Two-dimensional nonlinear problems of elastic equilibrium of multiply connected bodies

1970 ◽  
Vol 6 (2) ◽  
pp. 157-163 ◽  
Author(s):  
Yu. I. Koifman
Keyword(s):  
Elastic Equilibrium ◽  
Nonlinear Problems ◽  
Two Dimensional ◽  
Multiply Connected

Dynamic Response of Surface-Moored Vertical Barrier to Wave Action by Analog and Digital Simulation

1974 ◽  
Vol 96 (1) ◽  
pp. 335-342
Author(s):  
J. R. Fowler ◽  
E. I. Bailey
Keyword(s):  
Theoretical Model ◽  
Digital Simulation ◽  
Nonlinear Problems ◽  
Analog Computer ◽  
Two Dimensional ◽  
Test Program ◽  
Analog Simulation ◽  
Vertical Barrier ◽  
Amplitude Data ◽  
Lab Test

The two-dimensional dynamics of an oil containment barrier, which was designed to have very low tensile loads due to current and waves, were simulated with a theoretical model. The model was solved on both analog and digital computers, and a lab test program conducted to verify the model. For nonlinear problems such as this, for which “exact” solutions do not exist, the analog computer has many advantages, principally rapid parameter studies and convenient plotting output, plus giving the engineer a real time “feel” for the problem. The problem treated here was especially well-suited to analog simulation. Charts and graphs present maximum force and amplitude data, and experimental verification of the solution was obtained from wave tank studies.

scholarly journals The rotation of two circular cylinders in a viscous fluid

1922 ◽  
Vol 101 (709) ◽  
pp. 169-174 ◽  
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Stream Function ◽  
Elastic Stress ◽  
Steady Motion ◽  
Elastic Equilibrium ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Concentric Circles ◽  
Hydrodynamical Problem

In a previous communication we employed the solution of the equation ∇ 4 ψ = 0 in bipolar co-ordinates defined by α + iβ = log x + i ( y + a )/ x + i ( y - a ) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two non-concentric circles. There is a well-known analogy between plain elastic stress and two-dimensional steady motion of a viscous fluid, for which the stream-function satisfies ∇ 4 ψ = 0. The boundary conditions are, however, different in the two cases, and the hydrodynamical problem has its own special difficulties.

scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading

1902 ◽  
Vol 70 (459-466) ◽  
pp. 491-496
Keyword(s):  
Approximate Solution ◽  
Special Reference ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Equilibrium ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Applied Stresses

The paper investigates the elastic equilibrium of a long bar of rectangular cross-section in those cases where the problem may be treated as one of two dimensions, namely:— ( a .) When the strain being in the plane of xy , the elastic solid extends indefinitely in the direction of the applied stresses over the bounding planes y = ± b , x = ± a being the same for any two sections parallel to the plane of xy . We then have a strictly two-dimensional strain.

scholarly journals Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120558 ◽  
Author(s):  
Tomoo Yokoyama ◽  
Takashi Sakajo
Keyword(s):  
Stream Function ◽  
Contour Plot ◽  
Hamiltonian Vector Field ◽  
Multiply Connected Domains ◽  
Two Dimensional ◽  
Inviscid Flows ◽  
Multiply Connected ◽  
Word Representation ◽  
Multiple Obstacles ◽  
Structurally Stable

Let us consider incompressible and inviscid flows in two-dimensional domains with multiple obstacles. The instantaneous velocity field becomes a Hamiltonian vector field defined from the stream function, and it is topologically characterized by the streamline pattern that corresponds to the contour plot of the stream function. The present paper provides us with a procedure to construct structurally stable streamline patterns generated by finitely many point vortices in the presence of the uniform flow. Starting from some basic structurally stable streamline patterns in a disc of low genus, i.e. a disc with a small number of holes, we repeat some fundamental operations that append a streamline pattern by increasing one genus to them. Owing to the inductive procedure, one can assign a sequence of operations as a representing word to each structurally stable streamline pattern. We also give the canonical expression for the word representation, which allows us to make a catalogue of all possible structurally stable streamline patterns in a combinatorial manner. As an example, we show all streamline patterns in the discs of genus 1 and 2.

scholarly journals The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum inℝ2with Robin boundary conditions

2001 ◽  
Vol 25 (11) ◽  
pp. 717-726 ◽  
Author(s):  
E. M. E. Zayed ◽  
I. H. Abdel-Halim
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Inverse Eigenvalue Problem ◽  
Robin Boundary Conditions ◽  
Two Dimensional ◽  
Equation Approach ◽  
Multiply Connected ◽  
Inverse Eigenvalue ◽  
Negative Laplacian ◽  
Robin Boundary

The spectral functionμˆ(t)=∑j=1∞exp(−itμj1/2), where{μj}j=1∞are the eigenvalues of the two-dimensional negative Laplacian, is studied for small|t|for a variety of domains, where−∞<t<∞andi=−1. The dependencies ofμˆ(t)on the connectivity of a domain and the Robin boundary conditions are analyzed. Particular attention is given to an arbitrary multiply-connected drum inℝ2together with Robin boundary conditions on its boundaries.

Application of Process Analysis Method to the Solution of 2-DNonlinear Progressive Gravity Waves

1992 ◽  
Vol 36 (01) ◽  
pp. 30-37
Author(s):  
S. J. Liao
Keyword(s):  
Gravity Waves ◽  
Process Analysis ◽  
Perturbation Expansion ◽  
Continuous Mapping ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Analysis Method ◽  
Perturbation Expansion Method

Based on continuous mapping, a kind of analytical method for nonlinear problems, namely, the Process Analysis Method, is described and used to solve two-dimensional nonlinear progressive gravity waves. Solutions at the fourth order of approximation are obtained and compared with Stokesian waves. In contrast to the perturbation expansion method, the Process Analysis Method is independent of small or great parameters and therefore can solve nonlinear problems without small or great parameters.

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