Introducing the Modified Time‐Weighted Residual Method for Joint‐By‐Joint Dynamic Analysis of Framed Structures: Application to Direct and Inverse Problems

This paper presents a novel “joint‐by‐joint” solution method for planar structures, considering members with distributed mass. The term “joint‐by‐joint” indicates that for the dynamic solution of the structures, the user only needs to solve a set of uncoupled 3 by 3 coefficient matrices in the time marching process, though the wave propagation effects are fully considered in each element. The presented method is a modified version of the time‐weighted residual method introduced recently. Thanks to the exponential functions, which satisfy the related wave equations, the information of the displacement and velocity of each time step is stored in the exponential basis coefficients, so the solution advances in time without requiring spatial discretization of the frame elements. In other words, by using the proper recursive relations, the exponential basis coefficients are updated, which results in a reduction of computational time. The present study employs the modified method, with enhanced computational speed, to solve direct and inverse dynamic problems of planar frames. More computational speed‐up may be expected when the present method is implemented in parallel computation schemes (not intended in this paper) since the joints and elements are processed independently. The paper also aims to demonstrate the validity of the results of the method. To this end, as a case study of direct problems, computation of structure response under support excitations has been considered. The validation process is supported by some laboratory tests performed for the first time in this paper. Using the nodal responses of the frames, the presented method has also been applied to the inverse problem of load identification. All numerical and laboratory studies indicate that the presented method can be effectively used in multi‐purpose dynamic analysis of structural problems.