板壳概率变分原理

本文建立了薄板、薄扁壳及考虑剪切变形板壳的概率变分原理及概率广义变分原理,它们是建立概率有限元法、概率有限条法及各种概率样条函数方法的理论基础。     

板壳非线性分析的新理论新方法

提出了板壳非线性分析的新理论新方法。首先建立了下列几个新的本构关系:塑性应变向量增量与总应变向量增量的新关系,热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系,粘塑性应变向量增量与总应变向量增量的新关系,热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系。这些关系分别称为弹塑性应变增量理论、热弹塑性应变增量理论、弹粘塑性应变增量理论及热弹粘塑性应变增量理论,避开了屈服曲面、加载曲面、流动法则及复杂的非线性应力应变关系。其次建立了非线性样条无网格法,这种方法是以新的本构关系、几何非线性理论、变分原理、广义变分原理、加权残数法及样条离散化为基础建立的,避免了经典本构关系及有限元法带来的巨大困难及缺陷,不仅计算简便,而且精度高,收敛速度很快。建立了板壳非线性分析的统一格式,对板壳的几何非线性分析、材料非线性分析及双重非线性分析都适用。     

工程中板壳结构的一种实用计算方法

本文采用—维B3样条插值─—半离散法，建立了正交各向异性板壳结构位移和内力的统一计算式。编制的程序适用于两对这简支另两对边任意支承的正交各向异性矩形双曲扁壳、圆柱形扁壳和板；适用于集中、均布、线性荷载或其组合。算例表明该方法能有效地解决板壳的计算。     

层合板壳稳定问题的样条函数解法

本文用样条最小二乘法求解任意铺层复合材料曲板壳的稳定问题，并对结果进行了分析。     

弹性动力学的多变量响应问题的解法

基于瞬时混合变分原理与乘积型二元三次B样条函数,以板壳为例,建立样条动力方程。引入样条参数及其对时间的导数作为状态变量,导出状态方程,对空间域采用混合样条元法,对时间域采用现代控制论中的状态空间法。文中还建立了一种状态变量的递推计算格式,可以直接计算出多变量动力响应值,数值计算结果表明,本文方法的计算精度与效率是令人满意的。本文方法对计算多输入与多输出,时不变与时变系统和线性与非线性系统等多变量动力响应问题,有广阔的应用与发展前景。     

样条函数配点法分析薄板的压曲及自由振动与薄壳的稳定问题

本文采用单五次B一样条函数配点分析了薄板的压曲以及自由振动,用九次样条函数配点分析了几种薄壳的稳定问题。计算了不同的例题并与解析解进行比较,证明样条函数配点法是分析板、壳稳定问题的简便、有较的方法。     

样条有限点法解非规则薄板弯曲问题

本文根据样条有限点法的计算原理,采取分条计算总势能等处理方法,建立了非规则薄板弯曲问题的计算公式,能够统一处理不同支承条件的梯形板、三角形板及某些具有曲线边界的非规则板,而且计算量小,精度高,应用方便,容易在微型机、袖珍机上实现。文中给出了梯形板算例。     

复合材料加筋板壳的承载能力问题

本文讨论了复合材料加筋板壳承载能力问题的复杂性,给出了计算复合材料加筋板壳承载能力的要点,计论了复合材料加筋板壳在面板局部失稳以后的有效刚度和有效宽度问题,指出了提高加筋板壳承载能力的主要途径。     

热冲击下的复合材料壳刚柔耦合动力学研究

研究了在热冲击下任意形状(仅一个方向有曲率)复合材料壳的非线性刚柔耦合动力学响应。根据Mindlin理论,建立了任意形状的复合材料壳的非线性应变-位移关系。借助于数学理论以及几何关系,描述了壳上任意点的变曲率。用虚功原理建立了动力学变分方程,并采用等参单元对壳的连续动力学方程进行离散,建立了中心刚体-复合材料壳的刚-柔耦合动力学方程。用高斯积分计算常值阵,为了提高计算效率,采用广义-α法结合Newton-Raph-son迭代法对动力学方程进行积分。将采用该方法计算得到的频率与ANSYS软件计算得到的作对比,验证了模型的正确性。通过算例分析了在热冲击作用下复合材料壳的线性、非线性的动力学特性,以及曲率、材料特性对动力学响应的影响。     

