Isogeometric Bernoulli beam element with an exact representation of concentrated loadings

Abstract

Isogeometric analysis, an alternative to standard FEA using CAD geometry representation directly for analysis, can be especially beneficial in the analysis of curved beams. The use of NURBS for both geometrical description and unknown approximations enables an exact representation of arbitrarily curved shapes and introduces higher continuity along an entire computational domain but causes oscillations in numerical solutions when concentrated loading is applied inside a domain.In this paper, this problem is clearly demonstrated and two possible methods for overcoming it are proposed and illustrated on the straight Bernoulli beam formulation. While the first method uses standard IGA procedures to reduce continuity, the second is specially tailored to the problem with no alteration of the initial basis. The advantages and disadvantages of the approaches presented are discussed and more complex problems are considered.