Isogeometric Analysis of Euler-Bernoulli Beam Element

Abstract: The Isogeometric analysis is a computational geometry based on a series of polynomial functions (Non-Uniform Rational B-Spline, NURBS) which are assembled to represent the exact geometry. In the Isogeometric analysis, the curvature geometry of the beam element can be represented exactly. The conventional beam element can be developed by using the Isogeometric approach which is based on Euler-Bernoulli principle which is under the assumption that the dimension of the beam cross section is small compared with the length of the beam. The geometric shape of the beam and the shape functions formulation of the element can be formulated by using the Isogeometric approach. This paper highlights the application of the NURBS for the Euler-Bernoulli beam element in the context of finite element analysis. Examples are given to verify the effectiveness of the Isogeometric approach in static and free vibration problems.