AN EFFICIENT METHOD FOR NONLINEAR DYNAMIC ANALYSIS OF 3D SPACE STRUCTURES
A nonlinear structural problem is a problem where the variables of the equations cannot be written as linear combinations of independent components. Hence, for the analysis of space structures under nonlinear behaviours, special techniques are required to achieve accurate results.
In the present work, an efficient method is proposed for the nonlinear dynamic analysis of space structures such as a cable-stayed bridge. The cable-stayed bridge belongs is a tension structure (Aschheim et al., 2007). Tensile steel cable is commonly used in tension structures. There are two advantages of using tensile steel in cables. Firstly, the tensile steel in cables increases the load-carrying capacity of the structure elements. Secondly, the tensile steel cables enable the use of large spans for roofs and bridges. These types of structures belong to the category of geometrically nonlinear structures and their nonlinear behaviour must be taken into account in analysis. A number of methods for the nonlinear static analysis of cable structures are investigated by Buchholdt (1982), Guo (2007), and Kaveh (2008). These researchers present theoretical analysis utilizing the continuous membrane approach. Tension structures can be presumed to be discrete systems and thereby unknown nodal variables can be obtained by solving the set of governing equations for all elements of the discrete system. The tension structure consists of a finite number of elements connected at joints or nodes. Nonlinear equations are set up for the condition of joint equilibrium in terms of joint displacements from which the equilibrium displacements can be found using an iterative process. Some researchers such as Kukreti (1989) discuss cable structures as discrete systems, but confine themselves to using variations of the Newton-Raphson method to establish static equilibrium. Other researchers such as Lopez and Yang (López-Mellado, 2002; Yang & Stepanenko, 1994) have used the steepest descent method to determine the static load equilibrium.
It is worth mentioning that the theory of nonlinear dynamic response analysis is still under development. Nevertheless, a number of methods have been developed for the dynamic response analysis of structural systems, but there are only a few methods which can be employed in nonlinear dynamic response analysis . In the present lecture, a theory for nonlinear dynamic response analysis of 3D space structures is developed based on the minimization of total potential dynamic work.
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