简化有限元方法的波纹管模态分析

采用简化方法对单层U型波纹管进行有限元模态分析。在长度,质量,对轴线转动惯量,体积,轴向弹簧比率以及周向弹簧比率不变的前提下,把波纹管简化成直壁薄管,用直壁薄管模型代替波纹管模型进行有限元模态计算。简化了计算模型,减少了计算量,提高了计算效率。本文给出了明确的等效直壁薄管的几何参数,物性参数的求解公式,改变了Broman人为设定直壁薄管厚度的方法,取得了更加准确的计算结果,使利用直壁薄管模型求解波纹管固有频率具有通用意义。进行了直壁薄管模型得到模态振型与波纹管模型得到模态振型之间的比较,认为直壁薄管模型可以求解波纹管的振型。     

薄壳失稳机理浅析

对薄壳失稳问题研究的理论与实验成果进行了总结和讨论，对薄壳后屈曲理论研究结果提出了不同的看法，同时应用动力学原理对薄壳失稳问题进行了探讨，并建立了计算模型。文中应用动力学原理描述了从加载初期的一个呈现静力学特征的薄壳随荷载的增加而逐渐成为一个呈现动力学特征的薄壳的过程，从薄壳受扰振动乃至共振的角度解释了失稳临界荷载实验数据值及其离散并低于失稳临界荷载理论值的原因。     

拟协调分层薄壳单元在圆柱薄壳结构弹-塑性分析中的应用

本文基于拟协调元的基本原理,引入薄壳分层子单元的概念,提出了用于圆柱薄壳结构弹-塑性分析的三角形和矩形拟协调分层圆柱薄壳单元的模型,给出了第k层薄壳分层子单元的弹-塑性矩阵和物理矩阵[D~(k)]的表达式,并最后给出了整个薄壳单元的物理矩阵和刚度矩阵的表达式。 根据上述原理和方法用Fortran语言编制了圆柱薄壳结构弹-塑性有限元分析程序,实例计算与实验结果较为吻合,从而说明用本方法进行圆柱薄壳结构的弹-塑性分析是可靠而行之有效的。     

用张量分析进行薄壳混杂模型三角形单元的构式

一般常用薄板单元分析薄壳内力,但由于内部边界联接斜率的不连续性而影响到求解精度。本文首先从薄壳的基本理论着手,用张量分析法建立了薄壳的势能原理和混杂变分原理。其次,对任意形状的薄壳,提出了采用混杂模型进行三角形单元的构式方法。最后,以螺旋曲面薄壳为例,导出了性质矩阵的形式。     

快Z—箍缩物理过程的简单分析

简单介绍了快－Z箍缩概念和物理过程,以及Z－箍缩物理过程不稳定性因素和简单分析。用PSPICE电路模拟方法解零维薄壳模型得到了箍缩时间、等离子体壳的速度、负载上的电流、电压变化规律等Z－箍缩物理量。     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅲ)--波纹管平面失稳的机理

波纹管无论是在内压还是在外压作用下都会发生环向屈曲或平面失稳,问题很复杂至今未得到妥善解决。本文首先指出了现行的有关“塑性铰”概念的某些不足之处,然后按文[8]的有限元法(考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理)对波纹管的环向屈曲进行了计算,并与前人的有关实验进行了对比分析,在此基础上解释了波纹管平面失稳的原因和发展过程。     

壁厚按线性变化的圆锥形薄壳轴对称问题

本文根据薄壳理论,建立了壁厚按线性变化的圆锥形薄壳轴对称问题力矩理论的复变量方程,并给出了精确解。     

波纹管式抛撒系统能量转换装置动态响应分析

摘要：采用LS-DYNA非线性动力学有限元程序，对某抛撒机构中的能量转换核心装置—波纹管在均布内压作用下的动态膨胀过程进行了数值分析，获得了波纹管动态响应规律；系统的考察了各种因素对波纹管的变形模式及其应力应变变化规律的影响；模拟了波纹管在内部压力和外围子弹群等共同作用下的耦合变形运动过程，对内弹道抛撒全过程进行了模拟，获得了波纹管耦合变形规律和子弹抛撒特性。模拟计算结果与试验现象基本一致。     

导电圆柱薄壳的热磁弹性效应分析

研究了磁场环境中受机械载荷作用的导电圆柱薄壳的热磁弹性问题.首先,根据电动力学方程和广义Ohm定律,得到了导电薄壳电流密度的分布,考虑到Joule热效应及热平衡方程,得到了导电薄壳的温度分布.其次,通过几何方程、物理方程、运动方程和电动力学方程导出了导电薄壳在机械场、电磁场以及温度场作用下的基本方程.最后,采用差分法及准线性化方法,得到了可以应用离散正交法求解的准线性微分方程组.对于导电圆柱薄壳,得到了Lorentz力表达式,并且推导了温度场积分特征值.讨论了导电圆柱薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对薄壳的应力、应变、温度的控制.     

?????????????????????????

