Numerical Treatment of Singularities in Elastic Contact Problems and Applications
New procedure is suggested for numerical and analytical treatment of elastic contact problems for non-classical domains. The numerical procedure is based on formulae derived for an accurate computer evaluation of singular integrals. These formulae define the value of the singular integral in the neighbourhood of the singularities while the regular part of the integral can be evaluated by any standard subroutine. The method allows practically exact solution of elastic contact problems for punches of various plan forms like, for example, rectangle, rhombus, triangle, oval, etc. The nature of the stress singularity at the boundary of the domain of contact is clarified. Numerical results presented for a rectangle indicate that the assumption of a square root singularity is wrong, and that the power of the singularity is not constant along a rectangle edge.
The new analytical approach is based on an integral representation for the kernel of the governing integral equation from which some simple yet accurate formulae are derived for the relationship between the applied forces and the genralized displacements of the punch. The method’s applicability is far beyond the field of elastic contact problems. It can be applied for the evaluation of the capacity of flat laminae, in the field of wave propagation it can be used for the evaluation the coefficients of electrical and magnetic polarizability, etc. Some specific examples of such use are given.
KeywordsContact Problem Approximate Formula Cubature Formula Angular Point Feedback Principle
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