scholarly journals A Meshfree Method for Signorini Problems Using Boundary Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanlin Ren ◽  
Xiaolin Li
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Inequality Constraints ◽  
Meshfree Method ◽  
Boundary Integral ◽  
Unknown Boundary ◽  
Nodal Data ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Point Interpolation

This paper presents a meshfree method for the numerical solution of Signorini problems. In this method, a projection iterative algorithm is used to convert the boundary inequality constraints into a fixed point equation. Then, the boundary value problem is reformulated as boundary integral equations and the unknown boundary variables are interpolated by the point interpolation scheme. Thus, only a nodal data structure on the boundary of a domain is required, and boundary conditions can be implemented directly and easily. The convergence of this method is verified theoretically. Numerical examples involving groundwater flow and electropainting problems are also provided to illustrate the performance and usefulness of the method.

scholarly journals An Analytical Approach for the Green's Functions of Biharmonic Problems with Circular and Annular Domains

2009 ◽  
Vol 25 (1) ◽  
pp. 59-74 ◽  
Author(s):  
J. T. Chen ◽  
H. Z. Liao ◽  
W. M. Lee
Keyword(s):  
Integral Equations ◽  
Analytical Solutions ◽  
Shear Force ◽  
Analytical Approach ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Kernel Functions ◽  
Unknown Boundary ◽  
Annular Domains ◽  
Biharmonic Problems

AbstractIn this paper, an analytical approach for deriving the Green's function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noticed that all the improper integrals were avoided when the degenerate kernels were used. After determining the unknown Fourier coefficients, the displacement, slope, normal moment and effective shear force of the plate could be obtained by using the boundary integral equations. The present approach was seen as an “analytical” approach for a series solution. Finally, several analytical solutions were obtained. To see the validity of the present method, FEM solutions using ABAQUS were compared well with our analytical solutions. The displacement, radial moment and shear variations of radial and angular positions were presented.

scholarly journals METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

2021 ◽  
Author(s):  
Assiyat Dadayeva ◽  
Lyudmila Alexeyeva
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Plane Boundary ◽  
Unknown Boundary ◽  
Singular Boundary

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

scholarly journals A numerical boundary integral equation method for elastodynamics. I

1978 ◽  
Vol 68 (5) ◽  
pp. 1331-1357
Author(s):  
David M. Cole ◽  
Dan D. Kosloff ◽  
J. Bernard Minster
Keyword(s):  
Integral Equations ◽  
Initial Value Problems ◽  
Numerical Scheme ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Unknown Boundary ◽  
Boundary Values ◽  
Initial Value ◽  
Time Stepping

abstract The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values. A specific numerical scheme is presented for antiplane strain problems and a numerical example is given.

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