Abstract
The shape optimal design of shafts and two-dimensional elastic structural components is formulated using boundary elements. The design objective is to maximize torsional rigidity of the shaft or to minimize compliance of the structure, subject to an area constraint. Also a model based on minimum area and stress constraints is developed, in which the real and adjoint structures are identical but have different loading conditions. All degrees of freedom of the models are at the boundary, and there is no need for calculating displacements and stresses in the domain. Formulations based on constant, linear and quadratic boundary elements are developed. A method for accurately calculating the stresses at the boundary is presented, which improves considerably the design sensitivity information. A technique for an automatic mesh refinement of the boundary element models is also developed. The corresponding nonlinear programming problems are solved by Pshenichny’s linearization method. The models are applied to shape optimal design of several shafts and elastic structural components. The advantages and disadvantages of the boundary element method over the finite element techniques for shape optimal design structures are discussed with reference to applications. A literature survey of the development of the boundary element method for shape optimal design is presented.
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
O. Pironneau, Optimal Shape Design for Elliptical Systems. Springer-Verlag (1984).
E. J. Haug, K. K. Choi and V. Komkov, Design Sensitivity Analysis of Structural Systems. Academic Press (1985).
O. C. Zienkiewicz and J. S. Campbell, Shape optimization and sequential linear programming, pp. 109–126 in Optimum Structural Design (Edited by R. H. Gallagher and O. C. Zienkiewicz). Wiley, New York (1973).
C. A. Mota Soares, H. C. Rodrigues, L. M. Oliveira Faria and E. J. Haug, Optimization of the geometry of shafts using boundary elements. J. Mech. Transm. Autom. Des. 106, 199–203 (1984).
C. A. Mota Soares, H. C. Rodrigues, L. M. Oliveira Faria and E. J. Haug, Optimization of the shape of solid and hollow shafts using boundary elements, pp. 883–889 in Boundary Elements (Edited by C. A. Brebbia). Springer-Verlag (1983).
C. A. Mota Soares, H. C. Rodrigues, L. M. Oliveira Faria and E. J. Haug, Boundary elements in shape optimal design of shafts, pp. 155–175 in Optimization in Computer Aided Design (Edited by J. S. Gero). North-Holland (1985).
H. C. Rodrigues and C. A. Mota Soares, Shape optimization of shafts. 3rd National Congress of Theoretical and Applied Mechanics. Lisbon (1983) (in Portuguese).
H. C. Rodrigues, Shape optimization of shafts using boundary elements. M.Sc. Thesis, Technical University of Lisbon (1984) (in Portuguese).
T. Burczynski and T. Adamczyk, Multiparameter shape optimization of a bar in torsion by the boundary element method. Proc. 28rd Symposium on Modelling in Mechanics, The Polish Society of Theoretical and Applied Mechanics. Gliwice (1984) (in Polish).
A. Zochowski and K. Mizukami, A comparison of BEM and FEM in minimum weight design, pp. 901–911 in Boundary Elements (Edited by C. A. Brebbia). Springer-Verlag (1983).
C. A. Mota Soares, H. C. Rodrigues and K. K. Choi, Shape optimal design of elastic structural components using boundary elements. 10th Int. Cong, on the Applications of Mathematics in Engineering Science, pp. 80–82. Weimar (1984).
C. A. Mota Soares, H. C. Rodrigues and K. K. Choi, Shape optimal structural design using boundary elements and minimum compliance techniques. J. Mech. Transm. Automat. Des. 106; 518–523 (1984).
R. P. Leal, Boundary elements in bidimensional elasticity. M.Sc. Thesis, Technical University of Lisbon (1985) (in Portuguese).
T. Burczynski and T. Adamczyk, The application of the boundary element method to optimal design of shape of structures. Proc. 4th Conf on Methods and Instrumentations of Computer Aided Design. Warsaw (1983) (in Polish).
T. Burczynski and T. Adamczyk, The boundary element formulation for multiparameter structure shape optimization. Appl. Math. Modelling 9, 195–200 (1985).
T. Burczynski and T. Adamczyk, The boundary element method for shape design synthesis of elastic structures. 7th Int. Conf. on Boundary Element Methods (Edited by C. A. Brebbia). Springer-Verlag (1985).
