EXACT STRUCTURAL REANALYSIS BY A FIRST-ORDER REDUCED BASIS APPROACH

It is shown in this article that in truss structures, the first-order (two-term) reduced basis expressions provide exact displacements and s tresses in terms of the cross-sectional variables. For changes in m me mbers the exact solution is achieved by considering the m first-order basis vectors. Each of the latter vectors is shown to be the constant sensitivity vector multiplied by a scalar variable. The multipliers of the reduced basis equations can readily be determined by solving an m x m set of equations. The main advantages of the method presented are as follows: (a) It is more efficient than the common exact analysis i n cases where a limited number of members is changed. (b) Unlike the c ommon approximations, the exact solution is achieved. This is particul arly important in cases where the accuracy of the results obtained by approximate methods is not adequate. (c) The method can be used also i n cases of changes in the structural layout (topological and geometric al optimization), where approximate methods might provide poor or mean ingless results.