SUMMARYIn this paper, a new method to solve the uncertain static displacement problem of structures with interval parameters is presented. It is di cult to obtain all possible solutions with sharp bounds even if an optimum scheme is adopted when there are many uncertain parameters. With the interval mathematics, the interval ÿnite element equation is developed. Based on the perturbation and the interval extension, the upper and lower bounds of the static displacements are obtained, in which the sharp bounds are guaranteed by the interval calculation operators. Two numerical examples, a box cantilever beam and an automobile frame, are given to illustrate the validity of the present method.

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SUMMARYAn adaptive iteration algorithm is presented in this paper for structural modal reanalysis of topological modiÿcations. The rules of adaptation are given. The method is based on matrix perturbation and can be implemented easily on the computer. A little computation e ort is involved, which is very important for topological modiÿcation with the increase of the joints and the number of degrees of freedom. In order to illustrate the method, three examples are given. The results show that the proposed method is e ective for structural modal reanalysis of topological modiÿcations.