D. Eizadian, Optimization of the shape of bidimensional structures by the boundary integral equation method. Ph.D. Thesis, National Institute of Applied Science of Lyon (1984) (in French).
D. Eizadian and Ph. Trompette, Shape optimization of tridimensional structures by the boundary element method. Conf. on CAD/CAM, Robotics and Automation in Design. Tucson, AZ (1985).
T. Futagami, Boundary element and linear programming method in optimization of partial differential systems, pp. 457–471 in Boundary Element Methods (Edited by C. A. Brebbia). Springer-Verlag (1981).
T. Futagami, Boundary element and dynamic programming method in optimization of transient partial differential systems, pp. 58–71 in Boundary Element Methods in Engineering (Edited by C. A. Brebbia). Springer-Verlag (1982).
T. Futagami, Boundary element method—Finite element method coupled with linear programming for optimal control of distributed parameter systems, pp. 891–900 in Boundary Elements (Edited by C. A. Brebbia). Springer-Verlag (1983).
M. R. Barone and D. A. Caulk, Optimal arrangement of holes in a two-dimensional heat conductor by a special boundary integral method. Int. J. Numer. Meth. Eng. 18, 675–685 (1982).
R. A. Meric, Boundary integral equation and conjugate gradient methods for optimal boundary heating of solids. Int. J. Heat Mass Transfer 26, 261–267 (1983).
R. A. Meric, Boundary element for static optimal heating of solids. ASME J. Heat Transfer 106, 876–880 (1984).
R. A. Meric, Boundary element methods for optimization of distributed parameter systems. Int. J. Numer. Meth. Eng. 20, 1291–1306 (1984).
P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science. McGraw-Hill (1981).
G. Fairweather, F. J. Rizzo, D. J. Shippy and Y. S. Wu, On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. J. Comput. Physics 31, 96–112 (1979).
C. A. Brebbia, J. Telles and L. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering, Springer-Verlag (1984).
B. N. Pshenichny and J. M. Danilin, Numerical Methods in Extremal Problems. MIR, Moscow (1978).
I. M. Gelfand and S. W. Fomin, Calculus of Variations. Prentice-Hall (1961).
N. W. Banichuk, Problems and Methods of Optimal Structural Design. Plenum Press (1983).
F. Hartmann, Elastostatics, pp. 84–167 in Progress in Boundary Element Methods Vol. I (Edited by C. A. Brebbia). Wiley (1981).
E. Alarcon, L. Avia and A. Revester, On the possibility of adaptative boundary elements. Int. Conf. on Accuracy Estimates and Adaptive Refinements in Finite Element Computations, pp. 25–34. Lisbon (1984).
J. Jlencis and R. L. Mullen, A self-adaptive mesh refinement technique for boundary element solution of the Laplace equation. 21st Annual Meeting of the Society of Engineering Science. Blacksburg, VA (1984).
K. K. Choi, E. J. Haug, J. W. Hou and V. M. Sohoni, Pshenichny’s linearization method for mechanical systems optimization. J. Mech. Transm. Autom. Des. 105, 97–104 (1983).
J. W. Hou, E. J. Haug and R. L. Benedict, Shape optimization of elastic bars in torsion, pp. 31–55 in Sensitivity of Functionals with Applications to Engineering Problems (Edited by V. Komkov). Springer-Verlag (1984).
E. J. Haug, K. K. Choi, J. W. Hou and Y. M. Yoo, A variational method for shape optimal design of elastic structures, pp. 105–137 in New Directions in Optimum Structural Design (Edited by E. Atrek, R. H. Gallagher, K. M. Ragsdell and O. C. Zienkiewicz). Wiley (1984).
R. J. Yang, K. K. Choi and E. J. Haug, Numerical considerations in structural component shape optimization. J. Mech. Transm. Autom. Des., to appear.
C. A. Mota Soares and K. K. Choi, Shape optimal design of structures based on stress constraints and boundary elements. Advanced Study Institute on Computer Aided Optimal Design: Structural and Mechanical Systems. Portugal (1986), to appear.
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
Soares, C.A.M., Choi, K.K. (1986). Boundary Elements in Shape Optimal Design of Structures. 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_8
Download citation
DOI: https://doi.org/10.1007/978-1-4615-9483-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-9485-7
Online ISBN: 978-1-4615-9483-3
eBook Packages: Springer Book Archive