Linear transient analysis of spatial curved Bernoulli – Euler beam using isogeometric approach

Abstract

In this paper, linear transient analysis of spatial curved Bernoulli – Euler beam with circular cross – section formulated using isogeometric approach has been presented. The isogeometric approach is based on the concept that the geometry of the beam, as well as the displacement field are defined using the Non – Uniform Rational B – Spline (NURBS) functions. Governing equations of motions are derived using the basic relations of the differential geometry and continuum mechanics. In order to conduct transient analysis, time discretization has been employed using explicit integration scheme. The validation of the proposed method has been carried out for the spatial curved cantilever beam subjected to the point load with constant magnitude. The results of the free end displacements obtained using proposed method have shown excellent convergence properties and agreement with the results obtained using finite element-based software. In comparison to the conventional finite element method, less number of degrees of freedom are required in order to obtain accurate results.