Deployment dynamics and topology optimization of a spinning inflatable structure

Inflatable space structures may undergo the vibration of a long duration because of their features of dynamic deployment, high flexibility, and low-frequency modes. In this paper, a topology optimization methodology is proposed to reduce the vibration of a spinning inflatable structure. As the first step, a variable-length shell element is developed in the framework of arbitrary Lagrange-Euler (ALE) and absolute nodal coordinate formulation (ANCF) to accurately model the deployment dynamics of the inflatable structure. With the help of two additional material coordinates, the shell element of ALE-ANCF has the ability to describe the large deformation, large overall motion, and variable length of an inflatable structure. The nonlinear elastic forces and additional inertial forces induced by the variable length are analytically derived. In the second step, a topology optimization procedure is presented for the dynamic response of an inflatable structure through the integration of the equivalent static loads (ESL) method and the density method. The ESL sets of the variable-length inflatable structure are defined to simplify the dynamic topology optimization into a static one, while the density-based topology optimization method is used to describe the topology of the inflatable structure made of two materials and solve the static optimization problem. In order to obtain more robust optimization results, sensitivity analysis, density filter, and projection techniques are also utilized. Afterwards, a benchmark example is presented to validate the ALE-ANCF modeling scheme. The deployment dynamics and corresponding topology optimization of a spinning inflatable structure are studied to show the effectiveness of the proposed topology optimization methodology. [Figure not available: see fulltext.].