Special Elements for Composites Containing Hexagonal and Circular Fibers

Abstract

In this paper, unidirectional fiber reinforced composites with periodic square array of circular and hexagonal fibers is studied by a novel fundamental-solution-based hybrid finite element model. Due to the periodicity of composites, a representative unit cell containing a single fiber with circular or hexagonal cross section is taken into consideration and analyzed using the proposed hybrid finite element model. In the present numerical model, special polygonal fiber elements with arbitrary number of sides are developed by coupling the independent element interior and frame displacement fields. The element interior displacement fields are approximated by the combination of fundamental solutions to prior satisfy the governing equation of the problem, so that the domain integral appeared in the weak-form hybrid functional in terms of dual variables is converted into boundary integrals. Independently the element frame displacement fields are approximated by the conventional shape functions to guarantee the continuity of adjacent elements. Following this, special polygonal fiber elements are constructed to reduce mesh effort in the fiber region and achieve good accuracy with fewer elements. Finally, numerical tests are carried out for assessing the performance of the present special elements.