scholarly journals Boundary elements method in the problem of diffraction at a narrow obstacle with a sharp back edge

2020 ◽  
Vol 73 (3) ◽  
pp. 62-70
Author(s):  
M.A. Sumbatyan ◽  
N.K. Musatova
Keyword(s):  
Boundary Elements ◽  
Back Edge ◽  
Boundary Elements Method

SHAPE ESTIMATION OF A CAVITY BY INVERSE APPLICATION OF THE BOUNDARY ELEMENTS 2D ELASTOSTATICS PROBLEM

2013 ◽  
Vol 10 (06) ◽  
pp. 1350042 ◽  
Author(s):  
MOHSEN DASHTI-ARDAKANI ◽  
MAHMUD KHODADAD
Keyword(s):  
Measurement Errors ◽  
Biaxial Tension ◽  
Spline Interpolation ◽  
Fitness Function ◽  
Boundary Elements ◽  
Initial Guess ◽  
Tension Test ◽  
Shape Estimation ◽  
Boundary Elements Method ◽  
Different Shapes

The boundary elements method (BEM), manipulated genetic algorithm (MGA), conjugate gradient method (CGM), and cubic spline interpolation (CSI) are implemented to identify the shape of a cavity located inside a 2D solid body using displacements measured from a biaxial tension test. A fitness function which is defined as the squared differences between the computed and measured displacements is minimized. The BEM is used to solve the direct 2D elastostatics problem for the boundary displacements. The MGA is used as a robust explorer to find the best circular initial guess needed by the CGM to achieve convergence. The CSI is finally employed to draw the best curve through the points found by the CGM which depict the boundary of the cavity. Several example problems with different shapes of the cavity such as elliptic, pear, heart and egg shaped are solved. The effects of the size of cavity and measurement errors on the estimation process are investigated.

A Time-Domain Boundary Elements Method Applied to Multi-Body Simulations With Large Relative Displacements

2015 ◽  
Author(s):  
Rafael A. Watai ◽  
Felipe Ruggeri ◽  
Alexandre N. Simos
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Numerical Solutions ◽  
Domain Boundary ◽  
Boundary Elements ◽  
Experimental Result ◽  
Exciting Forces ◽  
Boundary Elements Method ◽  
Meshing Scheme ◽  
Multi Body

This paper presents a time domain boundary elements method that accounts for relative displacements between two bodies subjected to incoming waves. The numerical method solves the boundary value problem together with a re-meshing scheme that defines new free surface panel meshes as the bodies displace from their original positions and a higher order interpolation algorithm used to determine the wave elevation and the velocity potential distribution on new free surface collocation points. Numerical solutions of exciting forces and wave elevations are compared to data obtained in a fundamental experimental text carried out with two identical circular section cylinders, in which one was attached to a load cell and the other was forced to move horizontally with a large amplitude oscillatory motion under different velocities. The comparison of numerical and experimental result presents a good agreement.

scholarly journals To the solution of the problem of bending of a cylindrical shell by the boundary elements method

2018 ◽  
Vol 230 ◽  
pp. 02032 ◽  
Author(s):  
Mykola Surianinov ◽  
Yurii Krutii
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Boundary Elements ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Various Boundary Conditions ◽  
Analytical Construction ◽  
Load Vector ◽  
Plates And Shells ◽  
Boundary Elements Method

The solution of the problem of the long cylindrical shell bending by a numerical and analytical boundary elements method is considered. The method is based on the analytical construction of a fundamental system of solutions and Green’s functions for the differential equation of the problem under consideration. This paper is devoted to the determination of these expressions. The semi-moment theory of the cylindrical shell calculation, proposed by V.Z. Vlasov, which for the problem under consideration leads to one eighth-order partial differential equation is used. The problem of the bending of a cylindrical shell is twodimensional, and in the numerical and analytical boundary elements method, plates and shells are considered as generalized one-dimensional modules, so the variational method of Kantorovich-Vlasov was applied to this equation to obtain an ordinary differential equation of the eighth order. Sixty-four expressions of all the fundamental functions of the problem are constructed, as well as an analytic expression for the Green’s function, which makes it possible to construct a load vector (without any restrictions on the nature of its application), and then proceed to the solution of boundary-value problems for the bending of long cylindrical shells under various boundary conditions.

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