A multi-scale model of fibre reinforced beams using hierarchical one-dimensional finite elements

A multi-scale model of fibre reinforced beams using hierarchical one-dimensional finite elements A multi-scale analysis of fibre reinforced composite beams was proposed by this presentation. At structural level, several higher-order refined beam theories can be easily implemented on the basis of Carrera's unified formulation (CUF) by deriving a fundamental nucleus that does not depend upon the approximation order nor the number of nodes per element (they are free parameters of the formulation). Under the framework of FE2 method, the effective properties of the fibre-reinforced composite material are found by numerical homogenization over representative volume elements, that is, the unknown constitutive relationship at the macro-scale is obtained by solving a local finite element problem at the micro-scale. Consequently, a coupled two-scale problem is obtained for linear cases. Results are validated in terms of accuracy and computational costs towards FEM solutions. Numerical investigations show that accurate results can be obtained with reduced computational costs.