通过对拱顶储罐罐壁承受轴向载荷、初始几何缺陷及轴压失稳状况研究，指 出在固定顶罐设计、建造和运行各阶段都应进行罐壁轴压稳定性校核. 根据圆柱薄壳稳定性 理论和轴压失稳临界应力数值分析计算结果，提出固定顶罐罐壁轴压稳定性校核方法和数学 模型，并运用回归分析方法建立罐壁轴压失稳临界应力计算公式. 对几种常用规格的拱顶罐 有初始挠度缺陷罐壁轴压稳定性分析表明：随储罐容积和罐壁初始挠度增大，罐壁轴压稳定 性呈减弱趋势.     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅰ)--基本方程及环板的屈曲

U型波纹管是现代管道系统中最常见的一种位移补偿器 ,它由环板和具有正、负Gauss曲率的半圆环壳组成 ,在管道所传输的介质的压力作用下会发生屈曲。其中环向屈曲最为复杂 ,精确的理论分析非常困难 ,有限元分析也不多见。作者在分析前人工作的基础上 ,以圆环壳段为单元 (特定的旋转壳段单元 ,能自动退化成环板单元 ) ,限于弹性范围和线性化特征值问题 ,对介质压力作用下U型波纹管及其相关结构 (圆环板、圆环壳、半圆环壳 )的环向屈曲问题进行了分析。考虑了结构屈曲前的弯曲 ,计及压力的二次势能 ,导出的应力刚度矩阵和载荷刚度矩阵是非对称的。全部工作分为三部分 :(Ⅰ )基本方程 ,环板的屈曲 ;(Ⅱ )圆环壳、半圆环壳的屈曲 ;(Ⅲ )波纹管平面失稳的机理。本文为第一部分 ,除推导公式外 ,对不同边界和不同内外径之比的环板在径向均匀压力作用下的环向屈曲进行了计算 (轴对称的径向屈曲作为特例得到 ) ,给出了前屈曲应力分布、临界载荷及相应的屈曲模态 ,并将临界压力的值与前人基于vonK偄ｒｍ偄ｎ大挠度板的精确解进行了比较 ,吻合良好。     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｌｌｏｗｓ,ａｓｈｅｌｌｏｆｗｒｉｎｋｌｅｄｍｅｒｉｄｉａｎｏｆｒｅｖｏｌｕｔｉｏｎ ,ｈａｓｂｅｉｎｇｉｎｃｒｅａｓｉｎｇｌｙｕｓｅｄｉｎｍｏｄｅｒｎｅｑｕｉｐｍｅｎｔａｓａｎｅｌａｓｔｉｃ＿ｓｅｎｓｉｔｉｖｅｅｌｅｍｅｎｔａｎｄａｆｌｅｘｉｂｌｅｊｏｉｎｔ.Ｔｈｅｆｏｒｍｅｒｉｓｕｓｕａｌｌｙｓｕｂｊｅｃｔｅｄｔｏｌａｒｇｅｄｉｓｐｌａｃｅｍｅｎｔｓａｔｉｔｓｅｎｄｓ,ａｎｄｔｈｅｌａｔｔｅｒｍａｙｐａｒｔｌｙｅｎｔｅｒｉｎｔｏｐｌａｓｔｉｃｓｔａｔｅ .Ｈｅｎｃｅ ,ｂ…     

Nonlinear buckling analysis of hyperbolic cooling tower shell with ring-stiffeners

This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are- length method is suggested. Finally, some conclusions having important significance for practice engineering are given.The Project Supported by National Natural Science Foundation of China.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads

In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated. The linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations.     

Nonlinear stability of large k-value shallow spherical shells with a symmetrically distributed line load

In this paper, we treat the nonlinear stability problem of shallow spherical shells with large values ofk(k=12(1–v) · 2f/h,f = shell rise,h = shell thickness) under the action of uniformly distributed line load along a circle concentric with the shell boundary. Load-deflection curves are computed at successive increments of uniformly distributed line loads by using both cubic B-spline approximations and iterative techniques. Our algorithm yields fairly good convergent results for values ofk as large as 400. The limiting case in which shells are loaded along a circle of small radius has been specially investigated and the computed critical loads are compared with those obtained with central point loads by other authors.     

Shakedown and Inadaptation Mechanisms of Bellows Subject to Constant Pressure and Cyclic Axial Force

Abstract

In the design of pipelines, a thermal expansion of the pipes is usually compensated for by a thin-walled, flexible shell of revolution, called a bellows. The process of cyclic loading of the structure may result in the formation of a sequence of plastic strain fields in the shell, which often leads to the collapse of the structure. Therefore, the question of whether the structure shakes down or collapses under the combined, cyclic loading is of particular importance to engineers

The Reissner-type equations for the perfectly elastoplastic model of the shell are formulated on the basis of the geometrically nonlinear third-order theory. Various mechanisms of plastic collapse (e.g., maximal load or formation of plastic hinge) are discussed for the quasistatically loaded S-type bellows, as well as for the bellows subjected to cyclic, complex loadings. The analogy between these cases, as far as the failure modes are concerned, is explained. The adaptation (shakedown) and inadaptation (nonsymmetric alternating plasticity, incremental collapse) domains for the particular case of the S-type bellows (C-type geometry) acted upon by internal pressure and variable repeated axial force are presented.     

Studies of nonlinear deformation and stability of noncircular cylindrical shells in transverse bending

The variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.