显式有限元方法求解二维壳体塑性大变形接触问题

本文系统论述了二维壳体塑性大变形接触问题的显式有限元求解方法，包括退化壳单元理论、弹塑性本构方程、应力回映算法、接触搜寻法及计算接触力的拉格朗日乘子法。本文方法已成功地应用到薄板成形过程的有限元分析之中，文中给出了几个计算实例，计算结果与实验结果相当吻合。     

计入剪切变形的正交各向异性扁壳的基本解

本文采用Ｈｏｒｍａｎｄｅｒ算子法将控制计入剪切变形的正交各向异性扁壳的偏微分方程组转化为含有一个未知函数的高阶偏微分方程，然后，利用平面波分解法将偏微分方程转化为常微分方程来求解。以定积分表示的形式提出了计入剪切变形的正交各向异性扁壳的基本解。     

复合材料多层圆柱壳振动和声辐射问题研究进展

鉴于复合材料优良的力学和声学性能，将其用于潜艇结构已成为未来的发展趋势和研究重点。而圆柱壳作为潜艇的主体结构形式，针对复合材料多层圆柱壳的振动和声辐射问题的研究已广泛开展。在满足水下承载能力的前提下，复合材料耐压圆柱壳趋于中厚壳，甚至厚壳，沿壳体厚度方向的横向剪切变形、压缩变形、截面翘曲变形不可忽略，这些因素直接决定了横向振动位移场描述的准确度，会进一步影响壳体周围声辐射场预报的准确性。现有的壳体理论主要有经典壳体理论、一阶剪切变形理论、高阶剪切变形理论、分层理论、锯齿理论和三维弹性理论等，这些理论发展比较成熟，但大多研究仍局限于正交各向异性薄壳结构的振动问题，涉及各向异性材料厚壳结构的声辐射研究较少，且目前对于这些壳体理论在复合材料圆柱壳的振动和声辐射问题的适用性方面缺乏系统的总结和研究。本文首先从复合材料的刚度特性出发说明其振动和声辐射问题求解的复杂性，然后从横向振动位移场的角度综述了这些理论的发展过程、研究现状以及各自的特点，最后给出了这些理论的适用范围和使用建议，并提出了有待进一步研究的问题，以期为复合材料多层圆柱壳结构的设计和振声性能分析提供参考。     

GSQ24壳体单元用于板壳结构的几何非线性分析

在考虑剪切变形的Von Karman大变形小应变假设下,基于全Lagrange描述方法,将平面内带有旋转自由度的GSQ24壳体单元用于板壳结构的几何非线性分析,给出了板壳结构大变形下的小位移刚度矩阵、初应力刚度矩阵、初位移刚度矩阵有限元列式。同时,文中也给出了既考虑材料非线性,又考虑几何非线性的强非线性问题的板壳结构分析时的有限元列式。数值算例与变分法和级数解结果比较,表明本文方法的可行性。     

高分子熔体的各向异性内部结构流变模型EI

提出了一个高分子熔体内部结构流变模型，采用大分子构象张量表述，并结合经典弹性力学与大分子动力学求得自由能各向异性唯象表达式，运用Ｈａｍｉｌｔｏｎｉａｎ／ＰｏｉｓｏｎＢｒａｃｋｅｔ方法从自由能函数和耗散张量推导建立了高分子构象张量动力学方程与相应的应力张量表达式。ＬＤＰＥ和ＰＳ在简单剪切流场中的粘弹特性的模拟结果与实验数据进行了分析对比，两者基本相符。本文还预测和讨论了上述流体大分子构象的变化过程以及各向异性参数的作用。     

正交各向异性多层双曲壳体理论

本文提出由多个正交各向异性层粘合而成的扁平双曲壳体的一种分析方法.文中以层间位移分量作为基本未知函数,并将层间应力平衡条件在建立基本平衡方程式之前,先行引进.此外:在计算各单层横向剪切变形影响时,采用单层中面法线变形后维持直线,但放弃层中面法线及其正交线之间变形后保持直角的假定.算题实践说明应用本文方法,计算方便,精度高.      

