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Spatial Contact Models of Elastic Bases
Abstract The first chapter presents some introductive data while reviewing spatial contact models in geotechnics. Classical fundamental solutions for the spatial theory of elasticity obtained by Boussinesq, Cerruti, Mindlin are quoted as well as their generalizations, suitable for calculating constructions on elastic nonclassical bases. The properties of the influence functions are analyzed, required for characterizing elastic bases with nonhomogeneous deformation properties (connected half-spaces, elastic layers of constant and variable thickness). A numerical-and-analytical procedure is developed for construction of fundamental solutions of spatial elasticity theory for multilayer bases without restrictions on the layer thickness and elastic parameters. Using the two-dimensional Fourier transformation, the formulae have been derived, enabling three-dimensional contact problems for complex-shaped structures deepened into spatially nonhomogeneous (layered) soils to be solved in the framework of the boundary-element method numerical algorithm. The final part of the first chapter contains the results on the formulation of influence functions for elastic bases with variable deformation properties. The Boussinesq problem is solved for an elastic half-space when the deformation modulus increases with depth according to a most general law. Proper relations, enabling adequate description of the experimental data, are considered. An efficient numerical-and-analytical procedure is developed for construction of the influence functions, taking into account the soil deformation modulus variation with depth. All the theoretical results for the influence functions were obtained within a unique approach enabling all the main types of nonhomogeneities of natural soil bases to be taken into account.
Spatial Contact Models of Elastic Bases
Abstract The first chapter presents some introductive data while reviewing spatial contact models in geotechnics. Classical fundamental solutions for the spatial theory of elasticity obtained by Boussinesq, Cerruti, Mindlin are quoted as well as their generalizations, suitable for calculating constructions on elastic nonclassical bases. The properties of the influence functions are analyzed, required for characterizing elastic bases with nonhomogeneous deformation properties (connected half-spaces, elastic layers of constant and variable thickness). A numerical-and-analytical procedure is developed for construction of fundamental solutions of spatial elasticity theory for multilayer bases without restrictions on the layer thickness and elastic parameters. Using the two-dimensional Fourier transformation, the formulae have been derived, enabling three-dimensional contact problems for complex-shaped structures deepened into spatially nonhomogeneous (layered) soils to be solved in the framework of the boundary-element method numerical algorithm. The final part of the first chapter contains the results on the formulation of influence functions for elastic bases with variable deformation properties. The Boussinesq problem is solved for an elastic half-space when the deformation modulus increases with depth according to a most general law. Proper relations, enabling adequate description of the experimental data, are considered. An efficient numerical-and-analytical procedure is developed for construction of the influence functions, taking into account the soil deformation modulus variation with depth. All the theoretical results for the influence functions were obtained within a unique approach enabling all the main types of nonhomogeneities of natural soil bases to be taken into account.
Spatial Contact Models of Elastic Bases
Aleynikov†, Sergey M. (author)
2009-09-14
89 pages
Article/Chapter (Book)
Electronic Resource
English
Concentrate Force , Elastic Layer , Influence Function , Deformation Modulus , Elastic Wedge 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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