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.

Vibrations of Moderately Elliptic Clamped Plates: A Perturbation Scheme for Eigenvalues

1991 ◽  
Vol 58 (3) ◽  
pp. 724-728 ◽  
Author(s):  
R. Parnes
Keyword(s):  
Perturbation Method ◽  
Fundamental Mode ◽  
Perturbation Scheme ◽  
Boundary Perturbation ◽  
Present Scheme ◽  
Higher Modes ◽  
Elliptic Plate ◽  
Modes Of Vibration ◽  
Boundary Perturbation Method

Frequencies of vibration of an elliptic plate, clamped along the edge, are determined by means of a perturbation scheme based on a boundary perturbation method (B.P.M.). Eigenvalues are obtained corresponding to higher modes of vibration containing elliptic nodes, in addition to the fundamental mode. Comparison with previously derived values in the fundamental mode reveals that the present scheme leads to accurate results for moderately elliptic plates.

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.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

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.

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