Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

This study investigates topology optimization of energy absorbing structures in which material damage is accounted for in the optimization process. The optimization objective is to design the lightest structures that are able to absorb the required mechanical energy. A structural continuity constraint check is introduced that is able to detect when no feasible load path remains in the finite element model, usually as a result of large scale fracture. This assures that designs do not fail when loaded under the conditions prescribed in the design requirements. This continuity constraint check is automated and requires no intervention from the analyst once the optimization process is initiated. Consequently, the optimization algorithm proceeds towards evolving an energy absorbing structure with the minimum structural mass that is not susceptible to global structural failure. A method is also introduced to determine when the optimization process should halt. The method identifies when the optimization method has plateaued and is no longer likely to provide improved designs if continued for further iterations. This provides the designer with a rational method to determine the necessary time to run the optimization and avoid wasting computational resources on unnecessary iterations. A case study is presented to demonstrate the use of this method.

Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.