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In a recent paper, Cho and Kim [Journal of Applied Mechanics] proposed a higher-order cubic zigzag theory of laminated composites with multiple delaminations. The proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. In this work, we investigate the dynamic behavior of laminated composite plates with multiple delaminations. A four-node finite element based on the efficient higher-order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response. Through the dynamic version of the variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method. To prevent penetration violation at the delamination interfaces, unilateral contact constraints by Lagrange multiplier method are applied in the time response analysis. The present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations.

Typically in the analysis of industrial data for product/process optimization, there are many response variables that are under investigation at the same time. Robustness is also an important concept in industrial optimization. Here, robustness means that the responses are not sensitive to the small changes of the input variables. However, most of the recent work in industrial optimization has not dealt with robustness, and most practitioners follow up optimization calculations without consideration for robustness. This paper presents a strategy for dealing with robustness and optimization simultaneously for multiple responses. In this paper, we propose a robustness desirability function distinguished from the optimization desirability function and also propose an overall desirability function approach, which makes balance between robustness and optimization for multiple response problems. Simplex search method is used to search for the most robust optimal point in the feasible operating region. Finally, the proposed strategy is illustrated with an example from the literature.