An Analytical Study on the Pure Bending of SMA Curved Beams

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Fazlali, Mohammad Reza | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49628 (09)
University: Sharif University of Technology
Department: Civil Engineering
Advisor(s): Eskandari, Morteza; Arghavani Hadi, Jamal
Abstract:
In this thesis, an analytical solution is presented for pure bending of SMA curved beams with rectangular cross section and both loading and unloading stages are considered. Moreover, by appropriate simplification, its application in elastoplastic pure bending of curved beams made of regular materials is investigated. Elastic-linear kinematic hardening behavior of the material is assumed and both loading and unloading stages are considered. Exact plane plasticity solution of the elastoplastic pure bending of curved beams made of regular materials which exists in loading and is available for rectangular cross section has many unknowns and longsome equations. Therefore, it is difficult to use it for early designs and to extend it to curved beams with other cross sections. First, Souza’s three-dimensional constitutive equation is reduced to one-dimensional form. Then, based on the beam’s geometry and equilibrium equations, the necessary equations for loading and unloading stages are derived, and analytical solution of the curved beam is done in five stages. Finally, the results are validated and possible errors are investigated
Keywords:
Shape Memory Alloy ; Curved Beams ; Pure Bending ; Elastopelastic Bending ; Linear Hardening ; Souza's Constitutive Equation