关键词: 复合材料层合板, 曲线纤维铺放路径, 拓扑优化, 本构关系

Abstract: Composite laminated plates with curvilinear fiber laying paths are taking as the research object in this paper. A model of curvilinear fiber laying path in single layer for the composite laminated plates was firstly constructed. Combined with the discretation and element equivalent principles of the laminated plates, the elemental equivalent constitutive relation of laminated plates with curvilinear fiber paths was established. Based on the material penalty model, a topology optimization model of composite laminated plates with curvilinear fiber paths under volume constraint was proposed to minimize the strain energy to evaluate the structural stiffness. The topology optimization model was solved based on finite element and moving asymptote method to obtain the optimal topological shape of laminated structures. Numerical examples were used to verify the accuracy of the design method. The results show that the topology optimization method can obtain effective topological shape, and the structural stiffness of cantilever beam and simply supported beam can be increased by 36.9% and 22.6% respectively. The performances are significantly improved by changing the curvilinear fiber laying paths.

Key words: composite laminated plates, curvilinear fiber laying paths, topology optimization, constitutive relation