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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
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幂率型非线性粘弹性裂纹尖端场 总被引:2,自引:0,他引:2
研究幂率型非线性粘弹性裂纹尖端场.为了推导的需要,首先列出了幂率型硬化材料的HRR奇异场和高阶渐近场.论证了它们实质上是各向同性、不可压缩、幂率型、非线性弹性裂纹尖端场.回颐了求解非线性粘弹性问题的弹性回复对应原理之后,给出了在第一类边界条件下求解幂率型非线性粘弹性材料裂纹问题的对应原理.得到了幂率型非线性粘弹性材料,特别是改性聚丙稀的裂纹尖端应力、应变和位移场的解答. 相似文献
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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
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开孔粘弹性薄板的非线性数学模型 总被引:2,自引:0,他引:2
应力函数的多值性和位移单值性要求,是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘性力学中的Boltzmann蠕变律,把开孔弹性薄板大挠度问题的一般数学理论推广到开孔弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上,提出了开孔粘弹性薄板的控制方程和初、边值条件,系统地建立了开也粘弹性薄板非线性分析的三类初一边值问题。 相似文献
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粘弹性界面裂纹奇异场 总被引:1,自引:0,他引:1
对于许多粘弹性问题,通常可以利用对应性原理,即由弹性问题的结果得到对应的粘弹性问题在拉普拉斯变换域内的解,再通过反演变换求得最终时域中的解.但是,由于界面裂纹场存在着振荡奇异性,弹性问题解的形式就已经非常复杂,对应的粘弹性问题要通过反演变换直接求得准确的解析解几乎是不可能的.本文在利用对应性原理时做了更简单的准静态处理,即将弹性结果中的材料参数用粘弹性材料参数做对应替代,得到了粘弹性界面裂纹场近似的经典解,并与有限元分析结果作了比较.同时,利用Comninou接触模型,对粘弹性界面裂纹在远场拉剪混合加载情况下的裂尖应力场和接触区做了考察,并与经典解作了比较. 相似文献
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各向异性非线性固体力学的规范空间理论 总被引:8,自引:0,他引:8
本文在弹性规范空间概念基础上,利用非平衡态热力学理论,证明了各向异性固体力学非线性问题规范空间场以及不可逆过程本征解的存在。损伤对结构刚度的弱化效应和损伤诱发各向异性效应分别反映在本征弹性和相应的模态向量中。在简正坐标中考察各向异性体变形时,材料的行为以六个普通的粘弹性Maxwell方程描述,总的响应由模态叠加得到。以此为基础给出的非线性本构方程具有坐标转换不变性,最后给出了二个具体的算例。 相似文献
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考虑轴和盘的质量及轴的几何非线性,建立了在周期轴向载荷作用下具不对称粘弹性支承弹性盘轴转子系统的非线性动力学方程.基于Lyapunov运动稳定性理论和Floquet判据,对系统的线性和非线性动力稳定性进行了分析. 相似文献
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求解非线性振动问题的一种新方法 总被引:1,自引:0,他引:1
首先把描述非线性振动的微分方程归结为一非线性积分微分方程,然后把此积分微分方程的求解转化为一无穷阶的非线性代数方程组的求解。从理论上讲,可得到满足任何精度要求的周期解。本文用此方法对Dufing系统进行了分析。 相似文献
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Parameter Iteration Method for Solving Nonlinear Problem 总被引:1,自引:0,他引:1
林建国 《应用数学和力学(英文版)》2001,22(7):836-841
IntroductionTherearemanymethodsforsolvingnonlinearproblemuptonow .Forexample,alotofperturbationmethodscanbeusedtosolvetheweaknonlinearproblems,buttheyaretoostronglydependentupontheso_called“smallparameters.”TheinterpolationperturbationmethodproposedbyY… 相似文献
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We consider classical solutions of the equilibrium equations of nonlinear elastostatics under prescribed boundary displacements
and body forces, both of which depend on a loading parameter. We employ recent results on global continuation [HS] that establish
general existence of global continua of solutions in nonlinear elastostatics. Under reasonable hypotheses on the stored energy
function we prove the existence of an unbounded branch of globally injective solutions to the boundary value problem.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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Abstract We consider the nonlinear aeroelasticity problem of the interaction between a viscous, incompressible fluid and Lin elastic solid undergoing large displacement. The non-linearities of the problem formulation include the solid and fluid governing equations. as well as thc dependence of the How geometry on the solid deformation. The resulting coupling is thus two-way. We develop domain-decomposition methods for solution and sensitivity analysis of the coupled problem. The domain decomposition is in the form of a block-Gauss-Seidel-like prcconditioncr that decomposes ihc coupled-domain problem into distinct nonovcrlapping fluid and solid subdotnain problems. The preconditioner thus enables exploitation or single-domain algorithms for solid and fluid mechanics discretization and solution. On the other hand, two-way fluid-solid coupling is retained within the residuals, which is essential for correct sensitivities. Sensitivities of field quantities can be found with little additional work beyond that required for solving the coupled fluid-solid system. The methodology developed here is illustrated by the solution of a problem of viscous incompressible flow about an infinite clastic cylinder. Sensitivities of the resulting velocity and displacement fields with respect to elastic modulus and fluid viscosity are computed. 相似文献
