Abstract: SUMMARY A generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed. In conventional optimization, only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted. A design space is speci9ed by the number of design variables, and the layout or con9guration. To solve this type of design space problems, a simple initial design space is selected and gradually improved while the usual design variables are being optimized. To make the design space evolve into a better one, one may increase the number of design variables, but, in this transition, there are discontinuities in the objective and constraint functions. Accordingly, the sensitivity analysis methods based on continuity will not apply to this discontinuous stage. To overcome the di=culties, a numerical continuation scheme is proposed based on a new concept of a pivot phase design space. Two new categories of structural optimization problems are formulated and concrete examples shown. Copyright ? 2001 John Wiley & Sons, Ltd.

Abstract: There is growing interest to adopt supersonic turbines for rocket propulsion. However, this technology has not been actively investigated in the United States for the last three decades. To aid design improvement, a global optimization framework combining the radial-basis neural network (NN) and the polynomial response surface (RS) method is constructed for shape optimization of a two-stage supersonic turbine, involving O(10) design variables. The design of the experiment approach is adopted to reduce the data size needed by the optimization task. The combined NN and RS techniques are employed. A major merit of the RS approach is that it enables one to revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a predefined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials consideration.

Abstract: A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element–based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.

Abstract: Weight reduction for an automobile body is sought to achieve fuel efficiency and energy conservation. Recently, the UltraLight Steel Auto Body (ULSAB) concept is suggested using a few methods. ULSAB pursues a lightweight automotive with steel structure. Tailor welded blank (TWB) is one of the ULSAB methods and TWB can be utilized for an automobile door. Optimization technology is applied to the inner panel of a door which is made by TWB. A design process is appropriately defined for the inner panel. The design starts from an existing component. At first, the inner reinforcements are removed to use TWB technology. In the conceptual design stage, topology optimization is conducted to find the distribution of the variable thickness. The number of parts and the welding lines are determined from the topology design. In the detailed design process, size optimization is carried out to find thickness while the stiffness constraints are satisfied. Size optimization is performed based on the welding lines determined from topology optimization. The final parting lines are tuned by shape optimization. The results from size optimization are considered constant in shape optimization. A commercial optimization software GENESIS is utilized for the optimization processes.

Abstract: Origin of the techniques of design optimization: Design methodologies in engineering Concept and formulation of optimum design Conclusion References Current state of optimization techniques: Types of optimum design Current state of optimization software References Laminated steel shapes: Introduction Design constraints applicable to metal sections Shape optimization of open laminated shapes Description of the SAFO code Application example Optimization of a reinforced beam with a constant strength modulus Application example Optimization of a standard shape, maintaining the depth as a constant Optimization of the series of shapes References Mechanical elements for automobiles: Introduction Shape optimization of a connecting rod References Prestressed concrete beams: Prestressed concrete beams Precasting of bridge decks Formulation of the optimization process General description of the VTOP code Practical examples Beam 1 Practical examples Beam 2 Practical examples Beam 3 References Structural bars: Introduction Architecture Covers for leisure and cultural complexes Factory covers Chemical and hydrocarbon plants Design constraints for aluminium open sections Formulating the optimization problem General description of the BALDO code Practical example References Vehicle chassis: Introduction Size optimization of a vehicle chassis References Future developments in optimum design technology: Multiobjective optimization Multidisciplinary optimization Integration of CAE systems and optimization Advanced visualization and optimization Final considerations References

Abstract: A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.

Abstract: A study of the topology optimization of a multi-spectral camera for space-use is presented. The optimization is carried out under self-weight and polishing pressure loading. As an objective function, a measure of Strehl ratio is used. Total mass of the primary mirror is given as a constraint to the optimization problem. The sensitivities of the objective function and constraint are calculated by direct differentiation method. The optimization procedure is carried out by an optimality criteria method. For the light-weight primary mirror design, a three dimensional model is treated. As a preliminary example, topology optimization considering a self-weight loading is treated. In the second example, the polishing pressure is also included as a loading in the topology optimization of the mirror. Results of the optimized design topology for the mirror with various mass constraints are presented.

