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卷积型加权残值法求解梁的动力学问题 总被引:3,自引:2,他引:3
利用卷积型加权残值法推导出Gurtin变分原理, 并应用卷积型加
权残值法计算了简支梁的振动、冲击问题, 算例表明此方法是成功的. 相似文献
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有效集法在数学规划加权残值法中的应用 总被引:2,自引:0,他引:2
本文研究有效集法在数学规划加权残值法求解微分方程问题中的应用。从理论上和实际应用方面 阐明,对于数学规划加权残值法和线性规划问题,有效集法比常用的单纯形法更简便、易程序化、计算速度更快,因此更适用于数学规划加权残值法求解微分方程问题。 相似文献
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为解决加权残值法求近似解的计算精度问题,将摄动法与加权残值法相结合,首先以板中心挠度为摄动参数进行摄动,将矩形板大挠度非线性偏微分方程组分解为线性偏微分方程组,然后用最小二乘法求解.求解中构造并应用了可以由控制参数,调节的升阶试函数族,计算结果与实验结果基本一致,与以前的研究比较,计算精度明显提高.该方法对于寻求最佳试函数和最佳近似值是一种有效的方法. 相似文献
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四边固定矩形板大挠度问题的摄动最小二乘解 总被引:1,自引:0,他引:1
本文将摄动法与加权残值法相结合,提出了求解大挠度问题的摄动加权法,编制了PWS计算程序,计算了四边固定矩形板在均布载荷下的大挠度问题。算例的结果与实验一致。 相似文献
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本文应用加权残值法分析阻尼介质对薄板塑性动力响应的影响。文中先以简支圆板在阻尼介质中的运动为例,给出用加权残值法分析塑性动力响应问题的方法及步骤。即先对结构的基本方程进行拉普拉斯变换,然后再利用加权残值法进行求解,计算结果与文(2)中结果一致。文中又以本文方法分析了阻尼介质对简支方板塑性动力响应的影响,并对计算结果进行了讨论。 相似文献
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本文研究数学规划加权残值法在非线性微分方程求解中的应用,利用数学规划加权残值法和LP模理论,把非线性微分方程边值问题转化为一个可微分的无约束非线性优化问题,从而运用成熟稳定的寻优方法求得问题的解。文中数字计算例子表明本文方法可以快速有效地求解非线性微分方程。 相似文献
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L. V. Kurpa E. I. Lyubitskaya I. O. Morachkovskaya 《International Applied Mechanics》2010,46(6):660-668
The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates
interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method
and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped
shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution
on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied 相似文献
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提出了一种分析交各向异性圆柱壳和阶梯圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Fluegge薄壳理论,通过定义广义位移变量和对应的广义力变量,建立了圆柱壳混合变量能量泛函;然后通过引入条形单元,定义混合状态变量和采用传递函数方法对超级壳单元求解,得到具有多种边界条件圆柱壳屈曲问题的半解析解;最后通过位移连续和力平衡条件,可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。 相似文献
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采用格林函数法,导出了U型波纹管圆环壳部分和截头扁锥壳部分的非线性的积分方程,其中的四个未知参数由圆环壳和截头扁锥壳的连接条件确定,联合应用梯度法和积分方程迭代法建立了U型波纹管大挠度分析的迭代算法,开发了相应的程序系统,数值结果表明,本文方法具有较高的精度,压缩角对峰值应力和刚度影响十分显著,应用作为波纹管设计的重要参数。 相似文献
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Two new approaches are proposed for the numerical and analytical stability analyses of imperfect shells. One approach is based on the generalized mesh method, whereas the other employs a modified reduced-stiffness method. Both approaches apply to shells with initial geometrical imperfections. Numerical results are compared with experimental data for shells with a single dent. Analytical results are also presented and compared 相似文献
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A. A. Artem’eva V. G. Bazhenov D. V. Zhegalov D. A. Kazakov E. V. Nagornykh 《Journal of Applied Mechanics and Technical Physics》2015,56(6):951-958
A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported. 相似文献
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A self-equilibrated stress obtained from the stress functions of thin shells is used for the static shakedown theorem as a residual stress. In combination with the finite element method, a linear programming formulation of the shakedown analysis of axisymmetric shells is derived. The physical meaning of the stress function method is clear and its computing amount is small. Some examples of the plates and shells show that the method is reasonable and efficient.The project was supported by the National Natural Science Foundation of China 相似文献
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《应用数学和力学(英文版)》2017,(4)
The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations. 相似文献
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The stress-fit method is a procedure for determining complete stress distribution in shells from experimental data. Displacement, slope and shearing-force distributions may also be calculated. The method is applicable to all shell configurations for which closed-form solutions have been formulated and may be applied to certain asymmetrically loaded shells as well as those loaded axisymmetrically. Application to cylindrical and spherical shells is discussed in detail, and the procedure is shown to be verfied experimentally. 相似文献
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IntroductionTheproblemofdelaminationbucklingofcompositelaminateshasgeneratedsignificantresearchinterestsandhasbeenthesubjectofmanytheoreticalinvestigationsinthisdecade.Afiniteelementmodel[1]waspresentedtosolvethepost_bucklingproblemofcompositeplateswit… 相似文献