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UBC Theses and Dissertations

Interactive nonlinear analysis of wind-loaded pneumatic membrane structures Han, Peng Siew


A nonlinear analysis of pneumatic membrane structures loaded by wind, taking into account the fluid-structure interactions, is presented here. The analysis comprises two parts: the flow part which is solved using a boundary element procedure and the structures part which is analysed with a finite element approach. These two numerical techniques are then coupled to capture the effects of the fluid-structure interaction in the analysis. The wind is represented by potential flow and thus Laplace's equation governs. The boundary element method employed in the analysis, features moving singularities of the fundamental solutions. The singularities are placed on an auxiliary boundary located outside the domain of interest. Results from solved examples show the technique to be highly accurate for the computation of wind loads. The method is however, nonlinear with the nonlinearity occuring in the determination of the auxiliary boundary. The membrane, assumed to be perfectly flexible and to exhibit only exten-sional rigidity, is modeled by a small strain-finite deformation theory. A Galerkin finite element approach is formulated for the analysis of two-dimensional pneumatic membrane structures. The analysis is based on an infinitely long cylindrical membrane with an initially circular cross-section. For three-dimensional pneumatic membrane structures, the analysis is accomplished with a continuum mechanics-based incremental finite element formulation using a convected coordinate description. The metric tensor for any deformed configuration is derived and from this, a consistent measure of deformation is obtained. In both analyses, the governing finite element equations are solved via Newton-Raphson iteration with an 'automatic' line-search scheme. A pertubation technique is developed to check the accuracy of the proposed two-dimensional finite element analysis for low wind speeds. At higher wind speeds, comparison with available solutions are made. To assess the performance of the proposed three-dimensional finite element analysis, a square membrane and a cylindrical membrane are analysed. Good agreement with published results is observed. Having established the accuracies of the boundary element and the finite element methods on independent flow and structures problems respectively, interactive analysis is then carried out. Two pneumatic membrane structures are analysed: an infinitely long cylindrical membrane as a two-dimensional example, and the air-supported roof of the BC Place Stadium as a three-dimensional example.

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