The fictitious absorption method in solving mixed problems for arbitrary simply-connected areas
UDC
539.3DOI:
https://doi.org/10.31429/vestnik-15-3-52-61Abstract
The work is dedicated to the development of methods for solving integral equations (IE) and systems of IE for mixed dynamic problems in the theory of elasticity, given in simply-connected areas of complex shape. A generalization of the fictitious absorption method to the case of a non-convex in the plane area occupied by a defect or stamp is presented.
The method makes it possible to describe solutions not only inside but also in the neighbourhood of the contact area boundaries and can be used to solve contact problems on the vibration of stamps, cavities or rigid inclusions of an arbitrary shape in the plane. For the areas of complex configuration, it is possible to present them as a union of convex bounded closed domains, possibly with common boundary sets.
We propose a modification of the method in the selection of the basis functions, presented in the solution only under the signs of the operators. As the latter, we choose the derivatives of the delta functions, which simplifies the construction of the solution. The results of solving the integral equation of the axisymmetric problem about steady-state oscillations of a stamp on the surface of an elastic layer with a clamped lower bound are given as an example.
Keywords:
fictitious absorption method, integral equation, oscillating kernel, area of complex configuration, factorizationAcknowledgement
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