caa a22 4500 445812354 CHVBK 20180317145215.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00419-009-0403-1 doi (NATIONALLICENCE)springer-10.1007/s00419-009-0403-1 Exact solution of 3D Timoshenko beam problem using linked interpolation of arbitrary order [Elektronische Daten] [Gordan Jelenić, Edita Papa] For arbitrary polynomial loading and a sufficient finite number of nodal points N, the solution for the 3D Timoshenko beam differential equations is polynomial and given as $${{\varvec \theta} = \sum_{i=1}^N I_i {\varvec \theta}_i}$$ for the rotation field and $${{\bf u} = \sum_{i=1}^{N+1} J_i {\bf u}_i}$$ for the displacement field, where I i and J i are the Lagrangian polynomials of order N−1 and N, respectively. It has been demonstrated in this work that the exact solution for the displacement field may be also written in a number of alternative ways involving contributions of the nodal rotations including $${{\bf u} = \sum_{i=1}^N I_i \left[ {\bf u}_i + \frac 1 N ( {\varvec \theta} - {\varvec \theta}_i ) \times {\bf R}_i \right]}$$, where R i are the beam nodal positions. Springer-Verlag, 2009 Linked interpolation nationallicence Timoshenko beam nationallicence Higher-order interpolation nationallicence Jelenić Gordan Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia aut Papa Edita Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia aut Archive of Applied Mechanics Springer-Verlag 81/2(2011-02-01), 171-183 0939-1533 81:2<171 2011 81 419 https://doi.org/10.1007/s00419-009-0403-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-009-0403-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jelenić Gordan Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia aut NATIONALLICENCE 700 1- Papa Edita Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/2(2011-02-01), 171-183 0939-1533 81:2<171 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer