Applying the Hillbert’s orthogonal theorem and Schmidt’s method, a new method for solving 3D non-axisymmetry mixed boundary problem is discovered, and on this basis, an analytical solution of rectangular plate on an elastic half space under arbitrary loads is provided. To achieve this purpose, the contact stress between plate and foundation is taken as the basic unknown quantity and expanded by Jacobi polynomials, then Fourier transform and Schmidt’s method are used to solve the dual integral equation, finally, the displacement and stress fields of entire system is obtained. Present formulation is carefully checked with existing solutions, and several numerical examples are further presented to demonstrate the practicability.
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Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 2, March-April, 2022.
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Wang, L.A., Yu, Y.Y. An Analytical Method for Solving 3D Non-Axisymmetry Mixed Boundary Problem and Its Application in Analysis of Rectangle Plate Resting on an Elastic Half Space. Soil Mech Found Eng 59, 183–192 (2022). https://doi.org/10.1007/s11204-022-09800-z
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DOI: https://doi.org/10.1007/s11204-022-09800-z