共查询到20条相似文献,搜索用时 109 毫秒
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基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件,从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上,对Erdogan基本解的使用条件进行了注解,修正了Erdogan基本解的一些错误,并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法(spline fictitious boundary element method, SFBEM)计算程序,计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性. 相似文献
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平面十次对称准晶中Ⅱ型Briffith裂纹的求解 总被引:1,自引:0,他引:1
应用应力函数法,求解了二维十次对称准晶中的Ⅱ型Griffith裂纹问题。特别是把二维准晶的弹性力学问题分解成一个平面应变问题与一个反平面问题的叠加,通过引入应力函数,把平面应变问题的十八个弹性力学基本方程简化成一个八阶偏微分方程,并且求出了其在Ⅱ型Griffith裂纹情况的混合边值问题的解,所有的应力分量和位移分量都用初等函数表示出来,并且由此得出了准晶中Ⅱ型Griffith裂纹问题的应力强度因子和能量释放率。 相似文献
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1 引言 近年来,许多人对近不可压缩材料弹性问题的混合有限元方法进行了深入的研究,其中文[9]中讨论了一类包含位移、增广应力(augment stress)和压力等三种变量的混合有限元公式.研究这种方法的好处在于:人们可以直接求解工程上最感兴趣的应力变量.不幸的是,由于相应的有限元公式有着“鞍点结构”,根据Brezzi和Babuska的理论,当位移、应力和压力有限元空间满足“BB条件”时,方能证明有限元解的存在唯一性,而这一严格的条件 相似文献
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提出了基于改进位移模式的二维有限元线法超收敛算法.利用单元内部需满足平衡方程的条件,推导了超收敛计算的解析公式的显式,即将高阶有限元线法解的位移模式用常规有限元线法解的位移模式表示.用常规有限元线法解的位移模式与高阶有限元线法解的位移模式之和构造新的位移模式,基于线性形函数,采用变分形式推导了有限元线法求解的修正的常微分方程组.该算法在前和后处理同时使用超收敛计算公式,在原有试函数的基础上,增加了高阶试函数.使得单元内平衡方程的残差减少,从而达到提高精度的目标.对于二维Poisson方程问题,给出了有代表性的算例,结点和单元内的位移、导数的收敛精度得到了极大的提高. 相似文献
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在初等代数中,常用列表法解一元高次不等式.由于这一方法是以多项式理论为基础的,所以有很大的局限性.本文将以连续函数的介值定理为依据,阐明区间法解不等式的一般原理,从而将区间法推广到解更广的一类不等式(基本上可包括初等代数中的全部不等式),并且对解法作进一步的改善与简化. 先回顾一下介值定理,它的证明可在任何 相似文献
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基于修正偶应力理论,将Timoshenko微梁的应力、偶应力、应变、曲率等基本变量,描述为位移分量偏导数的表达式.根据最小势能原理,推导了决定Timoshenko微梁位移场的位移场控微分方程.利用级数法求解了任意载荷作用下Timoshenko简支微梁的位移场控微分方程,得到了反映尺寸效应的挠度、转角及应力的偶应力理论解.通过对承受余弦分布载荷Timoshenko简支微梁的数值计算,研究了Timoshenko微梁的挠度、转角和应力的尺寸效应,分析了Poisson比对Timoshenko微梁力学行为及其尺寸效应的影响.结果表明:当截面高度与材料特征长度的比值小于5时,Timoshenko微梁的刚度和强度均随着截面高度的减小而显著提高,表现出明显的尺寸效应;当截面高度与材料特征长度的比值大于10时,Timoshenko微梁的刚度与强度均趋于稳定,尺寸效应可以忽略;材料Poisson比是影响Timoshenko微梁力学行为及尺寸效应的重要因素,Poisson比越大Timoshenko微梁刚度和强度的尺寸效应越显著.该文建立的Timoshenko微梁模型,能有效描述Timoshenko微梁的力学行为及尺寸效应,可为微电子机械系统(MEMS)中的微结构设计与分析提供理论基础和技术参考. 相似文献
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Sylvia Serfaty Juan Luis Vázquez 《Calculus of Variations and Partial Differential Equations》2014,49(3-4):1091-1120
In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a “mean field” equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results. We also show that solutions with finite second moment and radial solutions admit an asymptotic large time limiting profile which is a special self-similar solution: the “elementary vortex patch”. 相似文献
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《European Journal of Operational Research》2001,134(1):29-42
A “two-echelon” newsboy problem considers the interactive decisions between the “manufacturer” and the “retailer” – now recognized as two separate entities. Earlier papers on this problem assumed that the two parties share the same market information. We extend this problem by studying the situation in which the retailer has better market information than the manufacturer. Presented are several decision models that should be useful for guiding a manufacturer's decisions. Moreover, solutions to these models lead to various unexpected and interesting conclusions. For example, we found that improved retailer's market-knowledge always benefits the manufacturer and the system, though not necessarily the retailer himself. In contrast, improved manufacturer's knowledge benefits only the manufacturer himself at the expense of the retailer and of the system. 相似文献
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《Journal of Applied Mathematics and Mechanics》1999,63(1):55-62
