scholarly journals Divergent Integrals in Elastostatics: General Considerations

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Hypersingular Integrals ◽  
Integral Equation Methods ◽  
Weakly Singular ◽  
Easy Calculation ◽  
2D And 3D

This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constructed.

scholarly journals Regularization of the Divergent Integrals. I. General Consideration.

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
Vladimir Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
General Consideration ◽  
Science And Engineering ◽  
Hypersingular Integrals ◽  
Weakly Singular ◽  
Easy Calculation ◽  
Multidimensional Integrals

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals, have been constructed. Such approach may be easily generalized and applied to the calculation of multidimensional integrals with singularities of various types.

scholarly journals The Regularization of the Divergent Integrals in 2-D Elastostatics

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Elements ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Green's Theorem ◽  
Curved Boundary ◽  
Green’S Theorem ◽  
Weakly Singular ◽  
Easy Calculation

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in 2-D elastostatics. For their regularization, an approach based on the theory of distribution and application of the Green’s theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals for straight and curved boundary elements, have been constructed.

scholarly journals Boundary Element Methods in Solid Mechanics - a Tribute to Frank Rizzo

2007 ◽  
Vol 1 (1) ◽  
Author(s):  
Subrata Mukherjee
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Linear Elasticity ◽  
Solid Mechanics ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Seminal Paper ◽  
Good Fortune ◽  
The Subject

Frank Rizzo proposed the first Boundary Integral Equation (BIE) formulation for linear elasticity in a seminal paper in 1967. I have had the very good fortune to call Frank a friend of mine for many years. The present paper describes some of my experiences with the BIE over nearly thirty years, some of it in the context of Frank’s pioneering contributions to the subject and my interactions with him.

Boundary Integral Equation Methods for a Refined Model of Elastic Plates

2006 ◽  
Vol 11 (6) ◽  
pp. 642-654
Author(s):  
Radu Mitric ◽  
Christian Constanda
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Normal Strain ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Neumann Problems ◽  
Integral Equation Methods ◽  
Transverse Normal Strain ◽  
System Of Equilibrium Equations

A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.

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