Sobre a utilização de beta -splines no metodo dos elementos finitos para a solução de barras, vigas e placas finas / About the use of beta -splines functions in finite element method to the solution of Bar and Beam structures and Thin Plates

AUTOR(ES)
DATA DE PUBLICAÇÃO

1999

RESUMO

The present Thesis is a step by step formulation for the use of B-splines Functions in the Finite Element Method to approximate de solution of Bars, Beams and Thin Plates structures. The smooth character of the B-Splines given by the C IND. 2 continuity of these cubic polynomials provides a robust frame to the trial functions, increasing thus convergence and precision of the solutions. One important contribution of this work is the addition of auxiliary nodes in the definition of the B-Splines in the vicinity of the structure boundaries. These auxiliary nodes allow the inclusion of a fourth polynomial term in the interpolation of Spline elements close to the boundaries, which garantees the completness of the approximation spaces. The auxiliary spline nodes also permits the introduction of an extra physical degree of freedom at the boundaries of the structures. This additional degree of freedom, together with a coordinate transformation, allow the system equation to be written in terms of the physical boundary quantities. This procedure is an improvement, when compared to other formulations, which require a modification in the Spline functions near the boundaries, to account for the correct boundary conditions. Numerical examples for one- and two-dimensional structures show the efficiency and accuracy of the proposed methodologies

ASSUNTO(S)

vigas barras (engenharia) spline teoria do metodo dos elementos finitos placas (engenharia)

ACESSO AO ARTIGO

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