Abstract
The shape optimization of realistic, three-dimensional automotive components is discussed, stressing the integration of the major parts of the total process—modeling, mesh generation, finite element and sensitivity analysis, and optimization. Stamped and solid components are treated separately. For stamped parts, a highly automated capability has been developed; the problem description is based upon a parameterized boundary design element concept for the definition of the geometry. Automatic triangulation and adaptive mesh refinement are used to provide an automated analysis capability which requires only boundary data and takes into account sensitivity of the solution accuracy to boundary shape. For solid components, a general extension of the two- dimensional boundary design element concept has not been achieved. In this case the parameterized surface shape is provided by using a generic modeling concept based upon isoparametric mapping patches which also serve as the mesh generator. Emphasis is placed upon the coupling of optimization with a commercially available finite element program. To combine these, it is necessary to modularize the program architecture and to obtain shape design sensitivities using the material derivative approach so that only boundary solution data are needed. Several realistic component designs demonstrate the effectiveness of both capabilities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. A. Schmit, Structural synthesis by systematic synthesis. Proc. 2nd Conf. on Electronic Computation ASCE, pp. 105–122. New York (1960).
G. N. Vanderplaats, Structural optimization—Past, present, and future. AIAA J. 20 (7) 992–1000 (1982).
O. C. Zinkiewicz and J. S. Campbell, Shape optimization and sequential linear programming, Chap. 7 in Optimum Structural Design (Edited by R. H. Gallagher and O. C. Zienkiewicz). John Wiley & Sons, New York (1973).
E. J. Haug, K. K. Choi, Y. M. Hou and Y. M. Yoo, A variational method for shape optimal design of elastic structures, in Optimal Structural Design II (Edited by R. H. Gallagher). John Wiley & Sons, New York (1983).
R. T. Haftka and R. V. Grandhi, Structural shape optimization—A survey. The 26th AIAA SDM Conf. CP No. 85–0772, pp. 617–628 (1985).
M. E. Botkin, Shape optimization of plate and shell structures. AIAA J. 20 (2), 268–273 (1982).
M. H. Iman, Three-dimensional shape optimization. Int. J. Numer. Meth. Eng. 18, 661–673 (1982).
M. H. Imam, Minimum weight design of 3-D solid components. Proc. 2nd ASME Computers in Engineering Conf. Vol. 3, pp. 119–126 (1982).
J. A. Bennett and M. E. Botkin, Structural shape optimization with geometric problem description and adaptive mesh refinement. AIAA J. 23 (3), 458–464 (1985).
V. Braibant and C. Fleury, Shape optimal design using b-splines. Comput. Meth. Appl. Mech. Eng. 44, 247–267 (1984).
M. E. Botkin, An adaptive finite element technique for plate structures. Tech. Note, AIAA J. 23 (5), 812–814 (1985).
J. C. Cavendish, Automatic triangulation of arbitrary planar domains for the finite element method. Int. J. Numer. Meth. Eng. 8, 679–696 (1974).
W. H. Frey and J. C. Cavendish, Fast planar mesh generation using the Delaunay triangulation. Society for Industrial and Applied Mathematics Meeting. Seattle, WA (July 16–20, 1984).
I. Babuška and W. D. Rheinbolt, Adaptive approaches and reliability estimates in finite element analysis. Comput. Meth. Appl. Mech. Eng. 17/18, 519–549 (1979).
M. S. Shephard, R. H. Gallagher and J. F. Abel, The synthesis of near-optimum finite element meshes with interactive computer graphics. Int. J. Numer. Meth. Eng. 15, 1021–1039 (1980).
J.J. Conner and G. Will, A triangular flat plate bending element. M.I.T., Department of Civil Engineering, Rep. TR-68–3. Cambridge, MA (1968).
M. E. Botkin and J. A. Bennett, Shape optimization of three-dimensional folded-plate structures. AIAA J. 23 (11), 1804–1810 (1985).
M. E. Botkin and G. S. Gressel, Shape optimization of sheet metal components with flanges. Proceedings of 6th SAE International Vehicle Structural Mechanics Conf. Detroit, MI, SAE Publication p-178, Paper No. 860803, 29–38 (Apr. 1986).
M. A. Yerry and M. S. Shephard, Automatic three-dimensional mesh generation by the modified-octree technique. Int. J. Numer. Meth. Eng. 20(11), 1965–1990 (1984).
E. J. Haug, K. K. Choi, J. W. Hou, and Y. M. Yoo, A variational method for shape optimal design of elastic structures, in New Directions in Optimum Structural Design (Edited by E. Atrek et al.). John Wiley & Sons, New York (1984).
K. K. Choi and E. J. Haug, Shape design sensitivity analysis of elastic structures. J. Struct. Mech. 11 (2), 231–269 (1983).
E. J. Haug, K. K. Choi and V. Komkov, Design Sensitivity Analysis of Structural Systems. Academic Press, New York (1985).
R. J. Yang and M. E. Botkin, The relationship between the variational approach and the implicit differentiation approach to shape design sensitivities. AIAA SDM Conf. CP No. 85–0774. Orlando, FL (Apr. 1985).
R. J. Yang, K. K. Choi and E. J. Haug, Numerical considerations in structural component shape optimization. J. Mech. Transm., Autom. Des. Paper No. 84-DET-219 (1984).
C. V. Ramakrishnan and A. Francavilla, Structural shape optimization using penalty functions. J. Struct Mech. 3 (4), 403–422 (1974–1975).
G. Vanderplaats, CONMIN—A FORTRAN program for constrained function minimization: User’s manual. NASA, TMX-62,282 (1973).
Y. M. Yoo, E. J. Haug and K. K. Choi, Shape optimal design of an engine connecting rod. J. Mech. Transm. Autom. Des. 106, 415–489 (1984).
R. J. Yang, K. K. Choi and E. J. Haug, Finite element computation of structural design sensitivity analysis. Rep. CCAD No. 84–3, The University of Iowa (1984).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
Botkin, M.E., Yang, R.J., Bennett, J.A. (1986). Shape Optimization of Three-Dimensional Stamped and Solid Automotive Components. In: Bennett, J.A., Botkin, M.E. (eds) The Optimum Shape. General Motors Research Laboratories Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9483-3_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-9483-3_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-9485-7
Online ISBN: 978-1-4615-9483-3
eBook Packages: Springer Book Archive