Shape design sensitivity analysis and optimization of two-dimensional periodic thermal problems using BEM

 A general procedure to perform shape design sensitivity analysis for two-dimensional periodic thermal diffusion problems is developed using boundary integral equation formulation. The material derivative concept to describe shape variation is used. The temperature is decomposed into a steady state component and a perturbation component. The adjoint variable method is used by utilizing integral identities for each component. The primal and adjoint systems are solved by boundary element method. The sensitivity results compared with those by finite difference show good accuracy. The shape optimal design problem of a plunger model for the panel of a television bulb, which operates periodically, is solved as an example. Different objectives and amounts of heat flux allowed are studied. Corresponding optimum shapes of the cooling boundary of the plunger are obtained and discussed. Received 15 August 2001 / Accepted 28 February 2002     

Multiobjective optimization of multi-cell sections for the crashworthiness design

Plastic deformation of structures absorbs substantial kinetic energy when impact occurs. For this reason, energy-absorbing components have been extensively used in the structural design of vehicles to intentionally absorb a large portion of crash energy to reduce the severe injury of occupants. On the other hand, high peak crushing force may to a certain extent indicate the risk of structural integrity and biomechanical damage of occupants. For this reason, it is of great significance to maximize the energy absorption and minimize the peak force by seeking for optimal design of these components. This paper aims to design the multi-cell cross-sectional thin-walled columns with these two crashworthiness criteria. An explicit finite element analysis (FEA) is used to derive higher-order response surfaces for these two objectives. Both the single-objective and multi-objective optimizations are performed for the single, double, triple and quadruple cell sectional columns under longitudinal impact loading. A comparative analysis is consequently given to explore the relationship between these two design criteria with the different optimization formulations.     

Adaptive improved response surface method for reliability-based design optimization

Reliability-based design optimization (RBDO) requires the evaluation of probabilistic constraints (or reliability), which can be very time consuming. Therefore, a practical solution for efficient reliability analysis is needed. The response surface method (RSM) and dimension reduction (DR) are two well-known approximation methods that construct the probabilistic limit state functions for reliability analysis. This article proposes a new RSM-based approximation approach, named the adaptive improved response surface method (AIRSM), which uses the moving least-squares method in conjunction with a new weight function. AIRSM is tested with two simplified designs of experiments: saturated design and central composite design. Its performance on reliability analysis is compared with DR in terms of efficiency and accuracy in multiple RBDO test problems.     

Response surface approximations for structural optimization

Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to find the region of interest containing the optimal design, and techniques for finding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the ‘best’ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-effective. In a further attempt to improve efficiency, different regression models were investigated. The results indicate that the use of the two methods investigated does not significantly improve the results. Finding an accurate global approximation is challenging, and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space. © 1998 John Wiley & Sons, Ltd.     

Thermal optimization in transient thermoelasticity using response surface approximations

Response surface methodology is used to construct approximations to temperature and stress in transient thermoelastic analysis of non-linear systems. The analysis forms the core component of a heating/cooling rate maximization problem in which the ordinates of the ambient temperature at equally spaced time intervals are chosen as the design variables. Polynomials or cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis. An experimental design method based on D-optimality and a genetic algorithm was used to select the design points used to create the approximations. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Two examples of which one is a thick-walled pressure vessel are used to illustrate the methodology. © 1998 John Wiley & Sons, Ltd.     

Reliability based design optimization using response surfaces in application to multidisciplinary systems

Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state functions are used to estimate the probability of failure. An outer loop is incorporated to ensure that the approximate RBDO converges to the actual most probable point of failure. The framework is compared with the exact RBDO procedure. In the proposed methodology, RSAs are employed to significantly reduce the computational expense associated with traditional RBDO. The proposed approach is implemented in application to multidisciplinary test problems, and the computational savings and benefits are discussed.     

Multi-objective optimization of tire carcass contours using a systematic aspiration-level adjustment procedure

 While forming a basic tire configuration and supporting most static and dynamic loads of automobiles, tire carcass influences major tire performances according to its contour. Among significant tire performances, we in this study intend to improve the automobile maneuverability and the tire durability by optimizing the sidewall carcass contour. In order to effectively maximize these multi-objectives, we refine the conventional satisficing trade-off methods (STOM) which were proposed originally for the multi-objective structural optimization, by introducing a systematic aspiration-level adjustment procedure. According to the systematic procedure, we perform the sidewall contour optimization that ideally distributes the sidewall carcass tension and minimizes strain-energy density at the belt edge. Since the tire analysis is highly nonlinear problem we employ an incremental analysis scheme, together with the finite-difference sensitivity scheme. Through the numerical experiment, we confirmed that the refined multi-objective optimization technique systematically leads to a final optimum sidewall contour, together with the stable and rapid convergence. Received: 20 August 2001 / Accepted: 29 July 2002 This work was supported by Kumho Industries Co., Ltd in Korea and by the Ministry of Science and Technology under the NRL program (M10203000017-02J0000-00910).     

Shape optimization of periodic structures

This paper describes a numerical approach to the optimization of effective properties of periodic perforations in an infinite body, in the frameworks of heat conduction and of linear elasticity. We implement a special finite element mesh in order to deal with the periodic nature of the problem. We compute the gradient of the functional to be minimized. We describe the process of mesh deformation and mesh regeneration. We give several numerical examples, some of them having practical relevance.     

Evolutionary optimization in thermoelastic problems using the boundary element method

 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. Received 6 November 2000     

Configuration design sensitivity analysis and optimization of beam structures

 A general method for configuration design sensitivity analysis over a three-dimensional beam structure is developed based on a variational formulation of the classical beam in linear elasticity. A sensitivity formula is derived based on a variational equation for the beam structure using the material derivative concept and adjoint variable method. The formulation considers not only the shape variation in a three dimensional direction, which includes translational as well as rotational change of the beam but also the orientation angle variation of the beam's cross section. The sensitivity formula can be evaluated with generality and ease even by employing a piecewise linear design velocity field despite the fact that the bending model is a fourth order differential equation. The design sensitivity analysis is implemented using the post-processing data of a commercial code ANSYS. Several numerical examples are given to show the excellent accuracy of the method. Optimization is carried out for a tilted arch bridge and an archgrid structure to show the method's applicability. Received 29 September 2001 / Accepted 20 March 2002