Asymptotic approach to analyze singular stress state in anisotropic multi-material: Application to the rivets

The problem of stress singularities due to multi-material junctions is described in this paper. A semi-analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions. The advantage of the present method is the quasi-explicit knowledge of the stress and displacement fields around the junctions. Thus, after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials, numerical results are presented concerning various configurations of an assembly with rivets included in a bi-layer composite that illustrate this method.     

Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.     

Determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments

In this paper, theoretical formulations based on the Stroh’s complex function approach were used to find the displacement field and H-integral of a sharp V-notch formed from several anisotropic materials. Displacements from the image-correlation experiments are then substituted into the least-squares formulation to find V-notch stress intensity factors (SIFs) in multi-material anisotropic wedges. Validations using the H-integral indicate that the experimental SIFs evaluated from the proposed method of acceptable accuracy. The major advantage is that the proposed method only requires displacements inside the specimen, and displacements near the notch tip, specimen boundaries, or notch surfaces are not necessary.     

Regularization in 3D for anisotropic elastodynamic crack and obstacle problems

We propose, in this paper, a unified method of generating a regularized integral equation in the double layer potential approach for 3D anisotropic elastodynamics. Our regularization preserves the causality in the time-domain. The method is based on a special decomposition of the hypersingular kernel which appears in the integral representation of the stress tensor.     

Thermally conductive elliptic inhomogeneities in 2D anisotropic solids

The problem of a thermally conductive elliptic hole embedded in an anisotropic thermoelastic solid under a remote uniform heat flow is considered. For the plane problem, solutions are derived by the use of an extended thermoelastic version of the Stroh formalism. The hoop stress around the elliptic hole is obtained in an explicit real form. We analyze the influence of the interior thermal conductivity and the cavity thickness on the temperature and stress on the boundary points of the hole. By comparison with the thermally insulated cavity, we show that the consideration of the interior conductivity may lead to significantly different thermomechanical behaviors. Ana Ursescu on leave from Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie no. 13, Bucharest, Romania.     

各向异性势问题充要的随机边界积分方程

本文针对各向异性势问题提出了一类充分必要的随机边界积分方程。数值计算结果表明在退化尺度附近，充要的随机边界积分方程较习用的随机边界积分方程有较大的优越性。     

Singularities on wave fronts of slow waves in anisotropic fluid-saturated porous media

Energy focusing is found on the wave fronts of slow waves, which is a new propagation characteristic for slow waves in fluid-saturated porous materials. The material parameters, as well as the propagation directions, are chosen as the control parameters. Combined with the two axial variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the propagation characteristic of slow waves in anisotropic fluid-saturated porous materials is discussed. The correspondence between the focusing on the wave fronts and the contours of zero Gaussian curvature on the slowness surface is explored. The development of the focusing patterns is investigated and the distinct trends in the energy flux focusing structures are revealed. This is helpful in further understanding the roles of the pore fluid in the damage of the fluid-saturated porous media.     

各向异性位势问题边界元法中几乎奇异积分的解析算法

导出了一种解析积分算法,精确计算了二维各向异性位势问题边界元法中近边界点的几乎奇异积分。对线性单元,几乎奇异积分可用解析公式直接计算。对二次单元,可将其细分为几个线性单元,采用该解析公式间接近似计算。当内点离积分单元较远时,仍然保持常规高斯数值积分模式;而当内点离其较近时,高斯积分结果失效,采用该解析积分取代高斯数值积分。数值算例证明了该算法的有效性和精确性。二次元比线性元计算结果更精确。     

Two contact problems in anisotropic thermoelasticity

Some basic equations recently derived by Clements are used to consider two contact problems in anisotropic thermoelasticity. The first problem concerns the determination of the thermal stress in an anisotropic half-space due to a heated load over a section of the boundary. The second problem concerns the indentation of a half-space by a heated rigid punch. In particular, indentation by a cylindrical punch is considered and some numerical results obtained.

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Zusammenfassung Einige Grundgleichungen, die Clements neulich abgeleitet hat, dienen als Grundlage, um zwei Kontaktprobleme in der anisotropischen Thermoelastizität zu betrachten. Im ersten Problem geht es darum, die Wärmespannung in einem anisotropischen Halbraum zu bestimmen, die von einer erhitzten Last über einem Teil der Grenzlinie hervorgebracht wird.Im zweiten Problem geht es darum, einen Halbraum durch eine erhitzte starre Punze auszuzacken. Insbesondere wird das Auszacken durch eine kreisartize Punze betrachtet, und es ergeben sich numerische Angaben.

