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

• Published in: Applied mathematics and computation 2007, Vol.184 (1), p.37-51
• Main Authors: del Coz Díaz, J.J., Lamarca, L. Peñalver, García Nieto, P.J., Martínez-Luengas, Alfonso Lozano, Vilán, J.A.Vilán
• Format: Article
• Language: English
• Subjects: Elasticity of concrete; Exact sciences and technology; Finite element modelling; Fundamental areas of phenomenology (including applications); Large displacements; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Physics; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Theory and numerical methods
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.07.073

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.