Material optimization: bridging the gap between conceptual and preliminary design

This paper presents a collection of tools for conceptual structure design. The underlying model is the ‘free material optimization’ problem. This problem gives the best physically attainable material and is considered as a generalization of the sizing/shape optimization problem. The method is supported by powerful optimization and numerical techniques, which allow us to work with bodies of complex initial design and with very fine finite-element meshes. The computed results are realized by composite materials. We consider a particular class of fibre-reinforced composite materials, manufactured by the so-called tape-laying technology. In the post-processing phase, stress/strain-trajectories are plotted which indicate how to place these tapes; they also show the proposed thickness of the tapes. Several examples demonstrate the efficiency of this approach to conceptual design of engineering structures.

[1]  G. Allaire,et al.  Shape optimization by the homogenization method , 1997 .

[2]  Michal Kočvara,et al.  Mechanical design problems with unilateral contact , 1998 .

[3]  M. Imam.  Three‐dimensional shape optimization , 1982 .

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

[5]  U. Ringertz.  On finding the optimal distribution of material properties , 1993 .

[6]  R. Kohn,et al.  Optimal design and relaxation of variational problems, III , 1986 .

[7]  Martin P. Bendsøe,et al.  Free material optimization via mathematical programming , 1997, Math. Program..

[8]  M. Beckers,et al.  Topology optimization using a dual method with discrete variables , 1999 .

[9]  Martin P. Bendsøe,et al.  Parametrization in Laminate Design for Optimal Compliance , 1997 .

[10]  Martin P. Bendsøe,et al.  An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design , 1994 .

[11]  Barry W. Peyton,et al.  Block Sparse Cholesky Algorithms on Advanced Uniprocessor Computers , 1991, SIAM J. Sci. Comput..

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

[13]  Michael Zibulevsky,et al.  Penalty/Barrier Multiplier Methods for Convex Programming Problems , 1997, SIAM J. Optim..

[14]  Arkadi Nemirovski,et al.  Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions , 1999, SIAM J. Optim..

[15]  J. Krammer,et al.  Constructive design models for multidisciplinary optimization of fiber composite structures , 1992 .

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

[17]  Björn Birnir,et al.  Complex hill's equation and the complex periodic korteweg‐de vries equations , 1986 .

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

[19]  Florian Jarre,et al.  Optimal Truss Design by Interior-Point Methods , 1998, SIAM J. Optim..

[20]  Arkadi Nemirovski,et al.  Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions , 1999, SIAM Rev..