Abstract
The exact description of the arbitrarily curved geometries, including conic sections, is an undeniable advantage of isogeometric analysis (IGA) over standard finite element method (FEM). With B-spline/NURBS approximation functions used for both geometry and unknown approximations, IGA is able to exactly describe beams of various shapes and thus eliminate the geometry approximation errors. Moreover, naturally higher continuity than standard C0 can be provided along the entire computational domain. This paper evaluates the performance of the nonlinear spatial Bernoulli beam adapted from formulation of Bauer et al. [1]. The element formulation is presented and the comparison with standard FEM straight beam element and fully three-dimensional analysis is provided. Although the element is capable of geometrically nonlinear analysis, only geometrically linear cases are evaluated for the purposes of this study.
Highlights
The desire for the automatic connection between Computer-aided design (CAD) and Finite element analysis (FEA) has been the crucial impulse for the development of isogeometric analysis [2]
The idea of isogeometric analysis (IGA) is to use the basis functions used for the geometry description in CAD as the approximation functions for the analysis
One of them is a possibility to exactly model arbitrarily curved geometries, including a conic sections which can be only approximated by standard polynomial basis functions
Summary
The desire for the automatic connection between Computer-aided design (CAD) and Finite element analysis (FEA) has been the crucial impulse for the development of isogeometric analysis [2]. The idea of IGA is to use the basis functions used for the geometry description in CAD as the approximation functions for the analysis. This results in the possibility of only one model shared between the design and analysis. One of them is a possibility to exactly model arbitrarily curved geometries, including a conic sections which can be only approximated by standard polynomial basis functions. This makes it very convenient for the use in the analysis of curved beams. The beam formulation is briefly introduced and the performance over standard FEM approaches is evaluated
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