0.5道次变形后,CEC与SETE下的边缘晶粒尺寸均较心部晶粒尺寸细小,且SETE下的晶粒细化程度更高。     

确定厚壁圆筒初始屈服压力的一种实验方法

基于厚壁圆筒的弹性失效准则所确定的圆筒的初始屈服压力与材料的屈服极限的关系，设计了一种测定厚壁圆筒初始屈服压力的实验方法，并测得了一组实验数据。通过对该实验数据的分析得到了圆筒的初始屈服压力。该实验值与理论值误差较小，表明了该实验方法具有较好的可靠性。     

ZL205A大厚板铝合金TIG堆焊组织与性能研究

目的 解决壁厚25 mm的ZL205A铸造铝合金在多层多道TIG焊过程中接头易出现气孔和虚焊等问题,进而实现大厚板ZL205A的高质量焊接。方法 采用TIG堆焊方法对25 mm厚的ZL205A进行焊接,研究不同层间焊接电流对接头组织和力学性能的影响。结果 焊后接头焊核区存在明显的气孔缺陷,随层间焊接电流的增大,气孔缺陷数量和尺寸显著增加。焊接接头根据组织特征分为焊核区、熔合区、热影响区和母材区,其中焊核区晶粒尺寸最小,约为20μm,仅为母材晶粒尺寸的1/5左右。在焊核区晶界处弥散分布了大量Al₂Cu、Al Cu及少量Al₁₂CuMn₂颗粒相。随焊接电流的增大,接头拉伸强度及伸长率呈现先增大后减小的趋势,其最大拉伸强度为母材强度的94%,最大伸长率仅为母材伸长率的41.72%。在最优焊接电流下,接头拉伸断裂位置为母材处和焊缝处,气孔缺陷是导致焊缝断裂的主要原因,而母材断裂的主要原因为晶界间存在较多脆硬性AlCu/颗粒相。结论 采用TIG多层多道的焊接方法通过控制不同层间电流可以实现25mm厚ZL205A的高强度焊接。     

基于有限元仿真的板状物体的变形分析

根据线弹性薄板小挠度理论及有限元理论对板状物体的微变形情况进行了理论分析。应用有限元软件ANSYS及MATLAB对物体在四边固支和简支边界条件下受静态载荷的变形规律进行仿真分析,得到了薄板变形的挠度和应力分布,并将结果与有限元软件分析的结果进行对比,验证了有限元仿真变形分析的可行性。该研究对薄板在其他支撑条件下的受力机理分析具有一定的借鉴意义。