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1.
使用焦散线法与光弹法测定三维裂纹混合型应力强度因子 总被引:1,自引:0,他引:1
本文介绍了将焦散线法与应力冻结,“解冻”技术相结合,使焦散线法用于测量三维体内部裂纹前缘应力强度因子的实验方法,并针对复杂应力状态下三维裂纹前缘的不同应变奇异场,合理地综合运用焦散线法与三维光弹法,实际测量与分离了三维裂纹前缘混合型应力强度因子。 相似文献
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H. P. Rossmanith 《Journal of Elasticity》1982,12(2):193-200
By use of the complex stress function analysis of Muskhelishvili-Kolosov and conformal mapping procedures the general governing equations of the method of caustics or shadow spot technique have been developed for optically isotropic and anisotropic materials in static plane elasticity theory. Special cases of caustics formed about cutouts, cracks, and various singular regions in static elastic stress fields are obtained upon specialization. 相似文献
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Spatial decay estimates and upper bounds in elasticity for domains with unbounded cross-sections 总被引:1,自引:0,他引:1
RamÓn Quintanilla 《Journal of Elasticity》1997,46(3):239-254
In this paper we investigate spatial decay estimates and upper bounds for the solutions of elastic problems when the cross-sections of the three dimensional solid are semi-infinite strips. We obtain spatial decay estimates for the solutions of a static problem in the theories of homogeneous and isotropic linear elasticity and linearised elasticity. Energy bounds and some spatial decay estimates are obtained for the solutions of a dynamical problem in the case of anisotropic linear elasticity. For both kinds of problems we use the energy methods. 相似文献
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The optical method of caustics has been used with considerable success in recent years for determining stress-intensity factors in both static and dynamic problems. However the midplane analysis explaining the formation of transmission caustics has certain approximations that need to be examined. In this paper it is demonstrated that the midplane analysis is in good agreement with the numerical solution of the exact geometrical optical equations for mapping the light-ray path in a cracked plate. Since both these analyses are obtained by imposing a two-dimensional crack-tip stress field the sensitivity of the method to the deviations from the imposed stress field is examined next. The implications of this examination on the photoelastic technique are then discussed. 相似文献
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ntroductionThetheoreticalframeofnon_localelasticityhasbensetup[1,2].Manyimportantresultshavebengotbyusingnon_localtheorytosol... 相似文献
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We present a method for the parallel numerical simulation of transient three‐dimensional fluid–structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non‐overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time‐dependent domains. To this end, we present a technique to solve the incompressible Navier–Stokes equation in three‐dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time‐dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian–Eulerian formulation of the Navier–Stokes equations. Here the grid velocity is treated in such a way that the so‐called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well‐known MAC‐method to a staggered mesh in moving boundary‐fitted coordinates which uses grid‐dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second‐order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid–structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid–structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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《International Journal of Solids and Structures》2006,43(16):4739-4756
This paper presents an alternative efficient procedure to analyze plane elasticity problems of a circularly cylindrical layered media subject to an arbitrary point force. Based on the method of analytical continuation in conjunction with the alternating technique, the elastic fields of the three-phase media are derived. A rapidly convergent series solution which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem is obtained in an elegant form. As a numerical illustration, the interfacial stresses are presented for different material combinations and for different positions of the point force. 相似文献
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Axisymmetric problems in elasticity can be reduced to two dimensional ones, but they are a little more complicated than plane problems. Therefore, some special problems will be encountered in the boundary element programming of axisymmetric elasticity. In this paper, the methods to treat these problems and some remarks are given according to our experience in programming. Numerical examples are presented for the checking of these treatments. 相似文献
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We consider two problems of elasticity, namely, the Boussinesq problem about the action of a lumped force on a half-space and the related problem about the interaction of the half-space with a cylindrical rigid punch with plane base. In the classical statement, these problems have singular solutions. In the Boussinesq problem, the displacement under the action of the force is infinitely large, and in the punch problem, the infinitely large variable is the pressure on the punch boundary. In the present paper, these problems are solved with the use of relations of generalized elasticity derived regarding a medium element of small but finite dimensions rather than a traditional infinitesimal element. The structure parameter of the medium contained in the solutions can be determined experimentally. The obtained generalized solutions of the problems under study are regular. 相似文献
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带双裂纹的椭圆孔口问题的应力分析 总被引:5,自引:1,他引:5
利用复变方法,通过构造新的保角映射,研究了带双裂纹椭圆孔口的平面弹性问
题,得到了I型与II型裂纹问题应力强度因子的解析解.在极限情形下,
不仅可以还原经典的Griffith裂纹的结果,而且可模拟出十字裂纹和带双裂纹的圆
形孔口问题. 相似文献
13.
A. E. Alekseev 《Journal of Applied Mechanics and Technical Physics》2001,42(3):497-504
A method for constructing nonlinear equations of elastic deformation of plates with boundary conditions for stresses and displacements at the face surfaces in an arbitrary coordinate system is proposed. The initial three–dimensional problem of the nonlinear theory of elasticity is reduced to a one–parameter sequence of two–dimensional problems by approximating the unknown functions by truncated series in Legendre polynomials. The same unknowns are approximated by different truncated series. In each approximation, a linearized system of equations whose differential order does not depend on the boundary conditions at the face surfaces which can be formulated in terms of stresses or displacements is obtained. 相似文献
14.
