The stiffness properties of variable stiffness (VS) composite plates can be controlled by manipulating the variation in the fiber angle, thereby significantly improving their buckling properties. Nonlinear fiber paths have attracted attention in the field of composites due to their large design space. The major challenge in adopting nonlinear fiber paths is obtaining a fiber path function within the design space that is easily computable and efficiently yields the highest buckling load of a VS plate. In this investigation, an innovative nonlinear function was proposed to describe the fiber orientation by integrating a center fiber angle into the conventional linear function. The parameters of the nonlinear function can directly represent the fiber angles at a fixed position. This novel approach has promising potential for improving the optimal efficiency of fiber paths because the linear and nonlinear functions are simplified with two identical path parameters. Furthermore, a multilevel optimization method was developed by combining finite element analysis (FEA) with an adaptive radial basis function (RBF) surrogate model, and it was found that the number of FEA cases could be reduced by iteratively inheriting training points. The integration of this nonlinear function with a surrogate model is a significant advancement in the structural optimization of composites. Subsequently, the optimal linear and nonlinear fiber paths were computed to maximize the buckling load of VS plates. The FEA results show that the computational efficiency was greatly improved by the proposed nonlinear function and optimization method. The buckling resistance could be enhanced by the nonlinear fiber path, and the reinforcement mechanism was the redistribution and reduction of in-plane compressive stress.

This paper analyzes the kinematic optimization design of the 4R 2-DOF parallel mechanism taking into account the force transmissibility. Three indices are introduced to reflect the force transmissibility. Based on these indices and their performance charts, the optimization design process with respect to the workspace is presented in detail. The results show that the designed mechanism is not only far from every singularity but also has good force transmissibility in its workspace. These kinematic optimization indices can be extended to other parallel mechanisms.