Isogeometric analysis applied to 2D curved beam elements

Gianluca Marchiori¹; Alfredo Gay Neto¹

¹ Polytechnic School at University of São Paulo

doi:10.20906/CPS/CILAMCE2017-0150

Resumo

Isogeometric analysis consists on building the exact geometry of the computational model with functions created by Computer Aided Design (CAD) technologies, such as B-Splines, NURBS (Non-Uniform Rational B-Splines) and T-Splines. Then, isoparametric concept is claimed, that is, the solution space is represented by means of the same functions used to describe the geometry. The Isogeometric concept was proposed by Hughes et al. (2005) and corresponds to the combination of Isoparametric analysis of finite elements with CAD description of geometry. Due to the easiness in generating the exact geometry of the model through CAD technologies, there are several works about isogeometric analysis being done. In this context, the aim of the present contribution is the study of isogeometric analysis applied to 2D beams. It begins with a description of CAD technologies used to describe the geometry, such as B-Splines and NURBS. Then, two formulations of isogeometric curved planar beam models are proposed, based on assumptions of Bernoulli-Euler and Timoshenko beams. Some examples of applications are presented and results are compared with analytical solutions, showing good agreement.

Palavras-chave: Isogeometric analysis; Splines; Beam; Finite element method