Numerical modelling of 2D composite solids accounting for local fibre bending stiffness

This contribution deals with the development of a four-node membrane composite finite element to analyse two-dimensional (2D) fibre-reinforced solids taking into account the local bending stiffness of fibres. This plane composite element is a combination of a four-node membrane element with rotational degrees of freedom (DOFs), modelling a unit of the matrix domain, and two-node Timoshenko beam elements that represent fibres crossing each matrix element. The so-called ’Projected Fibre Approach’ is then considered to express the beam elements variables in terms of their corresponding matrix elements. Accordingly, the obtained system of equations size is equivalent to that of a non-reinforced medium which considerably reduces the computing cost. To assess the accuracy of the proposed plane element, three examples are presented and the obtained results are found to agree well with the reference solutions.