Abstract
The Hashin’s strength criteria are usually employed in first ply failure and damage-onset analysis of fibre-reinforced composites. This work presents optimality conditions of local material orientations for these criteria, in terms of principal stresses and material strength parameters. Each criterion (matrix tensile/compressive, fibre tensile/compressive modes) has its conditions separately derived, analytically, based on a fixed stress field assumption. The conditions found show that orientations which coincide and do not coincide with principal stress directions may minimise local failure indices. These solutions are employed in a proposed algorithm, named HA-OCM (Hashin Optimality Criteria Method), which selectively satisfies the matrix failure modes (either tensile or compressive), iteratively and finite element-wise in composites. It is demonstrated that the HA-OCM is able to design single-layer plane structures with improved failure loads in comparison with designs following only maximum (in absolute) principal stress orientations. Results show that the material orientations have a trend to end up either aligned or at 90° with maximum in absolute principal stress directions. Global optima for compliance are, however, not guaranteed. To give an idea of gains in terms of failure loads, some HA-OCM designs show improvements of 71% and 140%, for example, in comparison with principal stress design.
Highlights
Fibre-reinforced polymers are composite materials (Jones 1998; Barbero 2010) which enable structures with high specific stiffness and strength
For comparisons with HA-OCM results, a principal stress design strategy was applied to the same examples, based on iteratively aligning, element-wise, the stiffest local material directions with the directions of the maximum principal stresses in absolute
It is seen that final designs differ and, in view of results shown in Table 4, design (a) has a failure load 100% higher than (b). These results show that the HA-OCM was again able to obtain a design with improved failure load compared with principal stress design
Summary
Fibre-reinforced polymers are composite materials (Jones 1998; Barbero 2010) which enable structures with high specific stiffness and strength Their utilisation is well established in several industrial fields, including aerospace, automotive, naval and sport equipment. These composites are usually employed in laminates designed in terms of stacking sequences, which are defined by layer number and thickness, materials and fibre orientations. These parameters can be seen as design variables which may Responsible Editor: Ji-Hong Zhu assume many distinct values. An optimisation process can be classified as constant stiffness design, which according to Ghiasi et al (2009) deals with composite laminates with a uniform stacking sequence throughout the entire structure, or variable stiffness design (Ghiasi et al 2010), where the stacking sequence varies through the structural domain
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