Abstract
This chapter introduces the basic theory and numerical aspects of the boundary element method in elastostatics which will be used later on as a numerical analysis tool for shape optimization. After a historical review of the boundary element method in elastostatics, the boundary element formulation for elasticity is presented, followed by the numerical implementation. Final concluding remarks discuss the advantages and drawbacks of the boundary element method over the finite element method in the field of structural analysis, especially in the application of shape optimum design.
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
Kupradze, V. D., Potential Methods in the Theory of Elasticity, Oldbourne Press, 1965.
Rizzo, F. J., An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics, Applied Mathematics, 25, 1967, pp. 83–95.
Jaswon, M. A., Maiti, M., Symm, G. T., Numerical Biharmonic Analysis and Some Applications, Int. J. Solids Strutures, 3, 1967, pp. 309–332.
Cruse, T. A., Numerical Solutions in Three Dimensional Elastostatics, Int. J. Solids Struct., 5, 1969, pp. 1259–1274.
Cruse, T. A., Rizzo, F. J., A Direct Formulation and Numerical Solution of the General Transient Elasto-Dynamic Problem, J. Math. Analysis Appli., 22, 1968.
Lachat, J. C., A Further Development of the Boundary Integral techniques for Elastostatics, Ph.D. Thesis, University of Southampton, 1975.
Massonnet, C. E., Numerical Use of Integral Procedures, Stress Analysis (eds. O. C. Zienkiewicz and G. S. Holister), Wiley, 1965.
Oliveira, E. R. A., Plane Stress Analysis by a Gerneral Integral Method, J. ASCE. Mech. Div., 1968, pp. 79-85.
Beniumea, R., Sikarskie, D. L., On the Solution of Plane, Orthotropic elasticity problems by an Integral Method, J. Appl. Mech., 39, 1972, pp. 801–808.
Crouch, S. L., Solution of Plane Elasticity Problems by the Displacement Discontinuity Method, Int. J. Nemer. Meth. Engng., 10, 1976, pp. 301–343.
Banerjee, P. K., Integral Equation Methods for Analysis of Piece-Wise Non-Homogeneous Three-Dimensional Elastic Solids of Arbitary Shape, Int. J. Mech. Sci., 18, 1976, pp. 293–303.
Quinlan, P. M., O’ Callagham, M. J. A., The Edge-Function Method for Cracks, Cavities and Curved Boundaries in Elastostatics, Chapter 6, Topic in Boundary Element Research (ed. C. A. Brebbia), Vol.3, 1987.
Quinlan, P. M., The Edge-Function Method with Artitary Boundaries in Fracture, Elastostatics, Viscoelasticity and Heat Conduction, Proc. ICCM-88, Springer-Veralg.
Ghosh, N., Rajiyah, H., Ghosh, S., Mukherjee, S., A New Boundary Element Method Formulation for Linear Elasticity, J. Appl. Mech., Vol. 53, 1986, pp. 69–76.
Ghosh, N., Mukherjee, S., A New Boundary Element Method Formulation for Three Dimensional Problems in Linear Elasticity, Acta Mechanics, 67, 1987, pp. 107–119.
Hunt, B., Isaacs, L. T., Integral Equation Formulation for Ground-Water Flow, ASCE Hyd., Oct., 1981.
Hromadka, T. V., Lai, C., The Complex Variable Boundary Element Method in Engnieering Analysis, Springer-Verlag, 1987.
Telles, J. C. F., Brebbia, C. A., Boundary Element Solutions for Half-Plane Problems, Int. J. Solids Struct., 17, 1981, pp. 1149–1158.
Snyder, M. D., Cruse, T. A., Boundary Integral Equation Analysis of Cracked Anisotropic Plates, Int. J. Frac, 11, 1975, pp. 315–328.
Lachat, J. C., Watson, J. O., Effective Numerical Treatment of Boundary Integral Equations: A Formulation for Three-Dimensional Elastostatics, Int. J. Numer. Meth. Engng., 10, 1976, pp. 273–289.
Jun, L., Beer, G., Meek, J. L., Efficient Evaluation of Integrals of Order 1/r, 1/r2, 1/r3 Using Gauss Quadrature, Engineering Analysis, 2, 1985, pp. 118-123.
Telles, J. C. F., A Self Adaptive Coordinate Transform for efficient Numerical Evaluaton of General Boundary Element Integrals, Int. J. Numer. Meth. Engng., 1986.
Kayami, K., Brebbia, C. A., A New Coordinate Transformation Method for Singular and Nearly Singular Integrals over General Curved Boundary Elements, 9th Boundary Elements Conference (eds. C. A. Brebbia, W. L. Wendland, G. Kuhn), 1987.
Nardini, D., Brebbia, C. A., A New Approach for Free Vibration Analysis Using Boundary Elements, Boundary Element Method in Engineering, Springer-Verlag, 1982.
Nowak, A. J., Brebbia, C. A., The Multiple Reciprocity Method. A New Approach for Transforming BEM Domain Integrals to the Boundary, To be published in Engineering Analysis Journal.
