Analytic sensitivities and design oriented structural analysis for airplane fuselage shape synthesis

Abstract A finite element-based design oriented structural analysis of isotropic and composite fuselage structures is presented. Simple shape parameterization techniques are chosen to demonstrate the explicit dependence of node locations on global shape design variables. Elements, whose stiffness and mass matrices can be expressed explicitly in terms of their vertex locations, as well as their sizing and material design variables, are used. The skin is modeled using flat triangular elements: discrete Kirchhoff triangles for bending, and degenerate linear strain triangles with drilling degrees of freedom for plane stress action. Frame elements are used to model stiffeners and fuselage rings. Analytic sensitivities of displacements, stresses and natural frequencies with respect to global sizing, material and shape design variables are obtained. The results of numerical tests, designed to evaluate the performance of the design oriented finite element capability at varying mesh densities and element aspect ratios, are presented. Sensitivity of finite difference and semi-analytic derivatives to design variable step size is studied using the analytic sensitivities presented. In addition, parametric studies are used to evaluate the performance of direct Taylor series approximations based on analysis and gradient information at reference points in design space.

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