Abstract
In the present work we propose to compare the conventional finite element analysis and isogeometric analysis methods. We explore these two modeling methods in the same application in order to identify their differences. From the analytical point of view there is a difference in the type of the shape functions, the Lagrange polynomials used in finite element analysis interpolate the nodal points, and are C0 continuity at the nodal points, in the isogeometric analysis, the NURBS basis functions (Non Uniform Rational B-Spline) have a high continuity and do not interpolate control points. For the comparative study of the two modeling methods, we chose the standard Modal Assurance Criterion (MAC) to compare the eigenmodes. Because of the equality of the first order Lagrange polynomials and the first order NURBS functions, we obtain a perfect eigenmodes correlation of the two methods, but the correlation for the second order shows a slight difference, which highlights a different classification of the two modeling methods.DOI: http://dx.doi.org/10.5755/j01.mech.23.1.13890
Highlights
The thrust of the isogeometric analysis is to bring the finite element CAD modelling analysis by exploiting the geometric model as a support for the calculation. This can be done through the development of new types of finite element models using the same basis functions as those used in CAD models defining exact geometry
The basis functions and nodes vectors Ξ = [0 0 0 1/3 2/3 1 1 1] and H = [0 0 0 1/3 2/3 1 1 1] are subdivided into three inter-nodal areas to subdivide the thin plate into nine elements, the same number of elements as in the previous case in order to make a comparative study using the correlation function Modal Assurance Criterion (MAC)
The eigenvalues given by the two modeling methods in the case of first order shape functions are the same Fig. 2 and Fig. 6, this is due to the shape functions that are the same
Summary
The thrust of the isogeometric analysis is to bring the finite element CAD modelling analysis by exploiting the geometric model as a support for the calculation. This can be done through the development of new types of finite element models using the same basis functions as those used in CAD models defining exact geometry. The majority modelling tools uses NURBS functions (Non Uniform Rational B-Spline) for the geometric description. These have interesting properties and stable algorithms to generate and manipulate models. We compare the results obtained using the MAC (Modal Assurance Criterion) correlation function in structural dynamics [7, 8]
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