Adjoint method for the sensitivity analysis of composite beam cross-sections. (March 2019) - Callejo, Alfonso; Bauchau, Olivier A.; Diskin, Boris
Highlights: An overview of the design optimization of multibody systems including beams is provided. A novel adjoint method for the sensitivity analysis of beam cross-sections is presented. To show the accuracy and performance of the method, two numerical examples are investigated. Abstract: The structural components found in mechanical and aerospace engineering applications are often idealized as beams. The sectional stiffness and mass properties of beams made of homogeneous materials and presenting simple geometric shapes are evaluated easily. Axial and bending stiffness constants can be evaluated through simple formulas, whereas the computation of torsional stiffness is more cumbersome. In many aerospace and mechanical applications, wings and rotor blades present complex geometric shapes and are made of advanced, highly anisotropic composite materials. In such cases, the computation of the sectional stiffness properties is a complex task that requires the use of finite element models of the cross-section. The gradient-based optimization of these complex systems requires the evaluation of design sensitivities, which, in turn, calls for the evaluation of the sensitivity of sectional properties with respect to the parameters that define the configuration of the section. This paper presents an approach to this problem based on the adjoint method. Adjoint equations that enable the efficient computation of sensitivity derivatives of sectional stiffness properties with respect to composite design parameters are derived. Examples of cross-sections presenting various configurations and made of advanced composite materials are investigated. Real- and complex-step numerical differentiation methods are used to verify the proposed adjoint formulation.