Abstract: In this study, the multidisciplinary aerodynamicstructural optimal design is carried out for the supersonic fighter wing. Through the aeroelastic analyses of the various candidate wings, the aerodynamic and structural performances are calculated such as the lift coefficient, the drag coefficient and the deformation of the wing. Based on the calculated performances, the supersonic fighter wing is designed by using response surface methodology to have better aerodynamic performances and less weight than the baseline wing. In general, the supersonic fighter is maneuvered at various flight conditions. The optimal design, therefore, should be carried out on the multi flight conditions. In this study, three representative design points for the supersonic fighter wing are determined such as supersonic dash, long cruise range and high AOA maneuver. At each design point, single-point design is performed to obtain better performance only at that point. Finally, a multi-point design is performed to increase aerodynamic and structural performances at all the three design points. The optimization results of multi-point design are compared with those of the single-point design and analyzed in detail. INTRODUCTION Since the early 1990's, with the rapid advances in computational fluids dynamics(CFD) and computational structural mechanics(CSM), extensive studies have been carried out on the computational design methods for the aircraft. The development of computational design methods reduces the overall design costs and turn around time for the development of aircraft. The use of high fidelity tools, moreover, brings more confidence to the design. * Graduate Student * Professor, Senior Member AIAA, * Professor, Member AIAA Copyright © 2001 by the American Institute of Aeronautics and Astronautics Inc. All rights reserved The design of modern aircraft needs for the integration of multiple disciplines, such as aerodynamics, structures, propulsion and aeroacoustics. These disciplines are mutually interacting, not independent of each other and multidisciplinary design optimization(MDO) is a formal methodology for the integration of these disciplines. Generally, MDO should exploit the synergism of mutually interacting disciplines in order to improve the performance of a given design, while increasing the level of confidence that the designer places on the outcome of the design itself.' The accurate and adequate modeling of interactions among various disciplines is, therefore, the most important part which characterizes MDO. Especially in case of aircraft, the aerodynamic performance and the structural deformation of the wing are tightly coupled. The structural deformation of the wing changes the distribution of aerodynamic forces on the wing surface and this change of aerodynamic force distribution has a reverse influence on the structural deformation. The mutual interaction between aerodynamics and structures, therefore, should be well analyzed and considered during design process. hi general, the supersonic fighter, which carries out various missions, is maneuvered at various flight conditions. Accordingly the single-point design of wing, which considers only one flight condition, has no significant meaning and the multi-point design should be carried out by taking the various flight conditions into account. Over the past several decades, single discipline shape optimization has been successfully applied to two-dimensional airfoil and simple three-dimensional wing." In recent years, interest has grown in the application of multidisciplinary analysis and design optimization to complex three-dimensional wing and aircraft configuration." To give an example, MDO paradigm is successfully implemented for the aerodynamic-structural design optimization of HSCT (High Speed Civil Transport) utilizing variablecomplexity modeling and response surface methodo1 American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. logy(RSM)." But performing MDO for a complete airplane configuration is still a challenging task with high-fidelity analysis tools. In this study the multidisciplinary multi-point design of supersonic fighter wing is carried out in order to show the feasibility of MDO with highfidelity analysis tools. The MDO paradigm introduced here uses RSM, high-fidelity aeroelastic analysis tool combining CFD and CFM and a multiobjective approach. The objectives of the present research are summarized as follows; (1) to investigate the multidisciplineary multi-point design optimization of the supersonic fighter wing based on high-fidelity aeroelastic analysis; (2) to demonstrate the advantages of multi-point design as well as the limitations of the single-point design; (3) to develop a new design procedure for the multiobjective design problem which improves the performances evenly and moderately. To achieve these goals, the three-dimensional Euler code has been coupled with a nine-node shell mixed FEM(Finite Element Method) code for the accurate analysis of aeroelastic phenomena. For the development of MDO framework, RSM is employed to select candidate design points and to construct numerical approximation models for objectives and constraints. Because the design problem here is essentially a multidisciplinary and multi-point, there exists multiple objectives. In order to deal with the multiple objectives, the weighting method is introduced and the weighting factors are designed to improve the performances evenly by using genetic algorithm. RSM is a kind of approximation method based on design of experiment theory (DOE). In this method, a designer performs a limited number of computational analyses using experimental design theory to prescribe values for independent variables. With the resulting data, the designer creates mathematical approximation models using some type of function. The designer then uses the response surface model in subsequent calculations during optimization process.2' 4,17,20,21 Figure 1. Three-Dimensional Wing Mesh for CFD Calculation (O-Htype) with Van Albada limiter. AF-ADI time marching scheme is used for the time integration. The convergence of numerical analysis is accelerated through the use of the multigrid scheme and the implicit residual smoothing. A wing mesh for CFD calculation is shown in figure 1. It is generated by the transfinite Interpolation technique and has the O-H type grid topology. The number of mesh size is 121 along the airfoil surface, 33 along the spanwise direction and 33 normal to the wing surface. STRUCTURAL ANALYSIS Nine-node shell mixed finite element Nine-node shell mixed finite element has three translational degrees of freedom(DOF) and two rotational DOF per node as shown in figure 2, and each element has nine-node and 45 DOF per element. The element is constructed on the basis of the Hellinger-Reissner principle with the assumed displacement field as well as the independently assumed strain field, which lead to the equilibrium equation (1) and the compatibility equation (2).

