有限厚度、大压入的球压试验材料力学响应

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题，基于薄壳的几何方程、物理方程、运动方程、电动力学方程，建立其热磁弹性基本方程．应用线性化方法，得到了关于热磁弹性问题的线性迭代方程，转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体，给出Lorentz力表达式，导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律，并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

变厚度载流旋转壳体的热磁弹性分析

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题，基于薄壳的几何方程、物理方程、运动方程、电动力学方程，建立其热磁弹性基本方程．应用线性化方法，得到了关于热磁弹性问题的线性迭代方程，转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体，给出Lorentz力表达式，导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律，并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

壳体对爆炸空气冲击波强度的影响

壳体对爆炸空气冲击波强度有重要影响，本文提出一种计算壳体破片速度的新方法，分析了壳体对爆炸空气冲击波强度的影响。本文指出，壳体对爆炸空气冲击波强度的影响取决于产生壳体破片部位的壁厚(质量)，而不是壳体的全部质量。这反映了实际情况，也是本文的特点所在。通过重量和形状相同的两种装药爆炸空气冲击波对模拟目标的毁伤实验，考查了本文理论分析结果的可靠性。理论分析与实验结果相吻合。本文得到弹体破片最大速度的上限和下限。破片速度与壳体厚度有关，壳体越厚或质量越大．对空气冲击波强度的影响越显著。     

塑性节点法的研究及其在薄壳结构中的应用

本文采用变分原理及离散塑性流动定律假设研究了弹塑性有限元的新方法—塑性节点法及其所表示的物理意义。结果表明:该方法的物理实质是所述的塑性流动定理的离散。在一般意义下,本文对其进行了修正,典型板壳例题和复杂壳体结构的弹塑性有限元分析显示,计算结果与文献资料和实验数据符合较好。证明用文中方法进行壳体结构的弹塑性分析是行之有效的和可靠的。     

基于区域分解的薄壁回转壳自由振动分析

提出了一种区域分解法来分析不同组合边界条件的薄壁回转壳的自由振动.首先沿壳体母线方向将壳体分解为一些自由壳段,并采用广义变分和最小二乘加权残值法将壳体分区界面上的位移协调方程引入到壳体的势能泛函中;然后将壳段位移变量以Fourier级数和Chebyshev多项式展开,对总的势能泛函变分后得到回转壳的离散动力学方程.采用区域分解法分析了不同边界条件的圆柱壳、圆锥壳、抛物壳的自由振动,并将计算结果与其它文献值及 ANSYS 结果对比,结果表明:随着回转壳分区数目的增大,区域分解法计算出的壳体频率很快收敛;本文结果与其它方法计算结果非常吻合(相对误差不超过0.4%).采用该方法可高效计算不同组合边界条件回转壳体的低阶和高阶振动频率.     

基于元胞自动机的变厚度薄壁梁侧向耐撞性优化设计方法

薄壁结构是汽车等运载工具的重要防护装置,除了其轴向防撞能力外,侧向耐撞性能分析与提升方式也非常重要。研究基于薄壁结构厚度合理分布的侧向耐撞性能提升方式和建立基于元胞自动机的变厚度薄壁梁侧向耐撞性优化方法。以汽车B柱受力环境和性能要求为设计需求,首先利用所建立的方法给出了连续变厚度的薄壁梁厚度分布设计,其性能较常规的等厚度薄壁梁最大侵入位移大幅下降(下降82%),验证了变厚度设计的有效性;然后,考虑单向变厚度便于柔性轧制工艺制成TRB,给出了轴向连续变厚度薄壁梁的厚度分布设计,该设计较等厚度梁最大侵入位移下降73%;与连续变厚度梁相比,在侵入位移降低量略小的情况下,实现了可制造性。设计实例表明本文提出的连续变厚度设计能够有效提高侧向耐撞性能,所建立的方法能够获得合理的厚度分布设计,是有效的耐撞性优化设计方法。     

基于参数曲面描述的层合壳体结构分析的分片Ritz法

为了对层合壳体结构进行准确和有效的分析，给出了基于分片参数曲面描述的适用于层合壳体结构分析的分片Ritz法。该方法首先将壳体结构的参考曲面进行分片处理，利用参数曲面来描述分片的壳体参考曲面并将分片按照C^0连续性进行拼接。构造壳体参考曲面分片上的具有参数曲面特征的Ritz法的试解函数，并得到相应问题的泛函和控制方程。最后给出了两个典型的层合壳体结构的数值算例，结果表明该方法准确有效。     

厚度幂指数分布管状结构耐撞性设计准则与方法研究

厚度或质量连续分布技术对车身薄壁结构的轻量化和性能设计有着非常重要，甚至起到决定性的作用，从设计方法上研究连续变厚度结构在车身零部件中的耐撞性应用是安全性设计所需的主要工作。本文研究一种较新颖的薄壁吸能结构，其管壁厚度按照幂指数形式连续分布，根据此分布特点推导出了该薄壁结构在等质量条件下与其他管状结构（比如均匀管、拼焊管和锥管等）之间相关参数的定量解析关系，给出了前者的耐撞性设计准则，评估了不同梯度对幂指数管耐撞性能的影响。分析结果显示，该新颖管状结构比其他截面管具有更理想的耐撞特性。然后，在2个设计区间内对梯度指数分别采样并构造近似模型，采用遗传算法作为求解器得出了非劣解前沿，研究发现高阶响应面近似模型得到的设计结果不一定是最优的。     

