Multilevel Design Optimization Under Uncertainty with Application to Product-Material Systems

The main objective of this research is to develop a computational design tool for multilevel optimization of product-material systems under uncertainty. To accomplish this goal, an exponential penalty function (EPF) formulation based on method of multipliers is developed for solving multilevel optimization problems within the framework of Analytical Target Cascading (ATC). The original all-at-once constrained optimization problem is decomposed into a hierarchical system with consistency constraints enforcing the target-response coupling in the connected elements. The objective function is combined with the consistency constraints in each element to formulate an augmented Lagrangian with EPF. The EPF formulation is implemented using double-loop (EPF I) and single-loop (EPF II) coordination strategies and two penalty-parameter-updating schemes. The computational characteristics of the proposed approaches are investigated using different nonlinear convex and non-convex optimization problems. An efficient reliability-based design optimization method, Single Loop Single Vector (SLSV), is integrated with Augmented Lagrangian (AL) formulation of ATC for solution of hierarchical multilevel optimization problems under uncertainty. In the proposed SLSV+AL approach, the uncertainties are propagated by matching the required moments of connecting responses/targets and linking variables present in the decomposed system. The accuracy and computational efficiency of SLSV+AL are demonstrated through the solution of different benchmark problems and comparison of results with those from other optimization methods. Finally, the developed computational design optimization tool is used for design optimization of hybrid multiscale composite sandwich plates with/without uncertainty. Both carbon nanofiber (CNF) waviness and CNF-matrix interphase properties are included in the model. By decomposing the sandwich plate, structural and material designs are combined and treated as a multilevel optimization problem. The application problem considers the minimum-weight design of an in-plane loaded sandwich plate with a honeycomb core and laminated composite face sheets that are reinforced by both conventional continuous fibers and CNF-enhanced polymer matrix. Besides global buckling, shear crimping, intracell buckling, and face sheet wrinkling are also treated as design constraints

Multilevel Design Optimization Under Uncertainty with Application to Product-Material Systems

The main objective of this research is to develop a computational design tool for multilevel optimization of product-material systems under uncertainty. To accomplish this goal, an exponential penalty function (EPF) formulation based on method of multipliers is developed for solving multilevel optimization problems within the framework of Analytical Target Cascading (ATC). The original all-at-once constrained optimization problem is decomposed into a hierarchical system with consistency constraints enforcing the target-response coupling in the connected elements. The objective function is combined with the consistency constraints in each element to formulate an augmented Lagrangian with EPF. The EPF formulation is implemented using double-loop (EPF I) and single-loop (EPF II) coordination strategies and two penalty-parameter-updating schemes. The computational characteristics of the proposed approaches are investigated using different nonlinear convex and non-convex optimization problems. An efficient reliability-based design optimization method, Single Loop Single Vector (SLSV), is integrated with Augmented Lagrangian (AL) formulation of ATC for solution of hierarchical multilevel optimization problems under uncertainty. In the proposed SLSV+AL approach, the uncertainties are propagated by matching the required moments of connecting responses/targets and linking variables present in the decomposed system. The accuracy and computational efficiency of SLSV+AL are demonstrated through the solution of different benchmark problems and comparison of results with those from other optimization methods. Finally, the developed computational design optimization tool is used for design optimization of hybrid multiscale composite sandwich plates with/without uncertainty. Both carbon nanofiber (CNF) waviness and CNF-matrix interphase properties are included in the model. By decomposing the sandwich plate, structural and material designs are combined and treated as a multilevel optimization problem. The application problem considers the minimum-weight design of an in-plane loaded sandwich plate with a honeycomb core and laminated composite face sheets that are reinforced by both conventional continuous fibers and CNF-enhanced polymer matrix. Besides global buckling, shear crimping, intracell buckling, and face sheet wrinkling are also treated as design constraints

Optimal operation of active distribution grids: A system of systems framework

Active distribution grid is composed of autonomous systems which should collaborate with each other in order to operate the entire distribution grid in a secure and economic manner. This paper presents a system of systems (SoS) framework for optimally operating active distribution grids. The proposed SoS framework defines both distribution company (DISCO) and microgrids (MGs) as independent systems, and identifies the process of information exchange among them. As the DISCO and MGs are physically connected together, the operating condition of one might impact the operating point of other systems. The proposed mathematical model uses a decentralized optimization problem aimed at maximizing the benefit of each independent system. A hierarchical optimization algorithm is presented to coordinate the independent systems and to find the optimal operating point of the SoS-based active distribution grid. The numerical results show the effectiveness of the proposed SoS framework and solution methodology. © 2010-2012 IEEE

Topology Optimization of an Additively Manufactured Beam

This study investigates the application of topological optimization in conjunction with additive manufacturing (AM) process simulation for fabricating parts that meet strict quality and performance requirements while also minimizing printed geometry. Integrated Computational Materials Engineering (ICME) and GENOA 3D commercial software were used to simulate specimen fabrication and, along with commercial design optimization tools, create an optimized beam topology for simple loading conditions. Constraints were set in order to support any overhanging material with an appropriate inclination angle. These specimens were fabricated from Ti-6Al-4V using an EOS M290 direct metal laser sintering (DMLS) system with default parameters, as well as 95%, 90%, and 88% of default laser power in order to reduce the porosity in the overheated areas. Parts were subjected to X-ray CT scanning to quantify part porosity. It was determined that the process used allowed for the fabrication of specimens with optimized topology and minimal defects.Mechanical Engineerin