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The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues, The latter group can be further divided into α- and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed. 相似文献
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Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media 总被引：2，自引：2，他引：2
INTRODUCTION The traditional method of solving solutions of the transversely isotropic piezoelectric media belongs to Lagrange formulation so that the method of sepa- ration of variables cannot be applied due to the in- volvement of high order partial differentiation in the Euclidian space and is difficult for some problems. New theoretical system or method is a key for the investigation of piezoelectric materials. Since the foundational equations (Sosa and Pak, 1990) in transversely iso… 相似文献
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INTRODUCTION Since the phenomenon of piezoelectricity in natural crystals was discovered in 1880, it has been applied in many fields, such as smart structure, sensing devices and active control, because of its special properties. Combining electrical behavior with mechanical deformation is the special property which attracted great interest of researchers. Many models have been developed for studying piezoelec- tric effects. Dunn and Wienecke (1996) used Green’s functions for transverse… 相似文献
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与传统的半逆解法不一样,采用弹性力学平面直角坐标系辛体系,运用分离变量法,求出矩形梁非齐次边界条件的解.辛解法能够有效处理各种边界条件,特别是矩形梁受线性分布荷载时,显示该方法的有效性. 相似文献
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K. F. MARTIN 《European Journal of Engineering Education》1986,11(4):451-457
CAE has enabled vibrational problems, which were regarded as intractable 20 years ago, to be solvable by students using computational support. The paper describes a problem set to final year undergraduates which concerns the torsional vibrational response of a three degrees of freedom system which is subjected simultaneously to three different arbitrarily varying torques. The solution involves the use of standard library routines for matrix multiplication and eigensolutions, a Runge-Kutta routine to solve a second order differential equation and general competence in writing software. 相似文献
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马杭 《上海大学学报(英文版)》2002,6(2):101-110
With the aid of the properties of the hypersingular kernels,a geometric conversion approach was presented in this paper.The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method.Based on the conversion,the hypersingularity in the boundary integrals could be lowered by one order,resulting in the simplification of the computer code.Moreover,an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case.The approach is simple to use,which can be inserted readily to computer code,thus getting rid of the dull routine deduction of formulae before the numerical implementatins,as the expressions of these kernels are in general complicated.The numerical examples were gien in three-dimensional elasticity,verifying the effectiveness of the proposed approach,which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary. 相似文献
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阐述了应用Matlab解决数学问题的具体做法,探讨了利用Matlab解决数值微分、数值积分和非线性方程的数值解等问题。结果表明,该方法能够更加方便快捷地解决数学问题。 相似文献
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陈杰东 《内江师范学院学报》2005,20(6):88-90
由于几何拓扑网络设计中许多问题都可以归结为极小极大问题，而熵函数法正是求解极小极大问题的一个强有力的数学工具，所以本文试图运用熵函数法求解一些几何拓扑网络设计问题．理论分析和试验结果均表明了熵函数法求解这些问题的有效性． 相似文献
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由于几何拓扑网络设计中许多的问题都可以归结为极小极大问题,而熵函数法正是求解极小极大问题的一个强有力的数学工具,所以本文试图运用熵函数法求解一些几何拓扑网络设计问题。理论分析和试验结果均表明了熵函数法求解这些问题的有效性。 相似文献
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提出了一种利用函数逼近法求解常微分方程(ODE)初值问题的数值方法。在多项式空间中寻找函数,在某种距离意义下尽可能满足微分方程,从而获得微分方程的近似解。通过理论分析可知,求解常微分方程的欧拉法、梯形法是该方法的特例,数值试验进一步表明了该方法的有效性。 相似文献
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以二维弹性力学问题为研究对象,采用常单元和线性非连续元离散边界积分方程,给出系数矩阵计算的精确表达式。数值实施证实此方法的准确性。和有限元相比,边界元的目的非常明确。它还使数值计算的维数降低一阶,所以计算效率也更高。 相似文献
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以二维弹性力学问题为研究对象，采用常单元和线性非连续元离散边界积分方程，给出系数矩阵计算的精确表达式。数值实施证实此方法的准确性。和有限元相比，边界元的目的非常明确。它还使数值计算的维数降低一阶，所以计算效率也更高。 相似文献
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In the investigation of accidental explosion scene,the damage on the glass is one of the typical traces which can be used to decide the characteristic of the explosion source.To analyze the response of glass under the blast load,a numerical model was developed.In the model,the brittleness glass model was adopted.A 'node release' method,which had some special merits compared with the erosion method was used to simulate the rupture of the glass In the calculation,several problems which play major role in the response of the glass were discussed.The velocity and the displacement of the glass fragment were two major factors.The numerical results are very helpful for the design and hazard assessment. 相似文献
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INTRODUCTION Structural damage detection technique addresses the problem of how to locate and detect damage that occurred in a structure by using the observed changes of its dynamic and static characteristics. In recent years, damage assessment of structure has drawn wide attention from various engineering fields. Gen-erally, the existing approaches proposed in this area can be clarified into two major categories: the dy-namic identification methods using dynamic test data and the static … 相似文献
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验证了带五次项的非线性Schrdinger方程满足电荷守恒律和能量守恒律,讨论了该方程的Hamilton形式,并构造了它的单辛格式,最后用数值实验验证了该格式具有长时间的数值模拟能力. 相似文献
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通常,弹性大的商品降价能提高收益,弹性小的商品提价能提高收益。因而往往对需求弹性大的商品采取降价策略,对需求弹性小的商品采用提价策略。但价格策略的运用是有条件的,首先要考虑成本,其次是有效范围。此有效范围就是零增益点。该点可用函数△P/P=E-1/E=1-1/E（其中:E>1）表述,也可用图形说明。 相似文献
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Pure bending of simply supported circular plate of transversely isotropic functionally graded material 总被引：3，自引：0，他引：3
LI Xiang-yu DING Hao-jiang CHEN Wei-qiu 《浙江大学学报(A卷英文版)》2006,7(8):1324-1328
INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu… 相似文献