Numerically consistent regularization of force‐based frame elements

Recent advances in the literature regularize the strain-softening response of force-based frame elements by either modifying the constitutive parameters or scaling selected integration weights. Although the former case maintains numerical accuracy for strain-hardening behavior, the regularization requires a tight coupling of the element constitutive properties and the numerical integration method. In the latter case, objectivity is maintained for strain-softening problems; however, there is a lack of convergence for strain-hardening response. To resolve the dichotomy between strain-hardening and strain-softening solutions, a numerically consistent regularization technique is developed for force-based frame elements using interpolatory quadrature with two integration points of prescribed characteristic lengths at the element ends. Owing to manipulation of the integration weights at the element ends, the solution of a Vandermonde system of equations ensures numerical accuracy in the linear-elastic range of response. Comparison of closed-form solutions and published experimental results of reinforced concrete columns demonstrates the effect of the regularization approach on simulating the response of structural members. Copyright © 2008 John Wiley & Sons, Ltd.

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