     

Edge Singularities and Kutta Condition in 3D Aerodynamics

This review paper presents a unified formulation of the Kutta condition for steady and unsteady flows, implemented by removing all unbounded velocity singularities (of powerlaw and logarithmic type) at the trailing edge, and including nonlinear wakes and thick sweptback wings. A suitable boundary integral approach is adopted and the uniqueness issue is discussed for several wing configurations of interest in aerodynamics.Sommario. Si presenta una formulazione unificata della condizione di Kutta per flussi stazionari e non stazionari, ottenuta imponendo la limitatezza della velocità al bordo d'uscita, e valida nel caso nonlineare anche per ali a freccia. Si utilizza un opportuno approccio integrale al contorno e si discute il problema dell'unicità per svariate configurazioni alari di interesse nelle applicazioni.     

Navier solution for the elastic equilibrium problems of anisotropic skew thin plate wite variable thickness in nonlinear theories

This paper discusses the elastic equilibrium problems of anisotropic skew thin plate ofvariable thickness simply supported on all four sides in nonlinear theories,and uses theNavier method to seek an approach to the problem,and to illustrate the solution with theexamples.In conclusion,the mention is made of the scope of application and theconvergency of the solution.     

On some crack problems in anisotropic thermoelasticity

Some basic equations recently derived by Clements are used to consider crack problems in anisotropic thermoelasticity. The problems concern a single crack in an anisotropic material in which the displacement and stress are independent of one Cartesian coordinate. No symmetry elements of the material are assumed and the temperature, displacement and stress fields are determined for an arbitrary distribution of temperature or heat flux over the crack faces.     

Analysis of 2D infinite anisotropic elastic strips and semi-strips

Summary  Using Stroh's formalism and the theory of analytic functions, simple and explicit solutions for a line dislocation in an infinite anisotropic elastic strip are obtained. The two boundaries of the strip are free of traction. The problem of a dislocation in an anisotropic elastic semi-infinite strip with traction-free boundaries is also studied. A set of singular integral equations governing the unknown functions is derived. When the medium is orthogonal anisotropic and the coordinate axes x ₁ x ₂ x ₃ are coincident with the material principal axes, all the eigenvalues of the material coefficient matrix are pure imaginary. Explicit expressions of the unknown functions are given for this case. The results obtained are valid not only for plane and anti-plane problems but also for coupled problems between in-plane and out-of-plane deformations. Received 30 October 2000; accepted for publication 28 March 2001     

Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems

A numerical solution for shallow-water flow is developed based on the unsteady Reynolds-averaged Navier–Stokes equations without the conventional assumption of hydrostatic pressure. Instead, the non-hydrostatic pressure component may be added in regions where its influence is significant, notably where bed slope is not small and separation in a vertical plane may occur or where the free-surface slope is not small. The equations are solved in the σ-co-ordinate system with semi-implicit time stepping and the eddy viscosity is calculated using the standard k–ϵ turbulence model. Conventionally, boundary conditions at the bed for shallow-water models only include vertical diffusion terms using wall functions, but here they are extended to include horizontal diffusion terms which can be significant when bed slope is not small. This is consistent with the inclusion of non-hydrostatic pressure. The model is applied to the 2D vertical plane flow of a current over a trench for which experimental data and other numerical results are available for comparison. Computations with and without non-hydrostatic pressure are compared for the same trench and for trenches with smaller side slopes, to test the range of validity of the conventional hydrostatic pressure assumption. The model is then applied to flow over a 2D mound and again the slope of the mound is reduced to assess the validity of the hydrostatic pressure assumption. © 1998 John Wiley & Sons, Ltd.     

Pressure potential formulation of 2-D stokes problems in multiply-connected domains

In general Stokes problems, no boundary conditions exist for the pressure. But pressure is an L²(Ω) function and can uniquely be represented as the divergence of a precisely defined vector field. In the 2-D case, this vector field can in turn be represented as the sum of a gradient (of a pressure-potential) and the curl of a second scalar potential. The latter potential is entirely determined by the first one. A variational equation is obtained for such pressure potential class, which exists and is uniquely characterized. This variational problem is well-posed. Finite element approximations can easily be realized and ensure high convergence rates for the L²(Ω) norm of the pressure.