Optimal design of thin laminate plates for efficient airflow in ventilation via buckling

Abstract

This work studies an optimal design problem to maximize the airflow opening of a thin-walled structure for efficient ventilation. The airflow opening is defined in terms of nodal displacements as the area swept by a deformed free edge, or the volume formed between the deformed and undeformed configurations or their combination. In this study, a novel formulation for the airflow opening in a plate or shell with large deflections is derived by using the principle of virtual work and the constructed generalized virtual force. In this formulation, the airflow opening can be evaluated via only two finite element analyses for one real and one virtual load cases. By using the present formulation, the maximum airflow problem is formulated as a topology optimization problem for a laminated thin-walled structure, and is subsequently solved by using a moving iso-surface threshold method. Numerical examples are presented for the optimum laminated flat plates of three edges simply supported and one edge free with designable and non-designable layers and under in-plane compression along the two opposite simply-supported edges. The numerical results show that the airflow opening can be maximized when the optimized laminated plate deforms in a shape similar to its critical buckling mode and the opening is much larger than that of the flat plate with the same amount of material and constant thickness.