发电机复合材料护环的强度刚度分析和铺层设计

本文考虑了横向剪切变形的影响,采用“退化”的三维等参单元,建立承受非均匀表面力、离心体积力和热应力联合作用的一般层合各向异性壳的有限元公式和程序,并用它对25MW发电机玻璃纲护环进行刚度、强度分析。提出铺层缠绕的优化设计方案。      

爆炸复合接头剪切强度测试方法研究

参照正交各向异性层压复合板层间剪切强度的测试方法，提出了用于测试爆炸复合接头复合界面剪切强度的3种方法；并建立三雏有限元模型，分别对3种测试方法进行模拟；最后分别对3种方法进行了测试试验．结果表明，3种试验方法均能有效测试爆炸复合接头的剪切强度，其中对称试件双切口拉伸法最适合实际应用．     

相似结构动力响应的外推方法及精度特性

提出了大位移、大转动、大变形、弹塑性相似结构动力响应显式有限元分析结果的外推方法并分析了其精度特性。以 Ｂｕｃｋｉｎｇｈａｍ Ｐｉ定理为基础,运用量纲矩阵法,导出了动态大位移大转角弹塑性相似结构的相似关系。根据有限元法分块近似的基本思想及显式有限元法的积分格式,分析了外推法的精度特性。算例表明,本文方法切实可行。     

矩形橡胶复合材料层合板几何非线性分析

文中应用简单高阶剪切层合理论和大变形理论对各向异性纤维增强的矩形橡胶复合材料层合板进行了几何非线性分析。与线性一理论相比，本文作者进行的层合板大变形状态的几何非线性分析和所计算的层板应力分布，更准确性。     

实体退化板单元及其在板的振动分析中的应用

经典板壳单元是由板壳理论构造出来的,而经典的板壳理论是在空间弹性理论的基础上考虑板壳的基本假定得来的。在空间等参数单元的基础上,直接引入板壳的基本假定,修改空间等参数单元的弹性矩阵,从而构造出适合于厚薄板壳分析的20结点实体退化板单元,并将其应用于开口圆柱薄壳的静力分析和厚薄板的固有振动分析。数值算例表明,该单元收敛快,稳定性好,具有较高的精度。此外,该单元还可以用于曲边变厚度板、壳体及层合板的振动分析。     

复合材料加筋板热变形和热应力分析

复合材料及其结构的热响应是近年来复合材料力学研究的热点课题之一。本文用有限元法研究了复合材料加筋板的热变形和热应力。基于Mindlin假定导出了一阶剪切变形层合板梁理论。这两种理论也适用于中厚板和深梁。考虑的热载可以是瞬态的也可以是稳志的,实际工程应用表明,根据本丈模型研制的计算机程序具有较高的计算精度和效率。      

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.     

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。     

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.     

Dynamic stability of stiffened laminated composite plates and shells subjected to in-plane pulsating forces

The dynamic stability of laminated composite stiffened or non-stiffened plates and shells due to periodic in-plane forces at boundaries is investigated in this paper. A three-dimensional (3-D) degenerated shell element and a 3-D degenerated curved beam element are used to model plates/shells and stiffeners, respectively. The characteristic equations to find the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion. Then, the method of Hill's infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters, such as skew angle, lamination scheme, stiffened scheme, in-plane force type and curvature of cylindrical shell, on the dynamic stability of stiffened and non-stiffened plates and shells subjected to in-plane pulsating forces at boundaries.     

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.     

Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells

An elasto-plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three-dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine-node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber-Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.     

单双层球面扁网壳连续化方法非线性稳定理论临界荷载的确定

连续化方法是研究网壳结构稳定问题的一种重要途径,目前用连续化理论分析球面扁网壳的稳定问题还存在欠缺和不足。运用经典的壳体理论,将单层和双层球面扁网壳等代为实体薄壳并建立非线性稳定理论混合法基本方程,再用李兹法求出球面扁网壳上下临界荷载计算公式。通过参数分析,首次从1000多个算例中得出了正三角形网格单层和双层常用球面扁网壳临界荷载系数的精确解。与国内外现有文献的计算公式相比,结果更为完善和正确。即便在有限元技术日益成熟的今天,用连续化方法计算的网壳结构临界荷载仍然对工程设计有重要指导作用,也是有限元方法分析网壳稳定性的对比和补充。