期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 74, 期 7, 页码 1531-1541出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.04.025
关键词
Non-prismatic beams; Tapered beams; Isogeometric analysis; Mixed collocation methods; B-splines
资金
- Austrian Science Found (FWF) [M 2009-N32]
- 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
The present paper combines an effective beam theory with a simple and accurate numerical technique opening the door to the prediction of the structural behavior of planar beams characterized by a continuous variation of the cross-section geometry, that in general deeply influences the stress distribution and, therefore, leads to non-trivial constitutive relations. Accounting for these peculiar aspects, the beam theory is described by a mixed formulation of the problem represented by six linear Ordinary Differential Equations (ODES) with non-constant coefficients depending on both the cross-section displacements and the internal forces. Due to the ODEs' complexity, the solution can be typically computed only numerically also for relatively simple geometries, loads, and boundary conditions; however, the use of classical numerical tools for this problem, like a (six-field) mixed finite element approach, might entail several issues (e.g., shear locking, ill-conditioned matrices, etc.). Conversely, the recently proposed isogeometric collocation method, consisting of the direct discretization of the ODEs in strong form and using the higher-continuity properties typical of spline shape functions, allows an equal order approximation of all unknown fields, without affecting the stability of the solution. This makes such an approach simple, robust, efficient, and particularly suitable for solving the system of ODEs governing the non prismatic beam problem. Several numerical experiments confirm that the proposed mixed isogeometric collocation method is actually cost-effective and able to attain high accuracy. (C) 2017 The Authors. Published by Elsevier Ltd.
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