Determination of the precise dynamic response under various loads such as earthquake load, impact load, etc., has a significant role in the safe and economic design of structures. In this thesis, a new meshless method with the idea of time-weighted satisfaction of axial, flexural and torsional wave propagation equations is presented for the analysis of structures with one-dimensional members subjected to dynamic loads. The main idea of time-marching method is to use pre-integration relationships along with equilibrium equations. In this approach, the initial conditions are exactly satisfied in a time marching manner and the equilibrium equation is satisfied using a time-weighted residual method. Boundary conditions are also met at the ends of each element on the boundary of the problem and at the end of each step. The main advantage of this method is saving of the time step information on the coefficients of some exponential basis functions (EBFs), so that the solution advances in time without the need of domain points for discretization. In the other words, just a recursive relation has been used for updating the EBF’s coefficients. In this study, due to the verification of the results by Key words: Time-marching method, Wave propagation, Exponential basis functions, Dynamic response, Two and three dimensional structures.