Nowadays,thecurrenttheoriesofplatesandshells,suchasKirchhoff’sthinplatetheoryandReissner’smoderatelythickplatetheoryetc.,aree... 相似文献
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Nobuatsu Tanaka 《国际流体数值方法杂志》2000,34(5):403-424
This is the second report on the development of a highly accurate interpolation method, which is called cubic interpolation with volume/area (CIVA) co‐ordinates, for mesh‐free flow simulations. In this paper, the method of determining the c‐parameter of CIVA using a constant curvature condition is first considered for the two‐ and three‐dimensional cases. A computation of a three‐dimensional passive scalar advection problem is performed for accuracy verification and for comparison with widely used methods. Then, an application algorithm of the CIVA method respecting incompressible fluid simulation is presented. As the incompressible condition based on Lagrangian approaches causes problems, in this paper we consider the condition based on the conventional Eulerian approach. The CIVA‐based incompressible flow simulation algorithm enables a highly accurate simulation of many kinds of problems that have complicated geometries and involve complicated phenomena. To confirm the facts, numerical analyzes are executed for some benchmark problems, namely flow in a square cavity, free surface sloshing and moving boundary problems in complex geometries. The results show that the method achieves high accuracy and has high flexibility, even for the flows involving high Reynolds number, complicated geometries, moving boundaries and free surfaces. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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The resonance frequencies and stability of a nanobeam in a longitudinal magnetic field are investigated. To this aim, a three dimensional beam model is used in which the small-scale effect is taken into account based on the nonlocal elasticity theory. The Lorentz forces are obtained in terms of the local elastic rotations of the beam and the thermal stress due to current is modeled as an axial compressive force. Using the Galerkin method, the governing equations of motion are solved and the stability boundary of the nanobeam is determined. 相似文献
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针对三维摩擦接触问题的求解,给出了一种基于参变量变分原理的二阶锥线性互补法. 首先,基于三维Coulomb摩擦锥在数学表述上属于二阶锥的事实,利用二阶锥规划对偶理论,建立了三维Coulomb摩擦接触条件的参变量二阶锥线性互补模型,它是二维Coulomb摩擦接触条件参变量线性互补模型在三维情形下的自然推广;随后,利用参变量变分原理与有限元方法,建立了求解三维摩擦接触问题的二阶锥线性互补法. 较之于将三维Coulomb摩擦锥进行显式线性化的线性互补法,该方法无需对三维Coulomb摩擦锥进行线性化,因而在保证精度的前提下所解问题的规模要小很多. 最后通过算例展示了该方法的特点. 相似文献
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G. A. Papadopoulos 《Experimental Mechanics》2004,44(4):440-443
The objective of this paper is the experimental estimation of the load distribution in roller-bearing by the metrhod of caustics.
Contact problems have many practical and important applications1. For the solution of such problems, besides mechanical analysis, the experimental method of caustics2 can also be applied. The optical method of caustics is suitable for the experimental study of singularities in stress fields
created either by discontinuities or by loading. Previously, caustics has been applied to the study of singular stress fields
developed near concentrated or uniformly distributed loads which are applied along straight boundaries.3,4 In this work, it is applied to study the load distribution in rollerbearings. 相似文献
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A fourth‐order accurate solution method for the three‐dimensional Helmholtz equations is described that is based on a compact finite‐difference stencil for the Laplace operator. Similar discretization methods for the Poisson equation have been presented by various researchers for Dirichlet boundary conditions. Here, the complicated issue of imposing Neumann boundary conditions is described in detail. The method is then applied to model Helmholtz problems to verify the accuracy of the discretization method. The implementation of the solution method is also described. The Helmholtz solver is used as the basis for a fourth‐order accurate solver for the incompressible Navier–Stokes equations. Numerical results obtained with this Navier–Stokes solver for the temporal evolution of a three‐dimensional instability in a counter‐rotating vortex pair are discussed. The time‐accurate Navier–Stokes simulations show the resolving properties of the developed discretization method and the correct prediction of the initial growth rate of the three‐dimensional instability in the vortex pair. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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随机杆系结构几何非线性分析的递推求解方法 总被引:2,自引:0,他引:2
建立了随机静力作用下考虑几何非线性的随机杆系结构的随机非线性平衡方程. 将和
位移耦合的随机割线弹性模量以及随机响应量表示为非正交多项式展开式,运用传统的摄动方法获
得了关于非正交多项式展式的待定系数的确定性的递推方程. 在求解了待定系数后,利用非
正交多项式展开式和正交多项式展开式的关系矩阵,可以很方便地得到未知响应量的二阶统计矩.
两杆结构和平面桁架拱的算例结果表明,当随机量涨落较大时,递推随机有限元方法比基于
二阶泰勒展开的摄动随机有限元方法更逼近蒙特卡洛模拟结果,显示了该方法对几何非线性
随机问题求解的有效性. 相似文献