层合板壳脱层曲面的有限元分析

通过建立一类新的参考面有限单元,得到适应于分析层合板壳脱层屈曲问题的有限元方法,指出了利用Ｍｉｎｄｌｉｎ假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元,这一方法确保了位移场的合理性和协调条件满足,为验证参考而单元的有效性和协调还对壳体脱层屈曲的几个算例作了数值分析。     

层合板壳脱层屈曲的有限元分析

通过建立一类新的参考面有限单元,得到适用于分析层合板壳脱层屈曲问题的有限元方法。指出了利用Mindlin假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元。这一方法确保了位移场的合理性和协调条件的满足。为验证参考面单元的有效性,还对壳体脱层屈曲的几个算例作了数值分析。     

压电曲壳结构的形状控制和优化设计

研究了使用最少和最合理的压电片布置,以及最合理的多点输入电压,对曲壳类结构实施最佳的形状控制.首先,采用HS-ANS法,构造能够克服剪切自锁、梯形自锁和厚度自锁的压电曲壳结构实壳单元.然后,利用遗传算法的组合优化,对作动器的数目和位置进行设计,进一步利用遗传算法的数值优化,对各作动器的作用电压值进行优化,并给出一般计算过程.最后的算例表明,给出的实壳单元和优化设计方法,可以非常有效地实现对曲壳类结构的形状控制.     

多夹层板壳的非线性理论及应用（Ⅲ）：扁壳的弯曲和稳定

本文根据文[1]获得的多夹层扁壳非线性基本方程，求解了各种载荷及边界条件下矩形底面多夹层扁壳的非线性弯曲问题，多夹层板、扁柱亮在轴向压力作用下的稳定问题，以及一般形状的扁壳在边界作用力下的变形．     

线性粘弹性壳的渐近分析——弯壳方程组的导出

应用渐近分析的方法和拉普拉斯变换,证明了3维线性粘弹性壳的位移在一定条件下收敛于2维线性粘弹性弯壳方程组的解．     

扁锥面网壳非线性动力分岔与混沌运动

对曲面为正三角形网格的3向扁锥面单层网壳,用拟壳法建立了轴对称非线性动力学方程．在几何非线性范围内给出了协调方程．网壳在周边固定条件下,通过Galerkin作用得到一个含2次、3次的非线性微分方程,通过求Floquet指数讨论了分岔问题．为了研究混沌运动,对一类非线性动力系统的自由振动方程进行了求解,继之给出了单层扁锥面网壳非线性自由振动微分方程的准确解,通过求Melnikov函数,给出了发生混沌的临界条件,通过数值仿真也证实了混沌运动的存在．     

用于平板和圆柱壳分析的势能—杂交／混合分离位移有限元格式

本文基于势能～杂交/混合有限元格式,导出了具有分离转动变量的4节点四边形Reissner-Mindlin板元MP4、MP4a和圆柱壳元MCS4.所有这些单元都显示了良好的收敛性;不含有多余机动模式;当趋于薄板/壳极限时,不存在“自锁”现象.本文还指明了在C~0和C~1连续的单元列式中使用的修正泛函,存在相互联系.本文的方法可导出Prathap的一致场列式,也可导出RIT/SRIT的位移协调模型.     

均布载荷作用下波纹扁壳的非线性振动

应用轴对称旋转扁壳的非线性大挠度动力学方程,研究了波纹扁壳在均布载荷作用下的非线性受迫振动问题．采用格林函数方法,将扁壳的非线性偏微分方程组化为非线性积分微分方程组．再使用展开法求出格林函数,即将格林函数展开为特征函数的级数形式,积分微分方程就成为具有退化核的形式,从而容易得到关于时间的非线性常微分方程组．针对单模态振形,得到了谐和激励作用下的幅频响应．作为算例,研究了正弦波纹扁球壳的非线性受迫振动现象．该文的解答可供波纹壳的设计参考．     

约束层阻尼圆柱壳的自由振动

给出了被动约束层阻尼圆柱壳(PCLD)的自由振动特性．波传播法被用来求解两端简支的PCLD圆柱壳的振动,而不是用有限元法、传递矩阵法和Rayleigh-Ritz法．基于Sanders薄壳理论,导出了PCLD正交各向异性圆柱壳的控制方程．数值结果表明当前的方法要比目前其它方法有效．讨论了粘弹性层和约束层的厚度,正交各向异性约束层的弹性模量比率和粘弹性层的复剪切模量对频率参数和损失因子的影响．     

边界条件对板壳稳定性的影响

本文论述了边界条件对板壳稳定性影响的理论和实际意义;介绍了近年来我们在理论和实验两方面的研究结果;指出了本研究对工程的指导作用,并将研究划分为两个阶段。     

球壳的环向剪切屈曲

通过球壳微元初始屈曲的微分几何分析,推导出一组新的精确的屈曲分支方程,并且应用Galerkin变分法研究铰支球壳承受环向剪切力时的整体稳定性,构造了接近分支点变形状态的屈曲模式,首次求得了从扁球壳到半球壳大范围内的扭转屈曲临界特征值,临界荷载强度和临界应力.     

Geometrically nonlinear shell finite element based on the geometry of a planar curve

An engineering approach for constructing a curved triangular finite element of a thin shell is considered. The approach is based on the assumption that the triangle sides are planar nearly circular curves before and after deformation. A geometrically nonlinear formulation of a triangular finite element of a thin Kirchhoff–Love shell is given. The predictive capabilities of the element are tested using benchmark problems of nonlinear deformation of elastic plates and shells.     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

Mechanical stability of functionally graded stiffened cylindrical shells

This paper is concerned with the elastic buckling of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations, the equilibrium and stability equations are derived using the Sander’s assumption. Resulting equations are employed to obtain the closed-form solution for the critical buckling loads. The results show that the inhomogeneity parameter and geometry of shell significantly affect the critical buckling loads. The analytical results are compared and validated using the finite element method.     

Postbuckling of a shear-deformable anisotropic laminated cylindrical shell under external pressure in thermal environments

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 789–822, November–December, 2007.     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

圆底扁球壳非线性稳定问题的自由参数摄动法解

用自由参数摄动法求解了圆底扁球壳在均布载荷作用下的非线性稳定问题．作为一种改进的正则摄动方法,使研究者可以不确定摄动参数具体意义而直接求得问题的全部特征方程．通过算例研究了扁球壳在失稳过程中变形和应力的变化特点,并与其他研究者的结果进行了比较．     

加肋圆柱壳在轴压作用下的屈曲和后屈曲

本文讨论完善和非完善的,纵向加肋和正交加肋圆柱壳在轴压作用下的屈曲和后屈曲性态.依据文[1]提供的圆柱薄壳屈曲的边界层理论及其分析方法,给出了加肋圆柱壳在轴压作用下的屈曲和后屈曲理论分析.本文同时讨论肋骨与壳板材料不同时对加肋圆柱壳屈曲和后屈曲性态的影响.