The Generalized Differential Quadrature (GDQ) and Newmark methods are chosen to solve time integration problems such as the dynamics of composite arches and vaults with constant and variable cross-sections, under seismic impulse loading applied at the base. A 2D Equivalent Single Layer (ESL) shell theory is used to analyze the problem numerically, where the governing equations of motion are solved in a strong form without passing through any variational formulation. The total time interval is discretized in time steps, as required by a Newmark approach, and the GDQ method is applied to solve a system of linear ordinary differential equations for each time step. The accuracy of the proposed method in predicting the dynamic response of the arched or vaulted structures is demonstrated by comparing the GDQ-based results for different geometries and external loadings, with the ones obtained with a standard Finite Element Method (FEM).
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