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An hysteretic quadrilateral plane stress element

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Abstract

In this work, a new plane stress element is proposed for the nonlinear static and dynamic analysis of plane stress/plane strain problems. The four node quadrilateral element formulation for the elastic case is extended by introducing a novel hysteretic constitutive relation, based on the Bouc–Wen model of hysteresis. The hysteretic model introduced is directly derived from the governing equations of classical plasticity based on the flow rule and specific hardening law. The stiffness matrix of the element is formulated using the principle of virtual displacements, where the elastic stress–strain relation is substituted by the hysteretic relation proposed. The derived stiffness matrix is expressed as a smooth function of the internal stress field both in the elastic and inelastic regime. The efficiency of the proposed element in the simulation of the cyclic behavior in plane structures is presented through illustrative examples.

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Authors and Affiliations

  1. Institute of Structural Analysis & Aseismic Research, National Technical University of Athens, NTUA, Zographou Campus, 15773, Athens, Greece

    Savvas P. Triantafyllou & Vlasis K. Koumousis

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  1. Savvas P. Triantafyllou
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  2. Vlasis K. Koumousis
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Correspondence to Vlasis K. Koumousis.

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Triantafyllou, S.P., Koumousis, V.K. An hysteretic quadrilateral plane stress element. Arch Appl Mech 82, 1675–1687 (2012). https://doi.org/10.1007/s00419-012-0682-9

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