Abstract: The shape optimization of blades is a crucial step within the design cycle of a whole turbomachine. This paper is a report on a joint project between academia and industry, leading to an efficient solution software for this problem to be used in the daily work of concerned engineers. The problem description and solution method, characterized as a partially reduced sequential quadratic programming (PRSQP) method, as well as numerical results are presented.

Abstract: The paper is devoted to application of evolutionary algorithms and the boundary element method to shape optimization of structures for various thermomechanical criteria, inverse problems of finding an optimal distribution of temperature on the boundary and identification of unknown boundary. Design variables are specified by Bezier curves. Several numerical examples of evolutionary computation are presented.

Abstract: A novel topology/shape optimization method, Metamorphic Development, is applied to an axisymmetric thermo-elasticity design problem. Based on solid modeling and finite element analysis, optimal profiles of minimum mass turbine disks are sought by growing and degenerating simple initial structures subject to both response and geometric constraints. Radial stress, axial stress, hoop stress and von Mises stress are analyzed throughout the optimization and a constraint is imposed on von Mises stress everywhere in the disk. The optimal structures are developed metamorphically in specified infinite design domains using both quadrilateral and triangular axisymmetric finite elements. Comparisons are made of the results obtained for different optimization scenarios: (a) with and without thermal loading; (b) with and without centrifugal body forces; (c) with and without a fit pressure on the inner surface of the hub; and (d) operating at different rotational speeds.

Abstract: The aim of this research is to determine the optimal shape of a constrained viscoelastic damping layer on an elastic beam by means of topology optimization. The optimization objective is to maximize the system loss factor for the first resonance frequency of the base beam. All previous optimal design studies on viscoelastic lamina have been size or shape optimization studies, assuming a certain topology for the damping treatment. In this study, this assumption is relaxed, allowing an optimal topology to emerge. The loss factor is computed using the Modal Strain Energy method in the optimization process. Loss factor results are validated by using the half-power bandwidth method, which requires obtaining the forced response of the structure. The ABAQUS finite element code is used to model the structure with two-dimensional continuum elements. The optimization code uses a Sequential Quadratic Programming algorithm. Results show that significant improvements in damping performance, on the order of 100% to 300%, are obtained by optimizing the constrained damping layer topology. A novel topology for the constraining layer emerges through the optimization process.Copyright © 2002 by ASME

Abstract: A design method is presented for layout optimization of linearly elastic–perfectly plastic disks subjected to multiparameter loading. The method is based on the static theorem of shakedown analysis and on the concept of porous material, where the material distribution of the discretized structure is described by the densities of the finite elements that are considered design variables. In addition to shakedown, two further compliance constraints are applied: bounds for the complementary strain energy of the residual stresses, and for the residual displacements. By the proper choice of these bounds the plastic behavior of the disk can be controlled and in special cases the elastic and fully plastic optimal solutions can be determined. The formulation of this problem yields to nonlinear mathematical programing. The application is illustrated by numerical examples. The method can also be applied to trusses, frames, and plates. *Communicated by M. Botkin. †Presented at ICTAM2000, held in Chicago in S...

