A novel CS-RBFs-based parameterization scheme for the optimization design of curvilinear variable-stiffness composites with manufacturing constraints

Recent advancements in additive manufacturing technology have made it convenient to design and fabricate composites with curvilinear fibers and the desired performance. For the optimization design of fiber-reinforced composite, two key issues are the description of spatially varying fiber angles and the mathematical representation of the manufacturing constraints. A novel parameterization scheme based on the compactly supported radial basis functions (CS-RBFs) is established to describe the spatially varying fiber angle vector field. Its main characters, including the nonnegativity, partition of unity, and differentiability, inherently ensure the fiber continuity, the bounds of the design variables and make it compatible with the gradient-based optimization design algorithm. Besides, a mathematical formulation is developed to construct the relationships between two common manufacturing constraints (minimum turning radius and gap/overlap) and the curl and divergence of the vector field. By the proposed parameterization scheme and p-norm aggregation function, these manufacturing constraints can be easily described in all elements and added to the optimization. Several numerical examples are conducted to investigate the influence of the varying support points, the radius of the CS-RBFs, initial design, load condition, norm parameter and the excitation frequency on the final design. The optimized results demonstrate the effectiveness of the proposed method.