Basic displacement functions in dynamic analysis of an arch dam as a curved beam resting on a continues elastic foundation

Abstract

In recent years several researches have been done on different ways of analyzing and designing arch dams but most of them were involved with cumbersome calculations and heavy loads of computations. In this paper a novel approach for dynamic analysis of arch dams is presented. The most commonly accepted method for analyzing arch dams assumes that the horizontal water load is divided between arches and cantilevers so that the arch and cantilever deflections are equal at conjugate points in all parts of structure. In this the arch dam is modeled as non-prismatic curved beam resting on continues elastic foundation. Based on structural and mechanical principals, a flexibility based method is used to evaluate exact structural matrices and by introducing the concept of basic displacement functions (BDFs), it is shown that dynamic shape functions are derived in terms of BDFs. The flexibility basis ensures the true satisfaction of equilibrium equations at any interior point of the curved element. Dynamic stiffness matrix is evaluated by solving the governing equation of motion. Differential Transform method, a powerful numerical tool in solving of ordinary differential equations, is used for this purpose. The method is capable of modeling any curved element whose crosssectional area and moment of inertia vary along beam with any two arbitrary functions and any type of cross-section with just few numbers of elements so that it can be used in most of engineering applications concerning non-prismatic curved beams and arch dams in particular. In order to verify the competency of the method, a numerical example are presented and the results and convergence of them are compared with other methods in the literature.