A displacement-free formulation for the Timoshenko beam problem and a corresponding isogeometric collocation approach
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We present a reformulation of the classical Timoshenko beam problem, resulting in a single differential equation with the rotation as the only primal variable. We show that this formulation is equivalent to the standard formulation and the same types of boundary conditions apply. Moreover, we develop an isogeometric collocation scheme to solve the problem numerically. The formulation is completely locking-free and involves only half the degrees of freedom compared to a standard formulation. Numerical tests are presented to confirm the performance of the proposed approach.
KeywordsTimoshenko beam Shear-deformable Locking-free Displacement-free Isogeometric Collocation
J. Kiendl was partially supported by the Onsager fellowship program of NTNU. J. Kiendl, A. Reali, and F. Auricchio were partially supported by the ERC Starting Grant No. 259229 ISOBIO. A. Reali was partially supported by Fondazione Cariplo–Regione Lombardia through the project “Verso nuovi strumenti di simulazione super veloci ed accurati basati sull’analisi isogeometrica”, within the program “RST–rafforzamento”. This support is gratefully acknowledged.
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The authors declare that they have no conflict of interest.
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