Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

The Scattering of SH Wave in a Nano Hole Embedded the Infinite Inhomogeneous Medium

Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.

THE GENERAL SOLUTION FOR THE STRESS PROBLEM OF CIRCULAR CYLINDRICAL SHELLS WITH AN ARBITRARY CUTOUT

In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution can be normal and effective by means of this method. Numerical results for stress concentrations in the shell with a circular, elliptic cutout are graphically presented.

ON THE STRESS CONCENTRATION IN THICK CYLINDRICAL SHELLS WITH AN ARBITRARY CUTOUT

In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained. The stress problem can be reduced to the solution of an infinite algebraic equation series, and can be normalized by means of this method. Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.

Seepage flow around twin circular tunnels in anisotropic ground revealed by an analytical solution

A new analytical solution is proposed for steady seepage flow around twin circular tunnels in fully saturated anisotropic ground.The solution is an exact one that fully satisfies all the boundary conditions and precisely considers the different permeabilities along two direc-tions and the interactions between twin tunnels.The solution provides a fast approach for the estimation of the seepage field and a useful tool for design optimization.The solution is successfully addressed using problem equivalence and the Schwartz alternating method com-bined with a mapping function.Using a coordinate transformation of the governing equation,the anisotropic problem of circular tunnels is first equivalent to that of isotropic elliptical tunnels,and the length of the ellipse along the anisotropic axis depends on the anisotropic permeability ratio.The Schwartz alternating method is then employed to address the solution of equivalent elliptical twin tunnel prob-lems,where a mapping function,with which an elliptical tunnel in the half-plane can be mapped into an annulus in the image plane,is introduced to solve the single tunnel problems in each iterative step.The iterative procedure is quite simple and efficient in its calculations and achieves good convergence,and the analytical solution agrees very well with the numerical results to reflect its high precision in the entire ground.Finally,parametric studies are performed to investigate the influences of the anisotropic permeability and tunnel spacing on the seepage field.This is the first study to provide the exact analytical solution of the seepage field of twin tunnel problems in aniso-tropic ground,and the procedure can be extended to multiple tunnel problems.