Summary
The solutions of nonhomogeneous boundary value problems which arise from the study of the dynamics of bounded, elastic solids are represented by the superposition of two components: (a) a “quasi-static” solution which satisfies the nonhomogeneous boundary conditions, and (b) an eigenfunction expansion which satisfies the corresponding homogeneous boundary conditions. The method obviates the frequently used but often cumbersome technique of integral transforms, and a resolution of the problem is achieved by the use of classical mathematical analysis. The general theory developed is illustrated by considering the problem of point symmetric motion of a suddenly loaded spherical shell for which a complete solution is presented.
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Results presented in this paper were obtained, in part, from research supported by the Air Force Offic of Scientific Research under Grant No. AF-AFOSR-71-1971A. Computer facilities were generously made available by the Computing Center of the State University of New York at Buffalo, which is partially supported by NIH Grant FR-00126 and NSF Frant GP-7318.
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Reismann, H., Pawlik, P.S. The nonhomogeneous elastodynamics problem. J Eng Math 8, 157–165 (1974). https://doi.org/10.1007/BF02353618
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DOI: https://doi.org/10.1007/BF02353618