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复合材料层合开顶扁球壳的非线性动态屈曲 总被引:10,自引:0,他引:10
研究了复合材料层合开顶扁球壳的非线性动态屈曲问题。建立了对称层合圆柱正交异性开顶扁球壳考虑横向剪切的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。 相似文献
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网格扁壳结构的非线性弯曲与稳定问题研究 总被引:7,自引:0,他引:7
本文利用作者分析得到的矩形网格扁壳结构的非线性控制方程,采用双重Fourier级数求解了该类结构的非线性问题。推导得到了外载与结构(中心)节点横向位移之间的三次非线性关系式。并作了算例分析,给出了结构产生失稳跳跃的条件。 相似文献
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带旋转自由度C^0类任意四边形板(壳)单元 总被引:5,自引:0,他引:5
基于Reissner-Mindilin板弯曲理论和Von-Karman大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Allman膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点C^0类板单元。大量算例表明:该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。 相似文献
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采用六模态的中厚壳理论研究了可压缩流体中球面各向同性球壳的自由振动,即在分析中考虑了剪切变形,旋转惯量和横向正应变的影响,引入5个辅助变量可以理到两类振动及其频率方程,对频率方程作了简化并算例进行了相应的探讨。 相似文献
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板壳有限变形精确理论及有限元列式 总被引:1,自引:0,他引:1
以位移型退化壳理论为基础,提出了板壳模型的有限变形精确理论,该理论引入转动伪矢量概念,充分发挥刚性线段的运动学模型和有限转动矩和作用,精确表达非线性位移-应变关系,抛弃以往的小位移、小应变、小转动增量乃至小加载小长等各种简化假设,并严格遵循能量共轭关系建立有限元平衡方程,能够可靠和有效地用于板壳结构的大位移、大转动分析。算例表明,该文列式在弹性范围内具明显的平方收敛效率,并且计算结果与加载步长无关。由于不受小加载步长、小转动增量等的限制,实现了板壳几何非线性问题的大步长加载。 相似文献
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考虑面层横向剪切变形以及横向剪应力在面层和芯层粘结处连续,应用Hamilton原理建立了正交铺设复合材料面层夹层扁壳新的非线性精化理论。在静力问题情形,控制方程和边界条件化简为用四个基本未知函数表述。作为理论的应用,分析了简支边界条件下正交铺设复合材料面层夹层圆柱壳和夹层球壳的非线性弯曲,得到了其挠度响应和层间应力响应。 相似文献
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IntroductionTheproblemofnonlinearvibrationisveryimportantnotonlyintheorybutalsoinapplication .Theconicshellplaysanimportantroleinarchitecture ,navigation ,spaceflightandwasusedastheelasticcomponentoftheinstrumentwidely .Thenonlinearvibrationofshellisacomplicatedproblemanditisdifficulttosolveinmechanicsandmathematics .Itismoredifficultiftheactionofouterloads (staticload ,thermalload ,magnetic)istakenintoaccount[1~7].Thereisdifferentinterestineventhenonlinearvibrationundertheactionofstaticload… 相似文献
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B. Kh. Eshmatov 《Mechanics of Solids》2009,44(3):421-434
We consider nonlinear vibration and dynamic stability problems for a viscoelastic circular cylindrical shell according to the refined Timoshenko theory, which takes into account the shear strain and the inertia of rotation, in a geometrically nonlinear setting. The problem data are reduced to systems of nonlinear integro-differential equations with singular relaxation kernels, which can be solved by the Bubnov-Galerkin method combined with a numerical method based on quadrature formulas. We study the numerical convergence of the Bubnov-Galerkin method. We analyze the shell dynamic behavior in a wide range of physical-mechanical and geometric parameters. We demonstrate the influence of the viscoelastic properties of the material on the nonlinear vibrations and dynamic stability of a circular cylindrical shell. We also compare the results obtained according to different theories. 相似文献
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本文针对目前广泛应用于网架与网壳结构中的薄壁空心球节点,对薄壁球壳在环线荷载作用下的非线性稳定性态进行了分析研究。应用B-样条函数及截断单项式。克服了理论分析中因剪力突变所带来的困难。数值分析结果表明,薄壳的非线笥稳定是工程中常用的空心球节点的控制因素。同时又表明现行规程公式的计算结果大于数值分析结果。 相似文献
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This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitude-frequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates. 相似文献
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V. S. Pavlovskii 《International Applied Mechanics》2000,36(10):1369-1379
