Geometric Nonlinear Analysis of Reinforced Concrete Folded Plate Structures by the Harmonic Coupled Finite Strip Method

Abstract

There is a great deal of RCFPS for which both the geometry and the material properties can be considered as constants along a main direction, straight or curved, while, generally, only the loading distribution may vary (e.g. thin-walled beams, cylindrical and prismatic shell roofs [2] and box-girder bridges [3,4]). In many cases, the performance of these structures is also improved by means of proper longitudinal prestressing systems. For these structures, the design process should lead to define the optimal morphology of the transversal cross-section, which means its geometry, size, shape and topology, as well as the layout of the prestressing system, described by the prestressing forces and the cables profile.In such context, the attention of this paper is focused on the optimal design of RCFPS composed by flat plates and subjected to multiple loading conditions, Fig. 1 (a). A proper modeling of these structures can be found within the framework of the FSM. As well known, this method is based on the formulation of a special class of finite elements that are as long as the structure and interconnected along the nodal lines that constitute the sides of the strips themselves. The FSM was originally developed by Cheung [1]. The well known uncoupled formulation, represents a semi-analytical finite element method (FEM). As far as linear analysis is concerned, it takes advantage of the orthogonality properties of harmonic functions in the stiffness matrix formulation.However, in the case of the geometric nonlinear analysis, the integral expressions contain the products of trigonometric functions with higher-order exponents, and therefore the orthogonality characteristics are no longer valid. All harmonics are coupled, and the stiffness-matrix order and bandwidth are pro-

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