An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem, and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to KKT points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems. I

Optimization of a frame structure subjected to a plastic deformation

An optimization method for a frame structure subjected to a plastic deformation is proposed in this paper. The method is based on the generalized layout optimization method proposed by Bendsøe and Kikuchi in 1988, where the solid-cavity composite material is distributed in the admissible domain and the cavity size is determined so that it becomes large in the area where the strain energy is small. Elasto-plastic analysis based on the homogenization method is carried out to obtain the nonlinear average stress-strain relations of a porous material first. Then the optimization algorithm of a frame structure is derived by taking plastification into account. Finally in order to demonstrate the effectiveness of the present algorithm, several numerical examples are illustrated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46071/1/158_2005_Article_BF01742592.pd

Optimal design of controlled structures

A formulation that finds the optimal design of a controlled structure is proposed. To achieve this goal, a composite objective composed of structural and control objectives is introduced to be optimized, and the effect of the control weighting is examined. A feedback control law is defined before the structural optimization and then the composite objective will only become a function of structural design variables. As a result, optimal structural design and control forces in steady state are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46072/1/158_2005_Article_BF01279651.pd

Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments

Composite shells, which are being widely used in engineering applications, are often under thermal loads. Thermal loads usually bring thermal stresses in the structure which can significantly affect its static and dynamic behaviors. One of the possible solutions for this matter is embedding Shape Memory Alloy (SMA) wires into the structure. In the present study, thermal buckling and free vibration of laminated composite cylindrical shells reinforced by SMA wires are analyzed. Brinson model is implemented to predict the thermo-mechanical behavior of SMA wires. The natural frequencies and buckling temperatures of the structure are obtained by employing Generalized Differential Quadrature (GDQ) method. GDQ is a powerful numerical approach which can solve partial differential equations. A comparative study is carried out to show the accuracy and efficiency of the applied numerical method for both free vibration and buckling analysis of composite shells in thermal environment. A parametric study is also provided to indicate the effects of like SMA volume fraction, dependency of material properties on temperature, lay-up orientation, and pre-strain of SMA wires on the natural frequency and buckling of Shape Memory Alloy Hybrid Composite (SMAHC) cylindrical shells. Results represent the fact that SMAs can play a significant role in thermal vibration of composite shells. The second goal of present work is optimization of SMAHC cylindrical shells in order to maximize the fundamental frequency parameter at a certain temperature. To this end, an eight-layer composite shell with four SMA-reinforced layers is considered for optimization. The primary optimization variables are the values of SMA angles in the four layers. Since the optimization process is complicated and time consuming, Genetic Algorithm (GA) is performed to obtain the orientations of SMA layers to maximize the first natural frequency of structure. The optimization results show that using an optimum stacking sequence for SMAHC shells can increase the fundamental frequency of the structure by a considerable amount

Safety margins for conservative surrogates

International audienc

Response surface techniques for diffuser shape optimization

The design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of flow devices. Two examples involving two and five design variables are treated, with the diffuser wall shapes described by polynomials and B-splines. In both cases monotonicity conditions drastically reduce the design space. In this irregularly shaped space, a pool of designs is selected by a D-optimality criterion and analyzed by a finite volume computational fluid dynamics (CFD) code. Quadratic polynomial response surfaces are then fitted to the pressure recovery coefficients. To improve the prediction accuracy, uncertain regressor terms and possible outlier design points are excluded based on statistical tests. A standard optimization algorithm is used to find the optimal diffuser design from the response surface approximations. The optimum diffusers exhibit minimal flow separation and yield similar wall shapes for the two parameterizations. A main asset of the response surface optimization approach lies in the smoothing of noisy response functions. Therefore, the issue of numerical noise in CFD results based on the use of two different analysis codes is addressed

Shape Optimization of a Membrane Wing for Micro Air Vehicles

An optimization of a flexible membrane wing using a rigid wing as surrogate was performed. An analysis of the final design has verified that the flexible wing can be improved by optimization of a rigid wing with the same geometry. The optimization leads to lower camber near the root and higher camber near the tip, while still leaving the camber slightly higher at the root than the tip, when compared to the baseline. The improvement in aerodynamics of the optimized wing was largely realized via reduced-form drag and better pressure distributions