Nonlinear Dynamic Response Structural Optimization of a Joined-Wing Using Equivalent Static Loads

The joined-wing configuration that was published by Wolkovich in 1986 has been studied by many researchers (Wolkovich, J., "The Joined-Wing: An Overview," Journal of Aircraft, Vol. 23, No. 3, 1986, pp. 161-178. doi:10.2514/3.45285). The joined-wing airplane is defined as an airplane that incorporates tandem wings arranged to form diamond shapes from both the top and front views. The joined wing can lead to increased aerodynamic performances as well as a reduction in the structural weight. However, the joined wing has high geometric nonlinearity under the gust load. The gust load acts as a dynamic load. Therefore, nonlinear dynamic (transient) behavior of the joined wing should he considered in structural optimization. In previous research, linear dynamic response optimization and nonlinear static response optimization were performed. It is well known that conventional nonlinear dynamic response optimization is extremely expensive. Therefore, in this research, nonlinear dynamic response optimization of a joined wing is carried out by using equivalent static loads. The concept of equivalent static loads is expanded and newly proposed for nonlinear dynamic response optimization. Equivalent static loads are the load sets that generate the same response field in linear static analysis as that in nonlinear dynamic analysis. Therefore, nonlinear dynamic response optimization can be conducted by repeated use of linear response optimization. For the verification of efficiency of the proposed method, a simple nonlinear dynamic response optimization problem is introduced. The problem is solved by using both the equivalent static loads method and the conventional method with sensitivity analysis using the finite difference method. The procedure for nonlinear dynamic response optimization of a joined wing using equivalent static loads is explained, and the optimum results are discussed.