Summary
To solve problems, in solid mechanics, like configurations of plates, shafts, or problems of fracture mechanics in two and three-dimensional space, it is very successful to work with the so-called hybrid stress method [1–6]. The main aim is to have, in the end, a procedure with which one can solve large problems with an influence matrix of band structure and of symmetrical and positive definite type. To obtain this, in general, for curved surfaces of bodies, in three-dimensional space, one can use the new method constructed in 1984 by E. Schnack, see 17, 81. This new method is a non-conforming method in variational formulation from mixed type. The finite element functions, especially the trial functions, have to be constructed by using an integral equation of quasi Fredholm type. Practical experience with this method shows the high convergence rate against conventional methods of FEM and BEM, and a, big advantage is, that one can work with the well-known software available from finite element packages.
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References
T.H.H. Pian, P. Tong: Basis of finite element methods for solid continua, Int. J. Num. Meth. Engng., Bd. 1, 1969, pp. 3–28.
E. Schnack: Beitrag zur Berechnung rotationssymmetrischer Spannungskonzentrationsprobleme mit der Methode der finiten Elemente, Diss. Techn. Univ. München, 1973.
P. Tong, T.H.H. Pian, S.J. Lasry: A hybrid element approach to crack problems in plane elasticity, Int. J. Num. Meth. Engng., Bd. 7, 1973, pp. 297–308.
E. Schnack, M. Wolf: Application of displacement and hybrid stress methods to plane notch and crack problems, Int. J. Num. Meth. Engng., Vol. 12, No. 6, 1978, pp. 963–975.
S.N. Atluri, H.C. Rhee: Traction boundary conditions in hybrid stress finite element model. AIAA Bd. 16, No 5, 1978, pp. 529–531.
T.H.H. Pian, K. Moriya: Three dimensional fracture analysis by assumed stress hybrid elements, in Luxmoore, A.R. Owen, D.R.J.: Proc. 1st and 2nd International Conference on “Numerical Methods in Fracture Mechanics.”, Pineridge Press, Swansea 1978 and 1980, pp. 363–373.
E. Schnack: Stress analysis with a combination of HSM and BEM, in Mathematics of Finite Elements and Applications V, (Ed. Whiteman J.R.), Mafelap, Uxbridge, England, 1984, pp. 273–281.
E. Schnack: A hybrid BEM model, Int. J. Num. Meth. Engng., Vol. 24, No. 5, 1987, pp. 1015–1025.
M. Wolf: Lösung von ebenen Kerb- und Rißproblemen mit der Methode der finiten Elemente, Diss. Techn. Univ. München, 1977.
E. Schnack: Singularities of cracks with generalized finite elements, in P. Grisvard, W. Wendland and J.R. Whiteman (eds) Proc. Singularities and Constructive Methods for Their Treatment, Oberwolfach, 20–26 Nov. 1983, Springer Verlag, 1985, pp. 258–277.
I. Becker, N. Karaosmanoglu, E. Schnack: Mixed Methods with BEM for Three Dimensional Fracture Mechanics, in C.A. Brebbia, W.L. Wendland, G. Kuhn (eds), Boundary Elements IX, Springer Verlag, Berlin Heidelberg, Vol. 2, 1987, pp. 227–241.
S. Ahmad, R. Carmine, E. Schnack: Construction of Equivalent Finite Element Functions using BEM, in C.A. Brebbia, W.L. Wendland, G. Kuhn (eds) Boundary Elements IX, Springer Verlag, Berlin Heidelberg, Vol. 1, 1987, pp. 291–304.
R. Carmine, N. Karaosmanoglu, E. Schnack: Coupling of FEM and BEM with Symmetric Influence Matrix, in IKOSS Congress, Baden-Baden, 16th–17th Nov. 1987
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Schnack, E., Carmine, R., Becker, I., Karaosmanoglu, N. (1988). Mixed Non-Conforming Technique for Coupling FEM and BEM. In: Atluri, S.N., Yagawa, G. (eds) Computational Mechanics ’88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61381-4_30
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DOI: https://doi.org/10.1007/978-3-642-61381-4_30
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