Geometrically Nonlinear Isogeometric Analysis of Functionally Graded Solids

Resumo

Functionally Graded Materials (FGM) are composites with a gradual and continuously varying com-
position. Given the constituents, the volume fraction is evaluated by a mathematical function and the effective

properties by a homogenization method. Composite structures made of FGM are commonly analyzed using Fi-
nite Elememt Method (FEM). Isogeometric Analysis (IGA) is an alternative to FEM where the displacement field

is approximated using the same basis functions employed in geometric representation, as B-Splines or NURBS.
This work presents an isogeometric formulation for geometrically nonlinear analysis of functionally graded solids
based on trivariate basis functions. Numerical results are evaluated for small and large displacements problems,

and excellent results are obtained in all examples and gradations studied. Furthermore, the results showed that us-
ing higher order functions leads to faster convergence, requiring fewer degrees of freedom in comparison to lower

order functions.