The nonlinear resonance vibrations and stability of nonlinear orthotropic shells partially filled with a liquid and subjected to longitudinal and transverse periodic loading are studied. The equations of motion are derived with regard for the existence and nonlinear interaction of conjugate flexural modes of the shell. Stationary regimes for forced and parametric vibrations are found and analyzed for stability under the conditions of fundamental and subharmonic resonances. The amplitude–frequency characteristics of these regimes are constructed for various parameters of the system 相似文献
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George Papadakis 《International Journal of Solids and Structures》2008,45(20):5308-5321
In this paper a set of stability equations for thick cylindrical shells is derived and solved analytically. The set is obtained by integration of the differential stability equations across the thickness of the shell. The effects of transverse shear and the non-linear variation of the stresses and displacements are accounted for with the aid of the higher order shell theory proposed by [Voyiadjis, G.Z. and Shi, G., 1991, A refined two-dimensional theory for thick cylindrical shells, International Journal of Solids and Structures, 27(3), 261–282.]. For a thick shell under external hydrostatic pressure, the stability equations are solved analytically and yield an improved expression for the buckling load. Reference solutions are also obtained by solving numerically the differential stability equations. Both the full set that contains strains and rotations as well as the simplified set that contains rotations only were solved numerically. The relative magnitude of shear strain and rotation was examined and the effect of thickness was quantified. Differences between the benchmark solutions and the analytic expressions based on the refined theory and the classical shell theory are analysed and discussed. It is shown that the new analytic expression provides significantly improved predictions compared to the formula based on thin shell theory. 相似文献
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采用小参数摄动法和Laplace变换研究了非线性弹性岩土中球壳对冲击波的动力响应问题。系统的非线性方程由小参数摄动渐近展开后,利用Stokes-Helmholtz矢量分解定理把它们简化为一系列的线性波动方程,并由Laplace变换和本征函数给出了各线性波动方程的求解。最后,对平面冲击波和球面冲击波给出了球壳动力响应的应力结果。 相似文献
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对曲边柱壳受轴向非均匀内压作用下的大转动几何非线性3-D动力学行为进行了研究.基于Nayfeh and Pai[1]非线性壳体理论,给出了考虑几何非线性的3-D混合型(含内力与位移)动力学模型.为了克服该强非线性模型难以求解的问题,依据分析获得的结构静动态变形关系,采用Lagrange方程推导建立了基于结构静态解的曲边柱壳多自由度3-D动力学方程,并对其进行了线性化与降阶处理,结合差分法获得了一套高效的求解算法.与LS-DYNA有限元结果的吻合,验证了本文方法的正确性.最后分析了单元数和计算时间步分别对有限元模型和本文方法的影响,发现求解精度随着计算时间步的减小不断提高直至趋于稳定.同时对采用本文方法获得的曲边柱壳动态变形模式的分析表明:结构动态响应与其所受内压载荷沿轴向的分布形式关系紧密,可以通过改变或者设计内压轴向分布形式来影响以及控制结构的动态变形模式,从而应用于曲边柱壳结构设计及优化的工程实际中. 相似文献
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Axisymmetric buckling analysis is presented for moderately thick laminated shallow, truncated conical caps under transverse load. Buckling under uniformly distributed loads and ring loads applied statically or as step function loads is considered. Marguerre-type, first-order shear deformation shallow shell theory is formulated in terms of transverse deflection w, the rotation ψ of the normal to the mid-surface and the stress function Φ. The governing equations are solved by the orthogonal point collocation method. Truncated conical caps with a circular opening, which is either free or plugged by a rigid central mass, have been analysed for clamped and simple supports with movable and immovable edge conditions. Typical numerical results are presented illustrating the effect of various parameters. 相似文献