Finite Element Analysis of Hyperbolic Cooling Towers

The analysis of thin shells of revolution in general has always occupied an important place in the theory of structures, and recently the problem of hyperbolic cooling towers has attracted many investigators due to the wide use of such shells in industry. Until the early 1960's these towers were of moderate size, probably not exceeding 76m (250ft) height. In this range, the structural safety and stability were not of primary concern because, the minimum wall thickness and reinforcement were sufficient to provide the required safety. It was not necessary to use very rigorous methods to analyse the problem. The analysis involved the following assumptions, i) flexural stresses were ignored (membrane tneory), ii) The geometry of the shell was assumed to be perfect and to be idealised as a set of straight sided conical frusta, and iii) The boundary conditions at the base were taken to be fixed or continuously hinged with full tangential restraint.

Contenu

1. Introduction.- 2. General Theory of Thin Elastic Shells.- 3. Linear Analysis of Thin Shells of Revolution Using Finite Element Method.- 3.1: Introduction.- 3.2: Geometric Parameters and Relations of Shells of Revolution.- 3.3: Basic Equations of Elasticity for Shells of Revolution.- 3.4: Fourier Analysis.- 3.5: Finite Element Formulation.- 3.6: Examples.- 4. Hyperbolic Cooling Towers on Discrete-Flexible Support System.- 4.1: Introduction.- 4.2: Continuous-Flexible Boundary Analysis.- 4.3: Discrete-Flexible Boundary Analysis.- 4.4: Results, Discussions and Conclusions.- 5. Hyperbolic Cooling Towers with Geometric Imperfection.- 5.1: Introduction.- 5.2: Method of Geometric Simulation of Imperfection.- 5.3: The Method of the Equivalent Load Simulation of Geometric Imperfections.- 5.4: Results, Discussions and Conclusions.- 6. Non-Linear Analysis of Hyperbolic Cooling Towers.- 6.1: Introduction.- 6.2: Structural Non-Linearity.- 6.3: Equilibrium Equation of Non-Linear Systems.- 6.4: Numerical Techniques.- 6.5: Theory and Formulation of Geometric Non-Linear Shells of Revolution.- 6.6: Overall Solution Procedure.- 6.7: Results and Conclusion.- References.- Appendix 1 Elasticity Matrix.- Appendix 2.- Appendix 3 Force Density Vectors.- Appendix 4 Derivation of Stiffness Matrix of the Support Columns at Interface.- Appendix 5 Derivation of Equivalent Nodal Forces of Distributed Edge Loading.