Adjoint-based analysis and optimization of beam-like structures subjected to dynamic loads

This paper presents the development of a framework to directly size and optimize a structure under dynamic loads with a special focus on enabling early aircraft design. Low degrees of freedom (DoF) beam models are used in lieu of high DoF models to represent the structure, thereby significantly reducing the computational cost (both runtime and memory). For a given residual system of equations, the adjoint method for time-dependent problems is solved using the stable backward difference formula scheme. This generalization allows for the implementation of a generic, equation-agnostic adjoint solver. Constraint aggregation techniques are extended to both spatial and temporal domains to constrain the strength-based stress yield criterion throughout the dynamic simulation. Consequently, the structure can directly be sized and optimized under the dynamic loads, without the need to rely on conversion to equivalent static loads. Finally, the developed framework is leveraged to demonstrate and quantify the consequence of neglecting dynamic loads on a notional ‘wing-like’ wingbox structure subjected to several dynamic gust load profiles.