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Dynamic Analysis of Discrete-Element Plates on Nonlinear Foundations
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1970-07-01
[PDF-4.87 MB]
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Abstract:This work describes a discrete-element method for the dynamic analysis of plates or slabs on nonlinear foundations. The method has been programmed for a high-speed digital computer and can be used to obtain solutions to a wide variety of plate vibration problems. A step-by-step numerical integration procedure is employed to numerically integrate the solution in time. The assumption of a linear variation of acceleration during the time-step interval is utilized to develop a recursive solution procedure. Recommendations for the selection of the time-step increment, based on the stability analysis of the algorithm, are presented. The nonlinear analysis is performed by an iteration procedure which adjusts the load rather than the foundation stiffness. This so-called load iteration method is presented as an alternative to the familiar stiffness adjustment procedures. Although the closure is slower with regard to the number of cycles required to reach equilibrium, a significant reduction in the computer time per cycle is realized by load iteration. The program has been developed to accept a general variation in the elastic properties of the plate and in the nonlinear foundation characteristics. Furthermore, there is considerable latitude in the description of the plan configuration and the dynamic loading. Several example problems demonstrating the method are included, as is an example of the preparation of data for computer input.
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