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A classical problem in the framework of nonlinear elasticity theory is the characterization of the materials that may sustain a pure state of anti-plane shear in the absence of body forces. This problem has been solved by Knowles and by Hill in the framework of isotropic and incompressible elasticity in the seventies. Here we provide a simpler and shorter proof of these classical results. Moreover, we extend these results to nonlinear elastodynamics and we provide some new special solutions. 相似文献
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空间杆系结构实用几何非线性分析 总被引:6,自引:0,他引:6
从简单实用的角度论述了空间杆系结构的几何非线性分析方法。文中分析了非线性有限元方法的求解过程,特别强调决定几何非线性收敛结果的关键问题,即由节点位移增量计算单元的内力增量。通过引入转随转坐标系,论述了平面和空间梁单元小应变时单元内力增量的计算问题。针对杆系结构的大应变问题,从有限应变理论出发进行分析,提出了对该问题的有效处理方法,并且用实例进行了验证。计算结果表明,该实用几何非线性分析方法是可靠和有效的。 相似文献
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The problem of beam-plates with a delamination located at an arbitrary site undergoing non-linear free vibration without damp
is investigated. For this problem, nonlinear governing equations as well as the continuity, equilibrium and compatibility
conditions are established. The Galerkin method and harmonic balance method are employed to find solutions. Finally, in some
examples amplitude-frequency curves of the delaminated structure are presented in order to reveal some special dynamic features.
Supported by the National Natural Science Foundation of China (No. 19872024). 相似文献
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M. Aron 《Journal of Elasticity》2000,60(2):165-172
The paper is concerned with solvability of a mixed boundary value problem of place and traction that describes the straightening
of annular cylindrical sectors composed of unconstrained isotropic hyperelastic solids. The existence and uniqueness of solutions
is discussed and several examples are exhibited.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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The assumption of constant local coefficients is one of the first restrictions in most of the smoothing theories for transport in porous media. In this paper we present a formal analysis of the effects produced by nonconstant local transport coefficients on the nonlinear behavior of the effective transport properties. In particular, we use the volume averaging method to study heat transport in a two-component system considering the local thermal conductivities as analytical functions of the temperature. Within this approach we obtain a general expression for the effective nonlinear thermal conductivity dependence on the averaged temperature gradient. The important result is that the effective conductivity is obtained by a linearly bounded problem (the closure problem), just as if the conductivities were constants, by replacing the constant conductivities by the actual temperature dependent ones. As an example, we model the porous medium as cylindrical inclusions in a periodic array and solve the closure problem for the case of the one-equation model. We analyze the values of the second derivative of the thermal conductivity with respect to the temperature to establish the range where the nonlinear corrections must be considered to correctly describe the effective transport. 相似文献