Abstract
Previous research on topology optimization focussed primarily on global structural behaviour such as stiffness and frequencies. However, to obtain a true optimum design of a vehicle structure, stresses must be considered. The major difficulties in stress based topology optimization problems are two-fold. First, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity. This problem increases the computational complexity of both the optimization and sensitivity analysis associated with the conventional topology optimization problem. The other difficulty is that since stress is highly nonlinear with respect to design variables, the move limit is essential for convergence in the optimization process. In this research, global stress functions are used to approximate local stresses. The density method is employed for solving the topology optimization problems. Three numerical examples are used for this investigation. The results show that a minimum stress design can be achieved and that a maximum stiffness design is not necessarily equivalent to a minimum stress design.
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References
Baumgartner, A.; Harzheim, L.; Mattheck, C. 1992: SKO: the biological way to find an optimum structure topology.Int. J. Fatigue 14, 387–393
Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method.Comp. Meth. Appl. Mech. Eng. 71, 197–224
Cheng, G.; Jiang, Z. 1992: Study on topology optimization with stress constraints.Eng. Opt. 20, 129–148
Díaz, A.; Kikuchi, N. 1992: Solution to shape and topology eigenvalue optimization problem using a homogenization method.Int. J. Num. Meth. Eng. 35, 1487–1502
Gea, H.C. 1994: Topology optimization: a new micro-structure based design domain method.ASME Advances in Design Automation 2, 283–290
Harzheim, L.; Graf, G. 1995: Optimization of engineering components with the SKO method.SAE Vehicle Struct. Mech. Conf. (held in Troy, MI), pp. 235–243
Haug, E.J.; Choi, K.K.; Komkov, V. 1986:Design sensitivity analysis of structural systems. New York: Academic Press
Jog, C.S.; Haber, R.B.; Bendsøe, M.P. 1994: Topology design with optimized, self-adaptive materials.Int. J. Num. Meth. Eng. 37, 1323–1350
Ma, Z.D.; Kikuchi, N.; Cheng, H.C.; Hagiwara, I. 1995: Topological optimization technique for free vibration problems.Trans. ASME, J. Appl. Mech. 62, 200–207
Mlejnek, H.P.; Schirrmacher, R. 1993: An engineer's approach to optimal material distribution and shape finding.Comp. Meth. Appl. Mech. Eng. 106, 1–26
Park, Y.K. 1995:Extensions of optimal layout design using the homogenization method. Ph.D. Thesis, University of Michigan, Ann Arbor
Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. 1995: Layout optimization of structures.Appl. Mech. Rev. 48, 41–117
Rozvany, G.I.N.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization.Struct. Optim. 4, 250–252
Sankaranaryanan, S.; Haftka, R.T.; Kapania, R.K. 1992: Truss topology optimization with stress and displacement constraints. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology design of structures, pp. 71–78. Dordrecht: Kluwer
Wang, B.P.; Lu, C.M.; Yang, R.J. 1996: Optimal topology for maximum eigenvalue using density-dependent material model.37th AIAA/ASME/ASCE/AHS/ASC Structures, Struct. Dyn. Mat. Conf. (held in Salt Lake City, UT), pp. 2644–2652
Yang, R.J.; Chahande, A.I. 1995: Automotive applications of topology optimization.Struct. Optim. 9, 245–249
Yang, R.J.; Chuang, C.H. 1994: Optimal topology design using linear programming.Comp. & Struct. 52, 265–275
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Yang, R.J., Chen, C.J. Stress-based topology optimization. Structural Optimization 12, 98–105 (1996). https://doi.org/10.1007/BF01196941
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DOI: https://doi.org/10.1007/BF01196941