Non-linear analysis of a reinforced concrete sheet cover (umbrella) of 40Â m diameter by the finite element method

The aim of this work is to determine the distribution of strains and stresses throughout a sheet cover known as “umbrella” due to the dead and alive loads taking into account large displacements by the finite element method (FEM) [K. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, New York, 1996; T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, New York, 2000; T. Chandrupatla, A. Belegundu, Introduction to Finite Elements in Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 1991; P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing Company, Amsterdam, 1978; C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, New York, 1987; S. Moaveny, Finite Element Analysis: Theory and Application with ANSYS, Prentice-Hall, Upper Saddle River, New Jersey, 1999; P.A. Raviart, J.M. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles, Masson, Paris, 1983; J.N. Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, New York, 2004; O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method: Solid and Fluid Mechanics and Non-linearity, McGraw-Hill Book Company, London, 1991]. The non-linearity is due to large displacements that governs the phenomenon. Finally we compare the analytical calculations with the FEM results and expose the conclusions reached in this study.