A total secant flexibility-based formulation for frame elements with physical and geometrical nonlinearities

  • Authors:

  • Hamid R. Valipour;Stephen J. Foster

  • Affiliations:

  • Centre for Infrastructure Engineering and Safety (CIES), School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia;Centre for Infrastructure Engineering and Safety (CIES), School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia

  • Venue:
  • Finite Elements in Analysis and Design
  • Year:
  • 2010

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Abstract

This paper presents the formulation for a novel flexibility-based 1D frame element that captures material and geometrical nonlinearities. Decomposing the total strain to elastic and inelastic components a secant solution strategy based on a direct iterative scheme is introduced and the corresponding solution strategy is demonstrated. Concerning geometrical nonlinearities, the strain and slope of the deformed element are assumed to be small; however the equilibrium equations are satisfied for the deformed element that takes account of P-@D effects. Using Simpson integration scheme along with piecewise interpolation of the curvature, the geometry of the deformed element is consistently updated. The implementation of the formulation in conjunction with a nonlocal damage model for capturing the response of element with softening such as reinforced concrete beam-columns is outlined and the formulation accuracy and efficiency is verified by some numerical examples on reinforced concrete frames.