具有连续纤维路径的纤维增强结构的全面拓扑优化,Computer Methods in Applied Mechanics and Engineering

Fiber-reinforced composite (FRC) structure design by topology optimization has become a hot spot in recent years. Nevertheless, the existing researches reveal several unfavorable issues including the fiber dis-continuity, the length scale separation, the decreased design freedom, as well as the complicated fiber orientation optimization. Thus, this paper proposes a full-scale fiber-reinforced structure topology optimization method that is capable of simultaneous design for the structural topology, continuous fiber path, and its morphology (i.e., fiber volume, spacing and thickness). The method builds upon a bi-material element-wise density-based topology optimization framework, where the matrix material and fiber material are considered in a uniform finite element model without the scale separation. Furthermore, a novel fiber generation scheme is developed, in which the bi-material constraint method is introduced by combining the total solid (composite) volume constraint and local fiber proportion constraint, so as to drive the evolution of the general topology, continuous fiber path and fiber morphology, respectively. In this way, it can avoid the above existing issues of the current FRC designs. The fiber-reinforced structures can be naturally generated with continuous fiber paths. Several numerical examples for compliance minimization problems are provided to show the merits of the full-scale optimization method for fiber-reinforced structures. The interpretation design procedure and post-processing error simulation analysis are also presented to further validate the applicability of the proposed method.