Boundary Perturbation Solution for Nearly Circular Holes and Rigid Inclusions in an Infinite Elastic Medium

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Thushan C. Ekneligoda ◽  
Robert W. Zimmerman
Keyword(s):  
Elastic Medium ◽  
Good Accuracy ◽  
Hydrostatic Stress ◽  
Perturbation Solution ◽  
Boundary Perturbation ◽  
Pore Compressibility ◽  
Effective Bulk Modulus ◽  
Circular Rigid Inclusion ◽  
Boundary Perturbation Method ◽  
Circular Holes

The boundary perturbation method is used to solve the problem of a nearly circular rigid inclusion in a two-dimensional elastic medium subjected to hydrostatic stress at infinity. The solution is taken to the fourth order in the small parameter epsilon that quantifies the magnitude of the variation of the radius of the inclusion. This result is then used to find the effective bulk modulus of a body that contains a dilute concentration of such inclusions. The corresponding results for a cavity are obtained by setting the Muskhelishvili coefficient κ equal to −1, as specified by the Dundurs correspondence principle. The results for nearly circular pores can be expressed in terms of the pore compressibility. The pore compressibilities given by the perturbation solution are tested against numerical values obtained using the boundary element method, and are shown to have good accuracy over a substantial range of roughness values.

Finite difference analysis of Rayleigh wave transmission past an upward step change

1984 ◽  
Vol 74 (3) ◽  
pp. 893-911
Author(s):  
Masahiko Fuyuki ◽  
Masayoshi Nakano
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Perturbation Method ◽  
Rayleigh Wave ◽  
Finite Difference Scheme ◽  
Step Change ◽  
Boundary Perturbation ◽  
Difference Analysis ◽  
Transmission Coefficients ◽  
Boundary Perturbation Method

Abstract Transmission coefficients of the Rayleigh wave past an upward step change are obtained by the finite difference scheme. In the region of large height of a step relative to a wavelength h/λ, individual phases of the transmitted wave are investigated and the dominant wave in each phase is clarified. For smaller values of h/λ, we examine to what extent the contribution of the diffracted wave due to a step change accounts for the discrepancy between the finite difference results and the prediction of the theory of Mal and Knopoff. In order to explain the transmission coefficients with h/λ close to zero, a boundary-perturbation method is extended to the second order.

Radiation of waves by a thin cap submerged in ice-covered ocean

2020 ◽  
Author(s):  
Arijit Das ◽  
Soumen De ◽  
B N Mandal
Keyword(s):  
Gravity Waves ◽  
Order Approximation ◽  
Added Mass ◽  
Damping Coefficient ◽  
Boundary Perturbation ◽  
First Order ◽  
Submerged Body ◽  
Boundary Perturbation Method ◽  
Flexural Gravity Waves ◽  
First Order Approximation

Summary The present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient have been analysed. Two types of caps (for example, concave upwards and concave downwards) have been considered for the numerical results. The effect of the concavity on added mass and damping coefficient has also been studied. The present study should be helpful to understand the nature of waves generated by a heaving submerged body in an ice-covered ocean.

Bending of Simply-Supported Elliptic Plates: B.P.M. Solutions With Second-Order Derivative Boundary Conditions

1989 ◽  
Vol 56 (2) ◽  
pp. 356-363 ◽  
Author(s):  
R. Parnes
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Higher Order ◽  
Point Load ◽  
Second Order ◽  
Boundary Perturbation ◽  
Simply Supported ◽  
Elliptic Plate ◽  
Elliptic Domain ◽  
Boundary Perturbation Method

A higher-order boundary perturbation method (B.P.M.) is formulated to treat a class of problems defined in an elliptic domain with associated boundary conditions expressed in terms of second-order derivatives. The method is applied to study a simply-supported elliptic plate subjected to a central lateral point load. The accuracy is investigated and the B.P.M. solution is found to yield highly accurate results for moderately elliptic domains.

scholarly journals Optimal Form for Compliance of Membrane Boundary Shift in Nonlinear Case

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Y. Yousfi ◽  
I. Hadi ◽  
A. Benbrik
Keyword(s):  
Perturbation Method ◽  
Sobolev Spaces ◽  
Nonlinear Pde ◽  
Elastic Membrane ◽  
Boundary Perturbation ◽  
Nonlinear Case ◽  
Optimal Form ◽  
Boundary Shift ◽  
Boundary Perturbation Method ◽  
Boundary Membrane

In this work, we search the existence shifting compliance optimal form of some boundary membrane, which is not elastic and not isotropic, generating nonlinear PDE. An optimal form of the elastic membrane described by the p-Laplacian is investigated. The boundary perturbation method due to Hadamard is applied in Sobolev spaces.

Strengthening of Circular Holes in Plates Under Edge Loads

1944 ◽  
Vol 11 (3) ◽  
pp. A140-A148
Author(s):  
Leon Beskin
Keyword(s):  
Stress Concentration ◽  
Critical Stress ◽  
Hydrostatic Stress ◽  
Axial Stress ◽  
Theory Of Elasticity ◽  
Stress Distributions ◽  
Common Basis ◽  
Circular Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors

Abstract In this paper, stress distributions are determined around strengthened circular holes in plates submitted to edge loads at infinity. Various proportions of circular strengthenings are considered, and three conditions of applied edge loads are investigated; uniform hydrostatic stress, uniform shearing stress, uniform axial stress. Stress distributions are found by methods of theory of elasticity, and the results are given in the form of stress-concentration factors. In order to reduce the results to a common basis, the stress-concentration factors have been defined by the ratio of the critical stress, computed by the distortion-energy theory, to the critical stress at infinity, which is the critical stress in the plate without hole.

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