Abstract: The objective of this work is to develop and implement efficient numerical procedures for gradient based shape optimization of steady, strongly coupled fluid–structure interaction problems involving turbulent flow. The governing equations are the Reynoldsaveraged Navier-Stokes equations combined with a large displacement formulation for the structure. The eddy viscosity is computed using either algebraic turbulence models or the two-equation k − ω model. The solution for state is obtained using finite element residual formulations based on a consistent weak formulation of the fluid–structure interaction problem. Due to the possible large displacements of the structure, the fluid mesh is updated using a modified elastic analogy. The resulting nonlinear equations are solved using an approximate Newton method, making it possible to do design sensitivity analysis (DSA) by the direct differentiation method in a very efficient way where the resulting sensitivity equations are solved by an incremental iterative method. Gradient based shape optimization is illustrated for finding the shape of both an infinitely stiff and a flexible valve. Such examples of semi-analytic DSA and gradient based shape optimization of strongly coupled fluid-structure interaction problems involving turbulent flow modeled using two-equation turbulence models have, at least to the knowledge of the authors, not been presented before in the literature and thus represent novel results.

Abstract: This paper deals with the reconstruction of three-dimensional (3D) geometric shapes based on observed noisy 3D measurements and multiple coupled nonlinear shape constraints. Here a shape could be a complete object, a portion of an object, a part of a building etc. The paper suggests a general incremental framework whereby constraints can be added and integrated in the model reconstruction process, resulting in an optimal trade-off between minimization of the shape fitting error and the constraint tolerances. After defining sets of main constraints for objects containing planar and quadric surfaces, the paper shows that our scheme is well behaved and the approach is valid through application on different real parts. This work is the first to give such a large framework for the integration of numerical geometric relationships in object modeling from range data. The technique is expected to have a great impact in reverse engineering applications and manufactured object modeling where the majority of parts are designed with intended feature relationships.

Abstract: A shape design model that reduces the amount of noise radiated from aircraft turbofan engines is studied in this paper. The model is formulated as shape control of the Helmholtz equation with radiation boundary conditions on part of the boundary and incoming waves specified as the source. Existence of optimal shape is proved to show that the model is appropriately established. A numerical experiment is conducted to demonstrate the efficiency of the model.

Abstract: This paper is concerned with a numerical solution of contact optimization problems using displacement-based hp-FEM. Small displacements and deformations are assumed for linear elastic material. The contact optimization problem is performed by controlling the contact pressure. The Coulomb friction is also considered. Special attention is paid to the treatment of the jumps in the displacement derivatives at special points. The mesh is adjusted adaptively so that both the boundary of the contact zone and the boundary of the adhesion and slip zones are nodal points. Examples are presented for axially symmetric problems. Copyright © 2001 John Wiley & Sons, Ltd.

Abstract: To enhance the critical current of superconducting coil, the magnetic field experienced by superconductor strand (tape) in a coil should be minimized. This is true for both low T c and high T c superconductors, and the difference between the two lies in their isotropic/anisotropic characteristics. In this paper, we propose a shape optimization algorithm to reduce radial magnetic field components in HTS solenoid to enhance critical current of a solenoid. In the algorithm, the finite element method and the continuum shape design sensitivity formula were employed. The objective function is to minimize the maximum radial magnetic fields in a solenoid with a constraint of constant solenoid volume condition. In this paper, the details on algorithm are introduced and the calculated optimized shapes are presented.