Solution of topology optimization problems with sequential convex programming

The function g0 is the objective function of the problem, i.e. a cost function or a performance index that one wants to minimize in order to have a better design. In topology optimization, this is for example the compliance of the structure under the considered load case. The set of constraint functions gj (in number m) are expressing the restrictions the design is subject to in order to be feasible. For example these functions are some bounds upon a stress measure to have resistance, restricted displacements, a volume resource or perimeter bound : : : The n variables xi are the design variables of the problem, that is, the parameters, which can be modi ed, to improve the design. In the topology optimization context, the xi variables are the element densities and the orientation parameters of the microstructure.

[1]  Claude Fleury,et al.  Mathematical Programming Methods for Constrained Optimization: Dual Methods , 1993 .

[2]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[3]  Hans-Peter Mlejnek,et al.  Second order approximations in structural genesis and shape finding , 1992 .

[4]  Pierre Duysinx,et al.  Topology Optimization with Different Stress Limit in Tension and Compression , 1999 .

[5]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[6]  C. Fleury,et al.  A generalized method of moving asymptotes (GMMA) including equality constraints , 1996 .

[7]  M. Kamat.  Recent Developments In Structural Optimization Methods , 1993 .

[8]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[9]  Claude Fleury,et al.  Efficient approximation concepts using second order information , 1989 .

[10]  Claude Fleury,et al.  Recent advances in convex approximation methods for structural optimization , 1994 .

[11]  Lucien A. Schmit,et al.  Advances in dual algorithms and convex approximation methods , 1988 .

[12]  Gengdong Cheng,et al.  STUDY ON TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS , 1992 .

[13]  Ole Sigmund,et al.  New Developments in Handling Stress Constraints in Optimal Material Distributions , 1998 .

[14]  J. Petersson,et al.  Slope constrained topology optimization , 1998 .

[15]  Pierre Duysinx,et al.  Layout Optimization : A Mathematical Programming Approach , 1997 .

[16]  U. Kirsch,et al.  On singular topologies in optimum structural design , 1990 .

[17]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[19]  G. I. N. Rozvany,et al.  Difficulties in truss topology optimization with stress, local buckling and system stability constraints , 1996 .

[20]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[21]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[22]  G. Buttazzo,et al.  An optimal design problem with perimeter penalization , 1993 .

[23]  穂鷹 良介.  Non-Linear Programming の計算法について , 1963 .

[24]  Pierre Duysinx.  OPTIMISATION TOPOLOGIQUE : DU MILIEU CONTINU A LA STRUCTURE ELASTIQUE , 1996 .

[25]  Lucien A. Schmit,et al.  Structural Synthesis by Combining Approximation Concepts and Dual Methods , 1980 .

[26]  G. Cheng,et al.  ε-relaxed approach in structural topology optimization , 1997 .

[27]  Ashok V. Kumar,et al.  A Sequential Optimization Algorithm Using Logarithmic Barriers: Applications to Structural Optimization , 2000 .

[28]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[29]  Mukund N. Thapa,et al.  Optimization of unconstrained functions with sparse hessian matrices-newton-type methods , 1984, Math. Program..

[30]  G. Allaire,et al.  Optimal design for minimum weight and compliance in plane stress using extremal microstructures , 1993 .

[31]  Michaël Bruyneel,et al.  Composite structures optimization using sequential convex programming , 2000 .

[32]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[33]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[34]  Raphael T. Haftka,et al.  Preliminary design of composite wings for buckling, strength and displacement constraints , 1979 .

[35]  C. Fleury,et al.  A New Separable Approximation Scheme for Topological Problems and Optimization Problems Characterized by a Large Number of Design Variables , 1995 .

[36]  George I. N. Rozvany,et al.  On singular topologies in exact layout optimization , 1994 .

[37]  C. Fleury.  Structural weight optimization by dual methods of convex programming , 1979 .