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Static Analysis of Contact Problems for an Elastic Half-Space
Abstract 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.
Static Analysis of Contact Problems for an Elastic Half-Space
Abstract 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.
Static Analysis of Contact Problems for an Elastic Half-Space
Aleynikov†, Sergey M. (author)
2009-09-14
43 pages
Article/Chapter (Book)
Electronic Resource
English
Boundary Element , Contact Problem , Boundary Integral Equation , Influence Matrix , Rigid Punch Engineering , Theoretical and Applied Mechanics , Appl.Mathematics/Computational Methods of Engineering , Earth Sciences, general , Mechanics , Computational Intelligence , Continuum Mechanics and Mechanics of Materials
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