INFLUENCE LINE ANALYSIS OF FINITE ELEMENT MODELS WITHOUT MODEL MODIFICATION BASED ON THE RECIPROCAL THEORY

Abstract

 In the design of structures subjected to moving loads, such as bridges, the influence line representing the response of stresses at a point of interest in terms of the location of the load is essential. To obtain the influence line for a finite element model requires the same number of analyses as the number of nodes on the surface to which the load is possibly applied. On the other hand, some methods based on the Müller-Breslau principle, which enable us to obtain the influence line by performing the finite element analysis only once, have been proposed. However, the methods require modification of the finite element model which increases the preprocess cost because it is necessary to provide a discontinuous displacement at the point of interest. Hence, this paper proposes an analysis method for influence lines that does not require model modification and can be easily implemented in any finite element codes. The proposed method is based on a reciprocal theorem applied directly to finite element discretized problems. The validity of the proposed method is confirmed by comparing the influence lines obtained by the proposed method with the results of the conventional finite element analysis with unit load for plane stress and three-dimensional problems.