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Theocaris, P. S.; Panagiotopoulos, P. D.

Neural networks for computing in fracture mechanics. Methods and prospects of applications. (English) Zbl 0782.73077

Comput. Methods Appl. Mech. Eng. 106, No. 1-2, 213-228 (1993).
Summary: A neural network is proposed and studied for the treatment of fracture mechanics problems. Both the cases of classical cracks and of cracks involving Coulomb’s friction or detachment (unilateral contact) interface conditions are considered. For the first case, the Hopfield model [J. J. Hopfield, Proc. Natl. Acad. Sci. 79, 2554-2558 (1982)] is appropriately modified, whereas for the second case, a neural model is proposed covering the case of inequalities. For this model, new results generalizing the results of J. J. Hopfield and D. W. Tank [Biol. Cybern. 52, 141-152 (1985; Zbl 0572.68041)] are obtained. Numerical applications illustrate the theory. Finally, the parameter identification problem for fractured bodies is formulated as a supervised learning problem.

Cited in 1 Review
Cited in 12 Documents

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence

Keywords:

unilateral contact; classical cracks; Coulomb’s friction; parameter identification; learning problem

Citations:

Zbl 0572.68041
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Full Text: DOI

References:

[1] Caudill, M.; Butler, C., Naturally Intelligent Systems (1990), MIT Press: MIT Press Cambridge
[2] Beale, R.; Jackson, T., Neural Computing. An Introduction (1990), IOP: IOP Bristol · Zbl 0723.68088
[3] Duvaut, G.; Lions, J. L., Les inéquations en Mécanique et en Physique (1972), Dunod: Dunod Paris · Zbl 0298.73001
[4] Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applications, Convex and Nonconvex Energy functions (1985), Birkhäuser: Birkhäuser Basel, Russian translation (MIR, Moscow 1989) · Zbl 0579.73014
[5] Panagiotopoulos, P. D., A nonlinear programming approach to the unilateral contact and friction-boundary value problem in the theory of elasticity, Ing. Arch., 44, 421-432 (1975) · Zbl 0332.73018
[6] Dubourg, M. C.; Villechaise, B., Unilateral contact analysis of a crack with friction, European J. Mech. A/Solids, 8, 309-319 (1989) · Zbl 0692.73078
[7] P.S. Theocaris and P.D. Panagiotopoulos, On the consideration of unilateral contact and friction in cracks. The indirect boundary integral equation method, Internat. J. Numer. Methods Engrg., in press.; P.S. Theocaris and P.D. Panagiotopoulos, On the consideration of unilateral contact and friction in cracks. The indirect boundary integral equation method, Internat. J. Numer. Methods Engrg., in press. · Zbl 0767.73089
[8] Panagiotopoulos, P. D.; Lazaridis, P. P., Boundary minimum principles for the unilateral contact problems, Internat. J. Solids and Structures, 23, 1465-1484 (1987) · Zbl 0626.73123
[9] Panagiotopoulos, P. D., Multivalued boundary integral equations for inequality problems. The convex case, Acta Mech., 70, 145-167 (1987) · Zbl 0656.73038
[10] Theocaris, P. S.; Panagiotopoulos, P. D., On debonding and delamination effects in adhesively bonded cracks. A boundary integral approach, Arch. Appl. Mech. (Ing. Arch.), 61, 578-587 (1991) · Zbl 0763.73072
[11] Panagiotopoulos, P. D., Boundary integral equations for inequality problems. The nonconvex case, Acta Mech., 72, 152-168 (1989)
[12] Panagiotopoulos, P. D.; Moreau, J. J.; Strang, G., Topics in Nonsmooth Mechanics (1988), Birkhäuser: Birkhäuser Boston · Zbl 0646.00014
[13] Moreau, J. J.; Panagiotopoulos, P. D., Nonsmooth Mechanics and Applications, (CISM, Vol. 302 (1988), Springer: Springer New York) · Zbl 0652.00016
[14] Theocaris, P. S.; Panagiotopoulos, P. D., On the \(T- and the S- criteria\) in fracture mechanics: New formulations and variational principles, Acta Mech., 87, 135-152 (1991) · Zbl 0738.73062
[15] Blandford, G. E.; Ingraffea, A. R.; Liggett, J. A., Two dimensional stress intensity factor computations using the boundary element method, Internat. J. Numer. Methods Engrg., 67, 387-404 (1981) · Zbl 0463.73082
[16] Zang, W. L.; Gudmundson, P., Frictional contact problems of kinked cracks modelled by a boundary integral method, Internat. J. Numer. Methods Engrg., 31, 427-446 (1991) · Zbl 0825.73895
[17] Theocaris, P. S.; Makrakis, G. N., The kinked crack solved by Mellin transform, J. Elasticity, 16, 393-411 (1986) · Zbl 0602.73100
[18] Theocaris, P. S.; Makrakis, G. N., Crack kinking in anti-plane shear solved by the Mellin transform, Internat. J. Fracture, 34, 251-262 (1987)
[19] McCulloch, W.; Pitts, W., A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys., 5, 115-133 (1943) · Zbl 0063.03860
[20] Widrow, B.; Hoff, M., Adaptive switching circuits, 1960 IRE WESCON Convention Record, (1960 IRE WESCON Convention Record (1960), IRE: IRE New York), 96-104
[21] Hopfield, J. J., Neural networks and physical systems with emergent collective computational abilities, (Proc. National Acad. Sci., 79 (1912)), 2554-2558 · Zbl 1369.92007
[22] Hopfield, J. J.; Tank, D. W., “Neural” computation of decisions in optimization problems, Biol. Cybernet., 52, 141-152 (1985) · Zbl 0572.68041
[23] Lippmann, R., An introduction to computing with neural nets, IEEE ASSP Mag., 4-22 (April 1987)
[24] Amari, Shun-ichi, Dynamic stability of formation of cortical maps in dynamic interactions in neural networks. Models and data, (Arbib, M.; Amari, S., Res. Notes in Neural Comp., Vol. 1 (1989), Springer: Springer Berlin) · Zbl 0672.92005
[25] Anderson, J.; Rosenfield, E., Neurocomputing. Foundations of Research (1988), MIT Press: MIT Press Cambridge, MA
[26] Durbin, R.; Miall, C.; Mitchison, G., The Computing Neuron (1989), Addison Wesley: Addison Wesley New York
[27] Soucek, B., Neural and Concurrent Real Time Systems (1989), Wiley: Wiley New York · Zbl 1079.68599
[28] E.N. Houstis, S.K. Kortesis and H. Byun, A workload partitioning strategy for PDES by a generalized neural network. Computer Science Department, Purdue University, West Lafayette, IN 47907, CSD-TR 934.; E.N. Houstis, S.K. Kortesis and H. Byun, A workload partitioning strategy for PDES by a generalized neural network. Computer Science Department, Purdue University, West Lafayette, IN 47907, CSD-TR 934. · Zbl 0799.65133
[29] Künzi, H.; Krelle, W., Nichtlinear Programming (1962), Springer: Springer Berlin · Zbl 0102.15502
[30] Panagiotopoulos, P. D., Optimal control of structures with convex and nonconvex energy densities and variational and hemivariational inequalities, Engrg. Structures, 6, 12-18 (1984)
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