The “inviscid” nature of the asymmetry is demonstrated using the example of the separating unsteady flow of an ideal incompressible fluid around a cylinder which is expanding at a constant velocity, that is, a non-steady-state analogue of steady-state flow around a cone at an angle of attack. An asymmetric flow structure is realized for a symmetrical positioning of the points of separation of the vortex sheets. This is evidence of the secondary role of viscosity, which can manifest itself through an “inverse” effect on the position of the points of separation. New asymmetric solutions and processes by which they arise, which are different from the classical bifurcation of the symmetric solution, are found. Together with an investigation of stability, an analysis of the global pattern of “self-similar” streamlines is carried out in the selection of the “realizable” solutions. The global pattern must correspond to the scheme adopted when constructing the theoretical model. 相似文献
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《偏微分方程通讯》2013,38(11-12):2211-2226
We prove the uniqueness of mild solutions and very weak solutions of the Navier-Stokes equations in C([0,T); LN (Ω)), where Ω is the whole space R N , a regular domain of R N or the torus T N with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a “dual” problem, a decomposition of the solutions and a “bootstrap” argument. 相似文献
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Yi Zhu 《Journal of Functional Analysis》2018,274(7):2039-2060
In this paper, we prove the global existence of small smooth solutions to the three-dimensional incompressible Oldroyd-B model without damping on the stress tensor. The main difficulty is the lack of full dissipation in stress tensor. To overcome it, we construct some time-weighted energies based on the special coupled structure of system. Such type energies show the partial dissipation of stress tensor and the strongly full dissipation of velocity. In the view of treating “nonlinear term” as a “linear term”, we also apply this result to 3D incompressible viscoelastic system with Hookean elasticity and then prove the global existence of small solutions without the physical assumption (div–curl structure) as previous works. 相似文献
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T. A. Yakubenko 《Computational Mathematics and Mathematical Physics》2006,46(6):1073-1080
Effective properties of composite and porous materials are determined by using an approach based on two-scale asymptotic expansions. Explicit approximate formulas are derived for the effective moduli of composite and porous materials of elongated structures. A numerical method is proposed for finding solutions to cell problems, which are used to determine “exact” effective moduli. Examples are computed for a two-dimensional porous medium with variously shaped pores and various degrees of “elongation.” The effective moduli produced by the explicit approximate formulas prove to be similar to those found by numerically solving cell problems. 相似文献
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Michael Shulman 《Annals of Pure and Applied Logic》2019,170(4):465-504
We study elementary theories of well-pointed toposes and pretoposes, regarded as category-theoretic or “structural” set theories in the spirit of Lawvere's “Elementary Theory of the Category of Sets”. We consider weak intuitionistic and predicative theories of pretoposes, and we also propose category-theoretic versions of stronger axioms such as unbounded separation, replacement, and collection. Finally, we compare all of these theories formally to traditional membership-based or “material” set theories, using a version of the classical construction based on internal well-founded relations. 相似文献