Analytical integration of elasto-plastic uniaxial constitutive laws over arbitrary sections

• Published in: International journal for numerical methods in engineering Vol. 91; no. 9; pp. 990 - 1022
• Main Authors: Marmo, Francesco, Rosati, Luciano
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 31.08.2012; Wiley
• Subjects: Applied sciences; Building structure; Buildings. Public works; Construction (buildings and works); Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); nonlinear analysis; Physics; reinforced concrete; Reinforced concrete structure; sectional analysis; Solid mechanics; Structural and continuum mechanics; Constitutive equation; Numerical integration; nonlinear analysis; Subdivision; sectional analysis; Modeling; Reinforced concrete; Inelasticity; Gaussian process; Normal stress; Elastoplasticity; Polygonal shape; Non linear effect
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4316

SUMMARY We present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto‐plastic uniaxial constitutive laws. By means of a suitable application of Gauss theorem, we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section. For this reason, the proposed approach has been termed fiber‐free to emphasize the fact that it does not require any subdivision of the section in fibers. Numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber‐free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis. Copyright © 2012 John Wiley & Sons, Ltd.