Exact and Accurate Reanalysis of Structures for Geometrical Changes

Abstract

A reanalysis approach for geometrical changes in structural systems is presented. The solution procedure is based on the combined approximations method, where the binomial series terms are used as basis vectors in reduced basis approximations. The calculations are based on results of a single exact analysis, calculation of derivatives is not required, and each reanalysis involves a small computational effort. The method is easy to implement, and can be used with general finite element programs. Exact solutions are obtained efficiently for low-rank modifications in the geometry. Accurate solutions are achieved in cases where the basis vectors come close to being linearly dependent. Such solutions are also achieved for nearly scaled geometries, when the angle between the two vectors representing the initial design and modified design is small. Numerical examples demonstrate the high accuracy achieved with a small number of basis vectors