Composite structures optimization using sequential convex programming

in Advances in Engineering Software (2002), 33(7-10, JUL-OCT), 697-711

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described ... [more ▼]

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described. Several modifications of these approximations are presented. They are now based on gradient information at two successive iterations, avoiding the use of the expensive second-order derivatives. A two-point fitting scheme is also described, where the function value at the preceding design point is used to improve the approximation. Numerical examples compare these new purely non-monotonous schemes to the existing ones for the selection of optimal fibers orientations in laminates. It is shown how these two-point based approximations are well adapted to the problem and can improve the optimization task, leading to reasonable computational efforts. A procedure is also derived for considering simultaneously monotonous and non-monotonous structural behaviors. The resulting generalized approximation scheme is well suited for the optimization of composite structures when both plies thickness and fibers orientations are considered as design variables. It is concluded that the newly developed approximation schemes of the MMA family are reliable for composite structures optimization. All the studied approximations are convex and separable: the optimization problem can then be solved using a dual approach. (C) 2002 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved. [less ▲]

A family of MMA approximations for structural optimization

Conference (2001, July)

This paper deals with the approximation concepts approach applied to structural optimization. In 1987, Svanberg proposed the method of moving asymptotes for solving structural optimization problems. This ... [more ▼]

This paper deals with the approximation concepts approach applied to structural optimization. In 1987, Svanberg proposed the method of moving asymptotes for solving structural optimization problems. This approximation is monotonous and can efficiently treat problems characterized by such a behavior. Svanberg (1995) proposed a modification of the MMA approximation by making it non monotonous. This property is based on an heuristically updated parameter. The resulting approximation is called GCMMA. In Bruyneel et al. (1999), it is shown that it is possible to generate non monotonous GCMMA based approximations, called GBMMA, by using the gradient and/or the function values from previous iteration. It was shown that such approximations improve the convergence speed of the optimization process. In many optimization problems (for example composite structures optimization or simultaneous sizing and optimal configuration of truss structures), the structural responses present both monotonous and non monotonous behaviors. A mixed monotonous/non monotonous approximation scheme has to be used for approximating in the best way the optimization problem (Zhang et al., 1998 and Bruyneel and Fleury, 2000). In this paper, we propose to show that it is possible to derive a very general approximation of the MMA family based on gradients and/or functions values at two successive design step, that present a mixed monotonous/non monotonous behavior. This approximation scheme is based on the GMMA approximation of Dusyinx et al. (1995) and on the non monotonous GBMMA approximations of Bruyneel and Fleury (1999). As the approximation scheme proposed in this paper is general, it contains all the approximations of the MMA family described above, that is MMA, GCMMA, GBMMA and GMMA. According to the characteristics of the problem under consideration, one of those approximations or of a mix of them is used to solve the optimization problem. This selection can be automatic or based on the designer’s knowledge. Numerical applications will show that the derived GMMA/GBMMA approximation scheme is efficient for solving structural optimization problems. Results will be compared with the ones obtained with the other approximations of the MMA family. [less ▲]

Composite structures design for strength and stiffness with respect to ply thickness and/or fibers orientation

in CHENG, Gen Dong (Ed.) Proceedings of the 4th World Congress of Structural and Multidisciplinary Optimization WCSMO4 (2001, June)

This paper presents an optimization approach that allows the design of composite structures under stiffness and strength criteria, with fibers orientations and plies thickness taken into account in the ... [more ▼]

This paper presents an optimization approach that allows the design of composite structures under stiffness and strength criteria, with fibers orientations and plies thickness taken into account in the same optimization loop. The approach is based on the sequential convex programming. An industrial application is presented. [less ▲]

An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

in International Journal for Numerical Methods in Engineering (2001), 52(9), 889-902

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate ... [more ▼]

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA)are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. [less ▲]

Enhanced Approximation Schemes for Classical Optimization Algorithm

Report (1998)

The report assesses the capabilities of the algorithms CONLIN, MDQA, an GCM available in Boss Quattro to solve composite structure optimization. The algorithms are evaluated with respect to the ... [more ▼]

The report assesses the capabilities of the algorithms CONLIN, MDQA, an GCM available in Boss Quattro to solve composite structure optimization. The algorithms are evaluated with respect to the optimization of sandwich panel parameters (ply thickness and orientation, and foam core thicknesss). [less ▲]

Topology optimization involving discrete variables

in Gutkowski, Witold; Mróz, Zenon (Eds.) Proceedings of the second world congress of Structural and multidisciplinary optimization: May 26-30 1997, Zakopane, Poland (1997)

A primal-dual approach in truss topology optimization

in Computers & Structures (1997), 64(1-4), 77-88

The objective of truss topology optimization is to find, for a given weight, the stiffest truss, defined as a subset of an initially choosen set of bars called the ground structure. The restrictions are ... [more ▼]

The objective of truss topology optimization is to find, for a given weight, the stiffest truss, defined as a subset of an initially choosen set of bars called the ground structure. The restrictions are bounds on bar volumes and the satisfaction of equilibrium equations. For a single load case and without bounds on bar volumes, the problem can be written as a linear programming problem with nodal displacements as variables. The addition to the objective function of a quadratic term vanishing at the optimum allows us to use a dual solution scheme. A conjugate gradient method is well suited to maximize the dual function. Several ground structures are introduced. For large networks, those where each node is connected to those situated in a certain vicinity give a good compromise between generating a reasonable number of bars and obtaining a sufficient number of possible directions. Some examples taken from the literature are treated to illustrate the quality of the solution and the influence of initial topology. (C) 1997 Civil-Comp Ltd and Elsevier Science Ltd. [less ▲]

A New Separable Approximation Scheme for Topological Problems and Optimization Problems Characterized by a Large Number of Design Variables

in Olhoff, Niels; Rozvany, Georges I.N. (Eds.) Proceedings of the First World Congress of Structural and Multidisciplinary Optimization (WCSMO1) (1995, May)

This paper is dedicated to a new convex separable approximation for solving optimization problems characterized by a very large number of design variables as in topology design. For such problems, the ... [more ▼]

This paper is dedicated to a new convex separable approximation for solving optimization problems characterized by a very large number of design variables as in topology design. For such problems, the convergence speed can be accelerated if one uses high quality approximation schemes for structural responses. To achieve this task, we propose, here, a new approximation procedure that belongs to the GMMA family. The originality of this new scheme is to rely on an automatic selection procedure of the asymptotes, using only first and zero order information accumulated during the previous iterations. This is possible owing to a diagonal Quasi-Newton update technique. Firstly, the new approximation procedure is validated on classical "benchmarks" of structural optimization. Then, it is compared to other schemes on a typical topology optimization problem. [less ▲]

Structural Shape Optimization with Error Control

in Proceedings of 20th ASME Design Automation Conference (1994, September)

A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as ... [more ▼]

A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as geometric modelling, automatic selection of independent design variables, sensitivity analysis using reliable mesh perturbation schemes, error estimation and adaptive mesh refinement. A numerical example is given to show the efficiency of the procedure. [less ▲]

Recent advances in convex approximation methods for structural optimization

in Topping, B. H. V.; Papadrakakis, Manolis (Eds.) Advances in Structural Optimization (1994)