Abstract
A new method is presented for first-order elastoplastic analysis of framed structures using a radial return predictor/corrector solution strategy. The proposed method assumes plastic hinge formation coupled with a yield surface. The yield surface is defined as a general function of axial force, shear forces, twisting, and biaxial bending moments on the cross-section of the frame. The material is regarded as linear and elastic-perfect plastic. The plastic deformations are governed by the normality criterion. Combining the Newton-Raphson method and the radial return algorithm, a consistent tangent modular matrix is proposed and fast and converging algorithms are presented. Examples demonstrate the accuracy and effectiveness of the proposed method.
Highlights
Over the last few decades, in the context of computational plasticity, efficient algorithms have been developed for the integration of constitutive models for fragile and ductile materials
This paper presents a new method for a first-order elastoplastic analysis i.e., small strains and small displacements of framed structures under loading-unloading cycle based on the concepts of a radial return predictor/corrector algorithm and b limit analysis or Mathematical Problems in Engineering the so-called “plastic hinge” approach
The radial return algorithms were tested with different yield surfaces given good results
Summary
Over the last few decades, in the context of computational plasticity, efficient algorithms have been developed for the integration of constitutive models for fragile and ductile materials. Excellent references on such integration schemes are the books of Simo and Hughes 1 , Crisfield 2, 3 , Doltsinis 4 , among others. In the literature there are research papers see e.g., 5–8 using implicit algorithms formulated in the stress resultant space for the collapse analysis of elastoplastic frames. For the plastic hinge analysis, this research presumes a generalized yield surface in the six-dimension space of stress resultants or generalized forces. At the end of the paper, three examples are presented and discussed demonstrating the accuracy and effectiveness of the proposed method
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