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SUMMARYThis paper describes the application of a structural optimization approach combined with the "nite element method for the optimal design of a raft}pile foundation system. The analysis takes into account the non-linear behaviour of the soil medium and the piles. For the optimization process, the sensitivity analysis is carried out using the approximate semi-analytical method while the constraint approximation is obtained from the combination of extended Bi-point and Lagrangian polynomial approximation methods. The objective function of the problem is the cost of the foundation. The design variables are the raft thickness, cross-section, length and number of piles. The maximum displacement and di!erential displacement are selected as the constraints. The proposed method is shown to achieve an optimum design of raft}pile foundation e$ciently and accurately.

SUMMARYFor the ®nite element non-linear analysis of engineering problems combined with an optimization method, two techniques Ð a semi-analytical sensitivity method and bi-point constraint approximation Ð have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more ecient than the ®nite dierence method and the bi-point approximation gives results which compare favourably with the ®nite element results. #

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