板锥网壳结构的静力有限元分析

板锥网壳结构是一种受力性能合理,技术经济效益良好的新型空间结构形式。本文采用组合结构有限元法对板锥网壳结构进行了线弹性静力分析,分别考虑了三种计算力学模型,着重研究了具有内节点的三角形板单元及复合材料层合板单元,编制了板锥网壳结构的专用计算程序。     

Non-linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method

In this paper, a mixed spline boundary element and finite element method is suggested to analyse non-linear bending of plates and shells. Only the fundamental solutions for plates are required in order to establish the boundary integral equations. A quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells. Numerical examples show that the approach developed in this paper is very effective and especially promising for the non-linear analysis of plates and shells.     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论，用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值，推导了复合材料层合板刚度阵，质量阵列式，阻尼阵列式，并由Lagrange方程导出了层合板的动力学方程，通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性，在Kirchhoff假设的基础上，对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计，数值算列验证了算法的有效性。     

复合材料迭层板壳有限单元法现状分析

本文从剖析单元构成因素的角度出发,综合评述了目前用于复合材料板壳结构分析的各种有限单元,分析了这些单元的特点及其适用范围,并说明Mindlin类等参板壳单元广泛应用迭层板壳的原因以及存在问题、解决办法。还深入地讨论了杂交单元应用至迭层板壳计算的优点。     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

厚度不连续悬臂梁板的自由振动分析

将厚度不连续梁板视为层合板, 分别应用Hamilton 正则方程半解析法建立每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性, 联立各层的方程得到整个结构的特征方程, 其主要的优越性表现为: 控制方程不限制不连续梁板的厚度, 并能适合处理厚度不对称且不连续的层合板。本文中的方法可修改或扩展用来分析加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳等问题。     

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.     

Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element

The natural frequencies of isotropic and composite laminates are presented. The forced vibration analysis of laminated composite plates and shells subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To develop a laminated shell element for free and forced vibration analysis, the equivalent constitutive equation that makes the computation of composite structures efficient was applied. The Mindlin-Reissner theory which allows the shear deformation and rotary inertia effect to be considered is adopted for development of nine-node assumed strain shell element. The present shell element offers significant advantages since it consistently uses the natural co-ordinate system. Results of the present theory show good agreement with the 3-D elasticity and analytical solutions. In addition the effect of damping is investigated on the forced vibration analysis of laminated composite plates and shells.     

Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element

In this paper, we investigate the vibration analysis of functionally graded material (FGM) and laminated composite structures, using a refined 8-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function, but in this method, their Poisson’s ratios of the FGM plates and shells are assumed to be constant. The finite element, based on a first-order shear deformation theory, is further improved by the combined use of assumed natural strains and different sets of collocation points for interpolation the different strain components. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The natural frequencies of plates and shells are presented, and the forced vibration analysis of FGM and laminated composite plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To validate and compare the finite element numerical solutions, the reference solutions of plates based on the Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are obtained. Results of the present theory show good agreement with the reference solutions. In addition the effect of damping is investigated on the forced vibration analysis of FGM plates and shells.     

A three-dimensional layer-wise constant shear element for general anisotropic shell-type structures

This paper deals with the development of a new three-dimensional element with two-dimensional kinematic constraints capable of analysing the mechanical behaviour of the laminated anisotropic shell-type structures. This element, originally developed for the linear analysis of plates, is extended for the linear analysis of laminated composite shells. The element can represent arbitrarily curved shells with variable number of layers and thicknesses, including ply drop-off problems. The element was validated in a previous work by the patch test. All the analytical details necessary to make possible the shell analysis are presented here. Examples are reported to show the capability of the element to predict the behaviour of complex structures and a refined computation of the stresses is carried out by integrating the equilibrium equations.