Tang, W., A Generalised Approach for Transforming Domain Integrals into Boundary Integrals in Boundary Element Methods, Ph.D Thesis, Computational Mechanics Institute, UK., 1988.
Zienkiewicz, O. C., Kelly, D. W., Bettes, P., The coupling of the Finite Element Method and Boundary Solution Procedures, Int. J. Numer. Meth. Engng., 11, 1977, pp. 355–375.
Brebbia, C. A., Georgiou, P., Combination of Boundary and Finite Elements in Elastostatics, Appl. Math. Modelling, 3, 1979, pp. 212–220.
Kohno, K., Tsunada, T., Seto, H., Tanaka, M., Hybrid Stress Analysis of Boundary and Finite Elements by Super-Element Method, Advance in Boundary Elements, CMP and Springer-Verlag, 1989.
Defigueredo, T. G. B., Brebbia, C. A., A New Hybrid Displacement Variational Formulation of BEM for Elastostatics, Advances in Boundary Elements, CMP and Springer-Verlag, 1989.
Mackerle, J., Brebbia, C. A., The Boundary Element Reference Book, CPM and Springer-Veralg, 1988.
Brebbia, C. A., The Boundary Element Method for Engineers, Pentech Press, 1978.
Banerjee, P. K., Butterfield, R., Boundary Element Methods In Engineering Science, McGraw-Hill, 1981.
Crouch, S. L., Starfield, A. M., Boundary Element Methods in Solid Mechanics, Allen and Unwin, 1983.
Brebbia, C. A., Telles, J. C. F., Wrobel, L. C., Boundary Element Techniques, Theory and Applications in Engineering, Springer-Verlag, 1984.
Brebbia, C. A., Dominguez, J., Boundary Elements — An Introduction Course, Computational Mechanics Pub., 1988.
Hartmann, F., Introduction to Boundary Elements. Theory and Applications, Springer-Veralg, 1989.
Brebbia, C. A. (ed.), Recent Advances in Boundary Element Methods, Proc. 1st Int. Conf. BEM., Southampton, Pentech Press, 1978.
Brebbia, C. A. (ed.), New Development in Boundary Element Methods, Proc. 2nd Int. Seminar, CML Publications, 1980.
Brebbia, C. A. (ed.), Boundary Element Methods, Proc. 3rd Int. Seminar, California, USA, CML Publications, 1981.
Brebbia, C. A. (ed.), Boundary Element Methods in Engineering, Proc. 4th. Int. Seminar, Southampton, CML Publications, 1982.
Brebbia, C. A., Futagami, T., Tanaka, M. (eds.), Boundary Elements, Proc. 5th Int. conf., Japan, CML Publications, 1983.
Brebbia, C. A. (ed.), Boundary Elements, Proc. 6th Int. Conf., The Queen Elizabeth 2, CML Publications, 1984.
Brebbia, C. A., Maier, G. (eds.), Boundary Elements, Proc. 7th Int. Conf., Italy, 1985.
Tanaka, M., Brebbia, C. A. (eds.), Boundary Elements, Proc. 8th Int. Conf., Japan, CML Publication, 1986.
Brebbia, C. A., Wendland, W. L., Kuhn, G. (eds.), Boundary Elements, Proc. 9th Int. Conf., Stuttgart, Germany, CML Publications, 1987.
Brebbia, C. A. (ed.), Boundary Elements Proc. 10th Int. Conf., Southampton, CML Publications, 1988.
Brebbia, C. A., Conner, J. J. (eds.), Boundary Elements, Proc. 11th Int. Conf., Boston, USA, CML Publications, 1989.
Brebbia, C. A., Noye, B. J. (eds.), BETECH 85, Proc. 1st BETECH Conf., Adelaide, Australia, CML Publications, 1985.
Conner, J. J., Brebbia, C. A. (eds.), BETECH 86, Proc. 2nd BETECH Conf., Cambridge, USA, CML Publications, 1986.
Brebbia, C. A., Venturini, W. S. (eds.), Boundary Element Techniques, Proc. 3rd BETECH Conf., Brazil, CML Publications, 1987.
Cruse, T. A. (ed), IUTAM Symposium on Advenced Boundary Element Method, Springer-Veralg, 1987.
Brebbia, C. A., Zamana, N. G. (eds.), Boundary Element Techniques: Applications in Engineering, Proc. 5th BETECH Conf., Windsor, Canada, CML Publications, 1989.
Timoshenko, S. P., Goodier, J. N., Theory of Elasticity, McGraw-Hill, 1987.
Zienkiewicz, O. C., Morgan, K., Finite Elements and Approximation, John Wiley & Sons, 1983.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Zhao, Z. (1991). The Boundary Element Method in Elastostatics. In: Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method. Lecture Notes in Engineering, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84382-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-84382-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53518-8
Online ISBN: 978-3-642-84382-2
eBook Packages: Springer Book Archive