共查询到16条相似文献,搜索用时 78 毫秒
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弹性力学的一种正交关系 总被引:8,自引:2,他引:8
在弹性力学求解新体系中,将对偶向量进行重新排序后,提出了一种新的对偶微分矩阵,对于有一个方向正交的各向异性材料的三维弹性力学问题发现了一种新的正交关系.将材料的正交方向取为z轴,证明了这种正交关系的成立.对于z方向材料正交的各向异性弹性力学问题,新的正交关系包含弹性力学求解新体系提出的正交关系。 相似文献
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各向同性平面弹性力学求解新体系正交关系的研究 总被引:13,自引:0,他引:13
在平面弹性力学求解新体系中,将文献[2]对偶向量进行重新排序后,提出了一种新的对偶微分矩阵L,对于各向同性平面问题发现了一种新的正交关系。文中证明了这种正交关系的成立,并研究了各向同性平面问题的功互等定理与正交关系的联系。对于各向同性平面问题,新的正交关系包含文献[2]的正交关系。 相似文献
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复本构理论中的对偶原则 总被引:8,自引:0,他引:8
复本构理论中的对偶原则何钟怡(哈尔滨建筑工程学院,150006)关键词复本构方程,对偶原则,强迫振动1复本构的对偶原则材料的本构方程完全可以不用复数形式表达,概括性很强的Noll泛函就是以实变量表示的.但是对于线性本构,采用复变量表示优越性很大.例如... 相似文献
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电磁波导的半解析辛分析 总被引:18,自引:1,他引:18
根据电磁波导的Hamilton体系,辛几何可用于任意各向异性材料,而且便于处理不同区段的界面条件,横向的电场和磁场构成了对偶向量.基于Hamilton变分原理用半解析法进行横向离散应当保持体系的辛结构.离散后可以运用应用力学的有效算法,求解其辛本征值问题.每段波导可以引入两端Riccati矩阵,用精细积分法求解其方程组. 相似文献
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求解一类可分离凸规划的对偶显式模型DP-EM方法 总被引:1,自引:0,他引:1
推导对偶目标函数的精确显式表达式,可选用更多成熟高效的求解方法,从而进一步提高了非线性规划对偶理论求解结构拓扑优化问题的效率.研究工作来源于非线性凸规划同其对偶规划的间隙为零,可以等价转化为对偶问题求解,通常可以大大地缩小问题的规模,可是二者不具有显式关系却影响了对偶解法的应用.所幸的是,结构优化当中一大类问题包括连续体结构拓扑优化问题,不仅具有凸性,而且具有变量可分离性,于是原变量和对偶变量之间有了显式关系,因此,对偶解法成了38年来被应用的有效方法之一.然而长期以来,对偶问题的目标函数并不是显式,这缘于含参数的极小化问题导致目标函数为隐式表达,常见的显式化方法是进行二阶近似.本文突破了对偶问题难以显式化只能采用近似显式的定势,将我们提出的"对偶规划-显式模型"(DP-EM)方法应用于连续体结构拓扑优化,并与对偶序列二次规划(DSQP)算法及移动渐近线(MMA)算法为求解器的方法进行计算效率对比,结果显示:(1)MMA算法比DP-EM算法和DSQP算法的外部迭代次数均多;(2)DP-EM算法与DSQP算法外循环次数相同,而内循环数显著减少.说明了DP-EM算法具有显式对偶函数的优势. 相似文献
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将准则法和数学规划法相结合,借助满应力准则将应力约束转化为动态尺寸约束,利用单位虚载荷法将位移约束转化为设计变量的显式表达式建立优化模型,然后用数学规划法求解;采用无量纲设计变量实现设计变量连接,对膜结构的厚度进行优化设计;根据对偶理论,应用对偶规划精确映射原问题,再按泰勒展式建立对偶问题的二阶近似。为了提高优化效率,采用射线步调整结构性态,运用粗选有效约束技术筛选约束,并采用主、被动变量循环确保收敛稳定。以MSC/Nastran软件作为结构分析的求解器,以MSC/Patran软件作为开发平台,完成了膜结构截面优化程序。对膜结构的单变位、多变位的结构优化问题进行了优化计算,并与MSC/Nastran优化模块的计算结果进行比较。算例结果表明程序的可靠性、高效性和稳定性以及理论算法的优越性。 相似文献
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IntroductionAsymplecticsystematicmethodology[1- 3]forelasticitywasestablishedbyZhongWan_xie .Hepresentedcreativelythedualvectorsandthesymplecticorthogonalrelationshipandopenedaworkplatformparalleledtothetraditionalelasticity[4 - 9].AnewdualvectorandanewdualdifferentialmatrixLwerepresentedforasymplecticsystematicmethodologyfortwo_dimensionalelasticityandaneworthogonalrelationshipwasdiscoveredforisotropicplaneproblems[4 ]byLuoJian_hui.Theneworthogonalrelationshipisgeneralizedfororthotropicelas… 相似文献
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The general conditions, obtained in Lacarbonara and Rega (Int. J. Non-linear Mech. (2002)), for orthogonality of the non-linear normal modes in the cases of two-to-one, three-to-one, and one-to-one internal resonances in undamped unforced one-dimensional systems with arbitrary linear, quadratic and cubic non-linearities are here investigated for a class of shallow symmetric structural systems. Non-linear orthogonality of the modes and activation of the associated interactions are clearly dual problems. It is known that an appropriate integer ratio between the frequencies of the modes of a spatially continuous system is a necessary but not sufficient condition for these modes to be non-linearly coupled. Actual activation/orthogonality of the modes requires the additional condition that the governing effective non-linear interaction coefficients in the normal forms be different/equal to zero. Herein, a detailed picture of activation/orthogonality of bimodal interactions in buckled beams, shallow arches, and suspended cables is presented. 相似文献
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Hamilton体系下环扇形域的Stokes流动问题 总被引:1,自引:0,他引:1
基于极坐标下Stokes流的基本方程,将径向坐标模拟为时间坐标,推导了Hamilton体系下Stokes流动问题的对偶方程,采用本征向量展开法对环扇形域Stokes流动问题进行了分析,并给出了相应的实际算例,其结果说明了本文方法的有效性。 相似文献
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A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. Moreover, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method. 相似文献