Dianzi Liu

Bilevel Optimization of Blended Composite Wing Panels

Two approaches are examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints: smeared-stiffness-based method and lamination-parameter-based method. In the firstmethod, thematerial volume is the objective function at the global level, and the stack shuffling to satisfy blending and manufacturing constraints is performed at the local level. The other method introduced in this paper is to use lamination parameters and numbers of plies of the predefined angles (0, 90, 45, and 45 deg) as design variables with buckling, strain, and ply percentage constraints while minimizing the material volume in the top-level optimization run.Given lamination parameters from the top-level optimization as targets for the local level, an optimal stacking sequence is determined to satisfy the global blending requirements. On a benchmark problem of an 18-panel wing box, the results from these two approaches are compared to published results to demonstrate their potential.

Bi-level Optimization of Blended composite Panels

Two approaches are examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints: smeared stiffnessbased method and lamination parameter-based method. In the first method, the material volume is the objective function at the global level and the stack shuffling to satisfy blending and manufacturing constraints is performed at the local level. The other method introduced in this paper is to use lamination parameters and numbers of plies of the pre-defined angles (0, 90, 45 and -45 degrees) as design variables with buckling, strength and ply percentage constraints while minimizing the material volume in the top level optimization run. Given lamination parameters from the top level optimization as targets for the local level, optimal stacking sequence is determined to satisfy the global blending requirements. On a benchmark problem of an 18-panel wing box, the results from these two approaches are compared to published results to demonstrate their potential.

Optimization of Blended Composite Wing Panels Using Smeared Stiffness Technique and Lamination Parameters

§** The smeared stiffness-based method is examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints . In this method, numbers of plies of the pre-defined angles (0, 90, 45 and -45 degrees) are design variables, buckling, strain and ply angle percentages are constraints and the material volume is the objective function at the global level . The ply shuffling to satisfy global blending and manufacturing constraints is performed at the local level to match zero values of lamination parameters. The latter requirement is due to the ply angle homogeneity through the stack that is assumed in the top level optimization. This integrated process utilizing the smeared stiffness technique and lamination parameters is demonstrated by the optimization of the root part of a generic aircraft wing structure. The local level optimization can be seen as a postprocessing phase for determining the detailed ply-book of the laminate.

Detailed design of a lattice composite fuselage structure by a mixed optimization method

In this article, a procedure for designing a lattice fuselage barrel is developed. It comprises three stages: first, topology optimization of an aircraft fuselage barrel is performed with respect to weight and structural performance to obtain the conceptual design. The interpretation of the optimal result is given to demonstrate the development of this new lattice airframe concept for the fuselage barrel. Subsequently, parametric optimization of the lattice aircraft fuselage barrel is carried out using genetic algorithms on metamodels generated with genetic programming from a 101-point optimal Latin hypercube design of experiments. The optimal design is achieved in terms of weight savings subject to stability, global stiffness and strain requirements, and then verified by the fine mesh finite element simulation of the lattice fuselage barrel. Finally, a practical design of the composite skin complying with the aircraft industry lay-up rules is presented. It is concluded that the mixed optimization method, combining topology optimization with the global metamodel-based approach, allows the problem to be solved with sufficient accuracy and provides the designers with a wealth of information on the structural behaviour of the novel anisogrid composite fuselage design.

Multipoint Approximation Method for Design Optimization with Discrete Variables

In this paper a new capability is introduced in the Multipoint Approximation Method (MAM) focusing on the development of metamodels for the objective and constraint functions as well as solving an optimization problem within a trust region when all, or some of, design variables are defined on a discrete set of values. This development targets an important class of industrial problems where it is allowed to perform a response function evaluation only for points that have discrete values of the design variables. The main aim is to develop an optimization technique applicable to large design optimization problems in which the response functions are computationally expensive, could be affected by numerical noise, and occasionally are impossible to evaluate at some points. The new discrete optimization capability is demonstrated on a well established benchmark problem and compared to published results. I. Introduction he multipoint approximation method (MAM) is an optimization technique utilising high quality explicit approximations in order to reduce the total number of calls for analysis needed to solve large-scale optimization problems. This approach has been influenced by the previous work 1-3 on two-point approximation methods. This was later generalized to multi-point approximations 4-6 . The present approach is based on the assembly of multiple metamodels. Such an approach was used in Refs. 7 and 8 where a metamodel assembly was based on the weighted sum formulation. In the current work, following the previous research for a case of continuous variables 6 , a metamodel assembly is built using linear regression. The regression coefficients of the assembly model are not scaled weights but tuning parameters determined by the least squares method. Therefore, the tuning parameters of the assembly model are not restricted to a positive range but may have negative values as well. This technique is utilized in the multipoint approximation method within the mid-range approximation framework 4-6 . In this paper a special attention is paid to a case when some of, or all, design variables are discrete. It is assumed that it is allowed to perform a response function evaluation only for points that have discrete values of the design variables 9 . This makes it impossible to initially ignore the discrete nature of the design variables, solve a continuous problem and adjust the result to the given set of the discrete values, as sometimes suggested 10 . Thus, new procedures for sampling, metamodel building, their use for solving an optimization problem with discrete properties within a rust region, and the trust region adaptation strategy is required. In this paper, a discrete form of the coordinate search algorithm 9 is implemented within the MAM to search for the solution in the sub-space of the discrete variables only starting from the optimal continuous values obtained by the Sequential Quadratic Programming method (SQP) on the approximated functions in a current trust region. This is compared to the use of a simple rounding-off method for the discrete variables. The new mixed discrete-continuous capability was implemented within the MAM and tested on well established benchmark problems including the ten-bar truss problem 11 . The obtained results are compared with the solution obtained by a binary GA and with a continuous case to demonstrate the efficiency of the technique.

