Three-dimensional second-order inelastic analysis of steel frames
Abstract
This research addresses accurate, efficient and rigorous finite element modeling of the three-dimensional second-order inelastic response of beam-column members and their interaction in general three-dimensional framing systems. To this end, two beam-column finite elements based on displacement-type and mixed approaches, that can represent the inelastic three-dimensional stability behavior of a member of open-walled cross-section, arbitrarily curved in space, are formulated. The beam-column kinematics of deformation include finite rotation, torsional warping of cross-sections and flexural-torsional coupling. Shear stresses due to uniform torsion are considered in addition to normal stresses due to axial force, biaxial bending and bimoments. A generalized variational principle is used to formulate the mixed finite element. Variationally consistent force recovery algorithms that are suitable for elastoplastic analysis are derived for two- and three-parameter mixed variational formulations. The finite elements are formulated both in Total Lagrangian (TL) and Total Lagrangian Co-Rotational (TL-CR) descriptions. A consistent transformation between TL and TL-CR formulations is derived. Along with the above aspects of formulation, this research also addresses return mapping algorithms and consistent tangent operators for multi-dimensional $J\sb {2}$ flow theory in a given constrained configuration subspace. The classical radial return mapping algorithm is adopted for strain constrained subspaces, and a plane stress return mapping algorithm developed by Simo is generalized for any stress constrained subspace. The constitutive model is implemented in an object-oriented environment such that the return mapping algorithms and the consistent tangent operators are obtained for any constrained configuration subspace. The above displacement-based and mixed bean-column finite elements are used in studying the inelastic two- and three-dimensional response of frames. The studies involve comparison with several well established, and recent insightful experimental investigations. The numerical studies indicate that the mixed element has better coarse mesh accuracy than the displacement element especially in the inelastic analysis. The developed finite elements are capable of representing the inelastic stability behavior of beam-column members that are arbitrarily deformed in space, and their interaction in general three-dimensional framing systems. The proposed research provides the necessary capabilities to perform a more realistic and rational three-dimensional second-order inelastic analysis of steel frames.
Degree
Ph.D.
Advisors
Chen, Purdue University.
Subject Area
Civil engineering|Mechanics|Aerospace materials
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