Nonlinearisation of the winkler model for the analysis of shells on elastic foundations

Several shell forms which are used in roofs, if inverted, can serve as foundations. Such shell foundations, under working load conditions are to be analysed as 'shells on elastic foundations,' invoking the shell-soil interaction. Among the tools of analysis of such systems, the Winkler spring model is the most common. This model, however, represents a linear elastic system which is of limited validity in dealing with a highly nonlinear material like the soil. In order to represent the actual nonlinear response of soil to the applied load, the existing Winkler model is nonlinearised by fitting the load-settlement data from a plate load test using different methods, from which different secant values of the subgrade modulus are obtained at different load levels. The Winkler analysis is carried out at each load using the corresponding value of the subgrade modulus and the results are collated to give the final nonlinear picture of the results. The work is fully automated by creating the necessary software support complete with a post-processor which plots the nonlinear variation of the results with load. The nonlinear results obtained as above are presented in respect of a rectangular hypar footing.