Metamodel assisted design optimization of piezoelectric flex transducer for maximal bio-kinetic energy conversion

Energy-harvesting devices have been widely used to generate electrical power from the bio-kinetic energy of human body movement. A novel piezoelectric flex transducer based on the Cymbal device has been proposed by other researchers for the purpose of energy harvesting. To further improve the efficiency of the device, optimal design of the piezoelectric flex transducer for maximum output power subject to stress and displacement constraints is carried out in this article. Sequential quadratic programming on metamodels generated with genetic programming from a 140-point optimal Latin hypercube design of experiments is used in the optimization. Finally, the optimal design is validated by finite element simulations. The simulations show that the magnitude of the electrical power generated from this optimal piezoelectric flex transducer harvesting device can be up to 6.5 MW when a safety design factor of 2.0 is applied.

Implementation of Discrete Capability into the Enhanced Multipoint Approximation Method for Solving Mixed Integer-Continuous Optimization Problems

Multipoint approximation method (MAM) focuses on the development of metamodels for the objective and constraint functions in solving a mid-range optimization problem within a trust region. To develop an optimization technique applicable to mixed integer-continuous design optimization problems in which the objective and constraint functions are computationally expensive and could be impossible to evaluate at some combinations of design variables, a simple and efficient algorithm, coordinate search, is implemented in the MAM. This discrete optimization capability is examined by the well established benchmark problem and its effectiveness is also evaluated as the discreteness interval for discrete design variables is increased from 0.2 to 1. Furthermore, an application to the optimization of a lattice composite fuselage structure where one of design variables (number of helical ribs) is integer is also presented to demonstrate the efficiency of this capability.

Metamodels for composite lattice fuselage design

This paper presents a novel design of an anisogrid composite aircraft fuselage by a global metamodel-based optimization approach. A 101-point design of numerical experiments (DOE) has been developed to generate a set of individual fuselage barrel designs and these designs have further been analyzed by the finite element (FE) method. Using these training data, global metamodels of all structural responses of interest have been built as explicit expressions of the design variables using a Genetic Programming approach. Finally, the parametric optimization of the fuselage barrel by genetic algorithm (GA) has been performed to obtain the best design configuration in terms of weight savings subject to stability, global stiffness and strain requirements.

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems: A comparative study

In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).,In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.,The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.,The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

Ply number rounding-off in optimization of composite structures using lamination parameters

A bi-level optimization strategy for finding the optimal ply numbers and stacking sequence in composite structures has become one of the most popular techniques in recent years. When the optimization technique is based on the use of lamination parameters, the top level optimization has two subsets of design variables for each substructure (e.g., a panel in wing design): lamination parameters treated as continuous design variables, and three integers that define the number of plies of 0, 90 and ±45 degree orientation. When a continuous optimizer is used, there is a need for an algorithm to perform a rounding-off of obtained continuous representation of the number of plies to an integer value that, ideally, does not alter the mechanical performance of a panel. In this paper three schemes based on the lamination parameter matching are introduced to determine the integer values of the ply numbers. The strategy is to use a binary code controlling the ply number rounding-off in order to obtain a discrete number of plies of each orientation per composite panel. An optimization problem is formulated where the objective function (to be minimized) defines how close the lamination parameter values and the panel thickness, obtained in the top level optimization, are to their values when integer ply numbers are considered. Such an optimization problem is solved by a permutation GA for each individual panel. A wing box benchmark problem is used to demonstrate the potential of these methods.