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Static Analysis of Contact Problems for an Elastic Half-Space

2009; Springer Nature; Linguagem: Inglês

10.1007/b11479_2

1860-6237

Sergey M. Aleynikov†,

Adhesion, Friction, and Surface Interactions

The second chapter is devoted to the mathematical formulation of mixed problems of the elasticity theory for a half-space and to the numerical-and-analytical methods of their solution. The results obtained in this chapter on developing the mathematical means are the reference data for BEM-based numerical modeling of the spatial contact interaction. The integrated boundary equations of the spatial contact problem are written for the case when the calculation scheme is accepted in the form of variously deepened punches undergoing the action of the spatial system of forces. It is shown how to reduce the initial integral equation system of the contact problem with respect to the contact stress function and the punch displacement parameters to the appropriate finite-dimensional algebraic analogue. Much attention is paid to calculating the matrix coefficients of the resolving system of algebraic equations. A numerical-and-analytical procedure is given for integrating Mindlin's fundamental solutions over flat triangular and quadrangular boundary elements, arbitrary oriented in the half-space. For convenience, to apply the developed approach in practical calculations, the boundary integral equations of the spatial contact problems for a number of essential special cases are presented. The contact problems at axial loading and torsion of absolutely rigid rotation bodies deepened into the half-space, are considered. Boundary-element formulations of the contact problems for complex-shaped punches with flat and smooth bases (shallow foundations), situated on spatially nonhomogeneous bases of the semi-infinite elastic massif type are presented.