共查询到20条相似文献,搜索用时 93 毫秒
1.
本文综合应用无网格方法(EFGM)、线性粘弹性与弹性力学之间的对应原理,Laplace变换和逆变换等方法求解了拟静态平面弹性和粘弹性力学问题。首先,利用Laplace变换和逆变换推导了平面问题的粘弹性本构关系,建立了拟静态粘弹性平面问题的边值问题;其次,利用粘弹性与弹性力学之间的对应原理得到了Laplace变换域中平面问题的基本方程,在Laplace变换域中建立了相应的泛函,并得到了用无网格方法离散的控制方程;同时,求解了几个拟静态弹性和粘弹性平面问题,给出了它们的表达式和数值结果;最后,采用Laplace逆变换和数值逆变换,得到了粘弹性力学平面问题在物理空间中的解,并比较了由解析解和无网格数值方法所得到的数值结果,可以看到它们是非常吻合的。说明本文方法的正确性和有效性。 相似文献
2.
本文以位移为基本未知量,利用非线性粘弹性力学中的Leaderman本构关系和线性几何假设,建立了非线性粘弹性平面问题的数学模型;在粘弹性泊松比为常数的情况下,利用Titchmarsh定理和Laplace变换法证明了非线性粘弹性平面问题与非线性弹性平面问题之间存在着某些对应关系,对应关系为粘弹性问题的求解提供了一种新的思路,利用这些关系可直接从相应弹性问题获得粘弹性平面问题的部分响应,与传统的时域有限差分法相比,计算时间明显缩短,另外,对应关系也揭示了粘弹性结构的失记效应,即结构的部分响应仅与外部输入的现时值有关,而与其历史无关。 相似文献
3.
4.
5.
6.
一维流体饱和粘弹性多孔介质层的动力响应 总被引:2,自引:1,他引:2
本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。 相似文献
7.
建立描述SHPB实验中线性粘弹性试件内部应力波传播的控制方程组,根据试件两端与入射杆及透射杆接触的应力波特征关系给出耦合边界条件.对方程组和定解条件进行Laplace变换,求得试件内部应力在变换域像函数的表达式.采用数值反变换技术进行反Laplace变换,获得试件两端的应力时程曲线.对现有的固定Tal-bot反变换算法进行改进:将入射波像函数分解为基本部分和延迟部分,利用固定Talbot算法对基本部分入射波作用下的波动问题求解,其他部分的解通过延迟定理得到,最终解为两部分的叠加.采用这种改进算法得到的不同入射波下粘弹性试件的内部应力解与传统的基于特征线数值模拟方法的结果吻合.在此基础上探讨了粘弹性试件的几何参数和材料本构参数对透射波波形的影响. 相似文献
8.
9.
10.
哈密顿体系与弹性楔体问题 总被引:2,自引:0,他引:2
将哈密体系引入到级坐标下的弹性力学楔体问题,利用该体系辛空间的性质,将问题化为本征值和本征向量求解上,得到了完备的解空间,从而改变了弹性力学传统的拉格朗日体系以应力函数为特征的半逆法的讨论去解决该类问题的思路,给出了一条求解该类问题的直接法。 相似文献
11.
A.M.ZENKOUR 《应用数学和力学(英文版)》2011,32(4):507-520
An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain
assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material.
It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic
properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions,
the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin’s
approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness
variation, constitutive, time parameters on the radial displacement, and stresses are investigated. 相似文献
12.
13.
A combined approach of the Laplace transform and Padé approximation solving viscoelasticity problems
《International Journal of Solids and Structures》2007,44(1):66-76
In this paper the Laplace transform method is combined with Padé approximations to solve linear viscoelastic problems. This approach allows to avoid the usual difficulties of original function determination. An algorithm is given to find solution with arbitrary precision. As an example the solution for problem of viscoelastic orthotropic half-plane stress state under concentrated normal force is given. 相似文献
14.
I. Yu. Tsvelodub 《Journal of Applied Mechanics and Technical Physics》2002,43(3):445-447
An isotropic linearelastic (viscoelastic) plane containing various physically nonlinear elliptic inclusions is considered. It is assumed that the distances between the centers of the inclusions are much greater than their dimensions. The problem is to determine the orientation of the inclusions and the loads applied at infinity which ensure a specified value of the principal shear stress in each inclusion. Necessary and sufficient conditions of existence of the solution of the problem are formulated for a plane strain of an incompressible inhomogeneous medium. 相似文献
15.
无限粘弹性平面中孔洞扩展的时变力学解析解 总被引:3,自引:0,他引:3
从粘弹性时变力学基本方程出发,针对Maxwell本构模型,导出了双向等压下粘弹性平面中圆孔半径任意规律扩展时的时变力学解析解.在内径线性时变时,其结果与用对应原理法得出的解相同,其解的可靠性得到验证.与对应原理法相比,文中的结果适用于半径任意时变情况,更具一般性. 相似文献
16.
17.
S. N. Aristov O. I. Skul'skii 《Journal of Applied Mechanics and Technical Physics》2002,43(6):817-822
An exact analytic solution of the problem of a generalized viscoelastic Jeffreys fluid flow in a plane channel under the action of a pressure gradient is found. The velocity profiles are obtained in a parametric form with a velocity gradient taken as a parameter. The critical values of the pressure gradient are determined, which, when exceeded, lead to weak tangential discontinuities in the longitudinal velocity profile. When the pressure gradient changes smoothly over some range of parameters, a hysteresis loop emerges on the graph of the flow rate versus the pressure gradient. 相似文献
18.
IntroductionTheedgecrackprobleminasemi_infiniteplanewasconsideredbymanyinvestigators.UsingtheFredholmintegralequationandthealternatingmethod ,anedgecrackprobleminasemi_infiniteplanewassolved[1].Theobtainedresultsarelimitedtothecasethattheedgecrackisnorm… 相似文献
19.
20.
Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account 总被引:1,自引:0,他引:1
Motivated by recent progress in viscoelastic indentation analysis, the identification of viscoelastic properties from nanoindentation
test data taking the real tip geometry into account is presented in this paper. Based on the elastic solution of the indentation
problem, the corresponding viscoelastic solution is obtained by the application of the method of functional equations. This
general solution, which accounts for the real geometric properties of the indenter tip, is specialized for the case of a trapezoidal
load history, commonly employed in nanoindentation testing. Three deviatoric creep models, the single dash-pot, the Maxwell,
and the three-parameter model are considered. The so-obtained expressions allow us to determine viscoelastic model parameters
via back calculation from the measured load–penetration history. The presented approach is illustrated by the identification
of short-term viscoelastic properties of bitumen. Hereby, the influence of loading rate, maximum load, and temperature on
the model parameters is investigated. 相似文献