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Operator split methods for the numerical solution of the elastoplastic dynamic problem. (English) Zbl 0501.73077


MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74B99 Elastic materials
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[1] Osias, J. R.; Swedlow, J. L., Finite elasto-plastic deformation—I. Theory and Numerical Examples, Internat J. Solids Structures, 10, 321-338 (1974) · Zbl 0273.73033
[2] McMeeking, R. M.; Rice, J. R., Finite element formulations for problems of large elastic-plastic deformation, Internat J. Solids Structures, 11, 601-616 (1975) · Zbl 0303.73062
[3] Krieg, R. D.; Key, S. W., Implementation of a time-independent plasticity theory into structural computer programs, (Stricklin, J. A.; Saczalski, K. J., Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects. Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, AMD, Vol. 20 (1976), ASME: ASME New York), 125-137
[4] Nagtegaal, J. C.; de Jong, J. E., Some computational aspects of elastic-plastic large strain analysis, Internat. J. Numer. Meths. Engrg., 17, 15-41 (1981) · Zbl 0463.73080
[5] Krieg, R. D.; Krieg, D. B., Accuracies of numerical solution methods for the elastic-perfectly plastic model, ASME J. Pressure Vessel Tech., 99, 510-515 (1977)
[6] Schreyer, H. L.; Kulak, R. F.; Kramer, J. M., Accurate numerical solutions for elastic-plastic models, ASME J. Pressure Vessel Tech., 101, 226-234 (1979)
[7] Santiago, J. M., On the accuracy of flow rule approximations used in structural and solid response computer programs, (Proceedings of the 1981 Army Numerical Analysis and Computers Conference. Proceedings of the 1981 Army Numerical Analysis and Computers Conference, ARO Rept. 81-3 (1981)) · Zbl 0508.73027
[8] Mendelson, A., Plasticity: Theory and Application (1968), McMillan: McMillan New York
[9] Ortiz, M.; Pinsky, P. M., Global analysis methods for the solution of the elastoplastic and viscoplastic dynamic problems, (Rept. No. UCB/SESM-81/12 (1981), Dept. of Civil Engineering, Univ. of California: Dept. of Civil Engineering, Univ. of California Berkeley, CA)
[10] T.J.R. Hughes, I. Levit and J. Winget, Unconditionally stable element-by-element implicit algorithms for heat conduction analysis, J. Engrg. Mech. ASCE (to appear).; T.J.R. Hughes, I. Levit and J. Winget, Unconditionally stable element-by-element implicit algorithms for heat conduction analysis, J. Engrg. Mech. ASCE (to appear). · Zbl 0487.73083
[11] Ortiz, M.; Pinsky, P. M.; Taylor, R. L., Unconditionally stable element-by-element algorithms for dynamic problems, Comput. Meths. Appl. Mech. Engrg., 36, 223-239 (1983) · Zbl 0501.73068
[12] Brézis, H., Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam · Zbl 0252.47055
[13] Rockafellar, R. T., Convex Analysis (1970), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0229.90020
[14] Zarantonello, E. H., Projections on convex sets in Hubert space and spectral theory, (Zarantonello, E. H., Symposium on Nonlinear Functional Analysis (1971), Academic Press: Academic Press New York), 237-424
[15] Prager, W.; Hodge, P. G., Theory of Perfectly Plastic Solids (1963), Wiley: Wiley New York
[16] Belytschko, T.; Schoeberle, D. F., On the unconditional stability of an implicit algorithm for nonlinear structural dynamics, J. Appl. Mech., 865-869 (1975)
[17] Hicks, D. L., Stability analysis of WONDY (a hydrocode based on the artificial viscosity method of von Neumann and Richtmyer) for a special case of Maxwell’s law, Math. Comp., 32, 144, 1123-1130 (1978) · Zbl 0388.76006
[18] Argyris, J. H., Energy theorems and structural analysis, Aircraft Engineering, 27 (1955) · Zbl 0161.21601
[19] also in book form (Butterworths, London, 1960, 3rd ed. 1967).; also in book form (Butterworths, London, 1960, 3rd ed. 1967).
[20] Argyris, J. H., Elasto-plastic matrix displacement analysis of three-dimensional continua, J. Roy. Aeronaut. Soc., 69, 633-636 (1965)
[21] Argyris, J. H., Continua and discontinua, Opening address to the Internat, (Conf. Matrix Methods on Structural Mechanics. Conf. Matrix Methods on Structural Mechanics, Dayton, OH, Wright-Patterson USAF Base, Oct. 1965. Conf. Matrix Methods on Structural Mechanics. Conf. Matrix Methods on Structural Mechanics, Dayton, OH, Wright-Patterson USAF Base, Oct. 1965, Conference Proceedings (1967)), 1-198
[22] Argyris, J. H.; Scharpf, D. W.; Spooner, J. B., Die elastoplastische Berechnung von allgemeinen Tragwerken und Kontinua, Ingr.-Arch., 37, 326-352 (1969) · Zbl 0175.23601
[23] Z. Angew. Math. Phys., 23, 517-551 (1972), also · Zbl 0249.73077
[24] Zienkiewicz, O. C.; Valliapan, S.; King, I. P., Elasto-plastic solutions of engineering problems, initial stress, finite element approach, Internat. J. Numer. Meths. Engrg., 75-100 (1969) · Zbl 0247.73087
[25] Balmer, H.; Doltsinis, J. St.; Konig, M., Elastoplastic and creep analysis with the ASKA program system, Comput. Meths. Appl. Mech. Engrg., 3, 87-104 (1974)
[26] Argyris, J. H.; Doltsinis, J. St., On the large strain inelastic analysis in natural formulation—Part 1. Quasistatic problems, Comput. Meths. Appl. Mech. Engrg., 20, 213-252 (1980) · Zbl 0437.73065
[27] Argyris, J. H.; Doltsinis, J. St., On the large strain inelastic analysis in natural formulation—Part II. Dynamic Problems, Comput. Meths. Appl. Mech. Engrg., 21, 91-128 (1980) · Zbl 0437.73067
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