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本文采用完全非线性弹性理论,研究了一类不可压缩橡皮类材料[1]在Ⅰ型荷载作用下的平面应力问题.指出裂尖变形由两个收缩区和一个扩张区三部分组成.裂纹尖端应力、应变分别具有R-1、R-1/n的奇异性,当趋近裂尖时,厚度以R1/4n的方式趋于零,n为材料常数. 相似文献
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本文对平面应变情况下不可压缩橡胶类材料裂纹尖端弹性场进行了有限变形分析.裂纹尖端场被分为收缩区和扩张区.借助于新的应变能函数和变形模式,推出了尖端场各区的渐近方程,得到了尖端场的完整描述.本文对奇异性作了讨论,得到了不可压缩橡胶类材料裂纹尖端应力及应变分布曲线,揭示了裂纹尖端应力应变场的特性. 相似文献
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不可压缩粘性流问题的数值计算是现代计算物理中的一个重要问题,但至今尚缺乏系统的差分解法和严格的误差估计,主要困难在于怎样处理非线性项和描述其计算的稳定性。 本文根据物理原则和网格步长非零的特点,提出了加权平均守恒法、修正逆风法、人工振动补偿法和非线性项局部显式-隐式法。根据非线性格式特点提出了广义稳定性,并证明了二类不等式,它们相当有助于高维、非线性、显式-隐式加权的多层差分格式的严格误差估计。文中还把上述方法应用于三维涡度方程、n维Navier-Stokes方程和k,d,V-Burgers方程等。 相似文献
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从不可压缩粘性流体的Navier-Stokes方程出发,给出了在均匀来流条件下的圆管入口段层流流动中央区的速度分布及压力分布的解析解. 相似文献
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Adopting a form of strain-energy function for highly deformableincompressible elastic materials recently proposed by Ogden,we study in this paper two deformations of a circular cylindricaltube. In the first deformation the tube is inflated by increasingits internal radius by an assigned factor, and in the secondthe tube is turned inside out. In each case it is assumed thatthe tube is free of longitudinal constraint to the extent thatthe normal tractions on the end-faces have zero resultant. Inflationand eversion are therefore accompanied by axial shortening orelongation. Detailed numerical results are presented and comparedwith the limited experimental data to hand. Consideration isalso given to the existence and uniqueness of deformations whichpreserve the shape of the tube and comply with the assumed boundaryconditions. Restrictions are obtained on the material constantsappearing in the strain-energy function which ensure the existenceof precisely one such solution to the problem of combined inflationand extension, and sufficient conditions for the existence ofat least one solution to the eversion problem are also found.These requirements agree with criteria for "physically realisticresponse" which have been established elsewhere. 相似文献
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We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The
deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers.
The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from
Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak
solutions for this problem. 相似文献
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This article describes a procedure for numerical analysis of the dynamics of viscous incompressible fluids in the framework of the classical Navier-Stokes model using a system of equations that preserve the reciprocal relationship between the dynamic equations and the energy equation and ensure that the law of mass conservation is satisfied with fairly high accuracy in numerical work. We report the results of numerical analysis of time-dependent flows in sufficiently long channels with various boundary and initial conditions. The existence of nonclassical solution structures is demonstrated.__________Translated from Prikladnaya Matematika i Informatika, No. 17, pp. 13–30, 2004. 相似文献
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对一类组合金属材料,即不可压缩、刚塑性、与应变率相关、各向同性、运动中硬化的材料,在非局部接触的Coulomb摩擦边界条件下,考虑其准稳定成型问题.导出一组耦合的变分公式,证明(含延迟时间的)变刚度参数法的收敛性,证明了所得结果的存在性和唯一性. 相似文献
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This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that affects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity. 相似文献
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In this paper we study a finite-depth layer of viscous incompressible fluid in dimension , modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A uniform gravitational field acts perpendicularly to the flat surface, and we consider the cases with and without surface tension acting on the free interface. In addition to these gravity-capillary effects, we allow for a second force field in the bulk and an external stress tensor on the free interface, both of which are posited to be in traveling wave form, i.e., time-independent when viewed in a coordinate system moving at a constant velocity parallel to the rigid lower boundary. We prove that, with surface tension in dimension and without surface tension in dimension , for every nontrivial traveling velocity there exists a nonempty open set of force and stress data that give rise to traveling wave solutions. While the existence of inviscid traveling waves is well-known, to the best of our knowledge this is the first construction of viscous traveling wave solutions. Our proof involves a number of novel analytic ingredients, including: the study of an overdetermined Stokes problem and its underdetermined adjoint problem, a delicate asymptotic development of the symbol for a normal-stress to normal-Dirichlet map defined via the Stokes operator, a new scale of specialized anisotropic Sobolev spaces, and the study of a pseudodifferential operator that synthesizes the various operators acting on the free surface functions. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. 相似文献
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