没有复杂几何概念的单方向场壳体有限变形模型综述

基于Simo和Fox的工作, 介绍一种没有复杂几何概念的现代壳体有限变形理论. 在 推导上, 使用三维连续介质理论, 运用现代力学的表示方法. 这个模型提供了非线性几何 精确壳体理论的力学分析基础. 这种模型的一个优点是虽然将壳体仍然看作二维结构, 但 是它没有复杂的微分几何概念, 如没有协变导数、Riemannian-Christoffel记号等. 另外, 还介绍了壳体局部平衡的弱形式或变分表示, 这种表示特别适用于数值计算.     

星载抛物面天线反射器瞬态热分析

星载抛物面天线反射器在周期性的冷热辐射作用下,产生不均匀的温度分布,过大的热变形严重影响卫星通信质量;采用一种8节点超参数壳单元,通过每个节点3个温度自由度表示厚度方向上温度的非线性变化,建立了单元内温度插值函数,基于Galerkin法推导出受太空冷热辐射作用的壳体结构瞬态热分析的有限元公式;运用几何解析法分析了抛物面壳体的自遮挡.对某静止轨道卫星抛物面天线进行稳态分析,与FDM结果比较表明该方法具有良好的计算精度;在不考虑地球辐射热流作用的一个运行周期的瞬态分析中,该反射器上瞬间温差达200 K,在日照区内温度变化达250 K.     

Heat conduction between confocal elliptical surfaces using the theory of a Cosserat shell

This paper is concerned with steady-state heat conduction in rigid shell-like interphase regions. By analogy this work may provide insight into related problems of electric, dielectric and magnetic behavior. Although the field equations for three-dimensional linear Fourier heat condition are rather simple, the solution of problems in shell regions is significantly complicated when the shell has a general geometry and variable thickness. Here, the problem of heat conduction between confocal elliptical surfaces is solved within the context of the theory of a Cosserat shell. This problem is of particular interest because the Cosserat solution can be compared with an exact solution and the influences of variable shell thickness and strong variations of the temperature field through the shell’s thickness can be explored independently. The results show that the Cosserat approach is reasonably accurate even for moderately thick shells, moderate ellipticity, and moderately strong variation of the temperature through the shell’s thickness.     

弹塑性板壳结构非线性有限元分析

本文根据塑性流动理论的基本公式，由隐式积分导出了与路径无关的变量更新算法和一致切线模量。采用单元广义应力应变直接离散塑性流动定律，构造了杂交应力单元一致切线刚度矩阵的显式表达式，编制了结构有限元程序ＳＡＦＥ，数值算例表明：本文的计算方法和计算程序是正确可靠的，可用于弹塑性板壳结构的非线性分析，计算结果屈曲临界载荷和极限承载能力。     

板壳问题的三维无网格伽辽金直接分析法

对于板壳问题,共有三种数值模拟方案:线性或非线性的板壳理论、退化连续体方案和直接三维连续体方案。无网格法近似函数可具有C1甚至更高的连续性,便于在K irchhoff-Love理论中应用。但当各种无网格法用于M ind lin-R e issner板理论时,会遇到数值锁死的困扰。对比之下,三维连续体方案是最简单,最精确但并不常用的一种方案。无网格法近似函数具有高度光滑性,在板壳的厚度方向仅布置2~5层点就可以很好地捕捉此方向场的梯度,同时还可以在一定参数范围内避免剪切和体积锁死,在处理复杂本构关系、非线性板壳等问题中更是具有很大优势。本文采用无网格伽辽金法(EFG)和三维连续体方案分析了线性板壳问题,与有限单元法做了对比,并讨论了数值锁死等问题。     

Vibration analysis of bi-layered FGM cylindrical shells

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain–displacement and curvature–displacement relationships are utilized from Love’s first approximation linear thin shell theory. The versatile Rayleigh–Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.     

Nonlinear stability of truncated shallow conical sandwich shell with variable thickness

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Vibrations of FGM thin cylindrical shells with exponential volume fraction law

In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love＇s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.     

Refined Stress Analysis of Flexible Multilayered Shells of Revolution with Orthotropic Layers of Variable Thickness

A refined theory of flexible layered shells with orthotropic layers of variable thickness is considered. The theory assumes that each layer has a local rotation angle due to lateral shear. This makes it possible to derive equations whose order does not depend on the number of layers. The basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading     

Stress-strain state of a parabolic shell of revolution subjected to external magnetic pressure

The paper investigates the stress-strain state of an axisymmetrically loaded shell which arises when a strong electric current flows in it. The shell with current is an element of a system intended for focusing π and K mesons in neutron experiments. The problem is solved by numerical integration on a computer of equations of the theory of shells by the two-sided matrix run-through method, and also by an approximate analytical solution. The algorithm being applied can be used to calculate an arbitrary shell of revolution of variable thickness. The results thus obtained are discussed.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.