×

On plastic dynamics of discrete structural models. (English) Zbl 0373.73044


MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
65N06 Finite difference methods for boundary value problems involving PDEs
65N99 Numerical methods for partial differential equations, boundary value problems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. I. Taylor,The Testing of Materials at High Rates of Loading, Jour. Inst. Civil Eng., vol. 2, p. 486, 1946. · Zbl 0063.07313
[2] Th. Von Karman, P. E. Duwez,The propagation of Plastic Deformation in Solids, Proc. Sixth Int. Congr. Appl. Mech., Paris, 1964; Jour. Appl. Phys., Vol. 21, p. 987, 1950. · Zbl 0040.10806
[3] H. A. Rachmatulin,Propagation of a Wave of Unloading, Appl. Math. and Mech., Vol. IX, no. 1; Prikl. Mat. Mekh. 9, p. 91, 1945.
[4] M. J. Manjoine,Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel, Jour. Appl. Mech., Ser. A, p. 211, 1944.
[5] M. P. White, Le Van Griffis,The Permanent Strain in a Uniform Bar Due to Longitudinal Impact, Jour. Appl. Mech, Trans. ASME, Vol. 69, p. A-337, 1947.
[6] L. E. Malvern,The Propagation of Longitudinal Waves of Plastic Deformation in a Bar of Material Exhibiting a Strain-Rate Effect, Jour. Appl. Mech., p. 203, June 1951. · Zbl 0044.40001
[7] E. H. Lee,The Theory of Wave Propagation in Anelastic Materials, Intern. Symp. on Stress Wave Propagation in Materials, Norman Davids Ed., Interscience Publ., 1960, p. 199.
[8] R. C. Schich,Analysis of Wave Propagation in a Nonlinear Strain-Hardening Medium, Int. Jour. Mech. Sc., 12 (10), p. 859, 1970. · Zbl 0218.73029 · doi:10.1016/0020-7403(70)90023-8
[9] T. C. T. Ting,On the Solution of Non Linear Parabolic Equation With a Floating Boundary Arising in a Problem of Plastic Impact of a Beam, Quart. Appl. Math., vol. 21, p. 1848, 1963. · Zbl 0131.39904
[10] E. H. Lee, P. S. Symonds,Large Plastic Deformations of Beams Under Transverse Impact, Jour. Appl. Mech., 19, p. 308, Sept. 1952.
[11] H. G. Kopkins, W. Prager,On the Dynamics of Plastic Circular Plates, ZAMP, Vol. 5, p. 317, 1954. · Zbl 0056.18407 · doi:10.1007/BF01587827
[12] P. G. Hodge, Jr.,The Influence of Blast Characteristics on the Final Deformation of Circular Cylindrical Shells, Jour. Appl. Mech., p. 617, Dec. 1956. · Zbl 0075.32802
[13] A. D. Cox, L. W. Morland,Dynamic Plastic Deformation of Simply Supported Square Plates, Jour. Mech. Phys. Sol., Vol. 7, p. 229, 1959. · Zbl 0090.16305 · doi:10.1016/0022-5096(59)90022-5
[14] P. S. Symonds,Impulsive Loading of Plastic Beams with axial Constraints, Jour. Mech. Phys. Sol. Vol. 6, p. 186, 1958. · Zbl 0090.16601 · doi:10.1016/0022-5096(58)90025-5
[15] R. S. Bodner, P. S. Symonds,Experimental and Theoretical Investigation of the Plastic Deformation of Cantilever Beams Subjected to Impulsive Loading, Jour. Appl. Mech., Trans. ASME, p. 719, Dec. 1962.
[16] N. Perrone,Impulsively Loaded Strain-rate-sensitive Plates, Jour. Appl. Mech. 34, p. 380, 1967.
[17] J. B. Martin,A Note on the Uniqueness of Solutions for Dynamically Loaded Rigid Plastic and Rigid Viscoplastic Continua, Jour. Appl. Mech., Vol. 33, p. 207, 1966. · Zbl 0218.73046
[18] A. N. Sherbourne, N. K. Srivastava,Elastic-Plastic Bending of Restrained Pin-Ended Circular Plates, Int. Jour. Mech. Sc., Vol. 13, p. 231, 1971. · doi:10.1016/0020-7403(71)90005-1
[19] N. Jones,Finite Deflections of a Rigid Visco-plastic Strain-Hardening Annular Plate Loaded impulsively, Jour. Appl. Mech. 35, p. 349, 1968.
[20] N. Jones,A theoretical Study of the Dynamic Plastic Behaviour of Beams and Plates With Finite Deflections, Int. Jour. Sol. Struct., Vol. 7, p. 1007, 1971. · Zbl 0241.73045 · doi:10.1016/0020-7683(71)90078-3
[21] P. S. Symonds, N. Jones,Impulsive Loading of Fully Clamped Beams with Finite Plastic Deflections and Strain-Rate Sensitivity; Int. Jour. Mech., Sc., Vol. 14, p. 49, 1972. · doi:10.1016/0020-7403(72)90006-9
[22] N. Jones, N. T. Ich,The Load Carrying Capacities of Symmetrically loaded Shallow Shells, Int. Jour. Sol. Struct., vol. 8, p. 1339, 1972. · Zbl 0247.73077 · doi:10.1016/0020-7683(72)90083-2
[23] J. B. Martin, P. S. Symonds,Mode Approximations for Impulsively-Loated Rigid-Plastic Structures, Proc. ASCE, EM5, p. 43, Oct. 1966.
[24] G. Augusti,Mode Approximations for Rigid-Plastic Structures Supported by an Elastic Medium, Inc. Jour. Sol. Struct., Vol. 6, p. 809, 1970. · Zbl 0194.28103 · doi:10.1016/0020-7683(70)90019-3
[25] G. Augusti,Rigid Plastic Structures Subject to Dynamic Loads, Meccanica Vol. 5, No. 2, p. 74, 1970. · Zbl 0194.28103 · doi:10.1007/BF02134211
[26] J. B. Martin,Extremum Principles for a Class of Dynamic Rigid-Plastic Problems, Int. Jour. Sol. Struct., Vol. 8, p. 1185, 1972. · Zbl 0266.73021 · doi:10.1016/0020-7683(72)90074-1
[27] J. B. Martin,Impulsive Loading Theorems for Rigid-Plastic Continua, Proc. ASCE, EM5 Vol. 90, p. 27, 1964.
[28] W. J. Morales, G. E. Nevill,Lower Bounds on Deformations of Dynamically Loaded Rigid-Plastic Continua, AIAA Jour., vol. 8, n. 11, p. 2043, 1970. · Zbl 0215.57602 · doi:10.2514/3.6044
[29] J. B. Martin,A Displacement Bound Principle for Inelastic Continua Subjected to a Certain Class of Dynamic Loading, JOur. Appl. Mech., Trans. ASME, Vol. 32, p. 1, 1965.
[30] J. B. Martin,Displacement Bounds for Dynamically Loaded Elastic Structures, Jour. Mech. Eng. Sc., vol. 10, No. 3, p. 213, 1968. · doi:10.1243/JMES_JOUR_1968_010_033_02
[31] J. B. Martin, A. R. S. Ponter,Bounds on Large Deformations of Impulsively Loaded Elastic-Plastic Structures, Proc. ASCE. EM 1, p. 107, 1972. · Zbl 0241.73008
[32] G. Maier,Upper Bounds on Deformations of Elastic Work-Hardening Structures in the Presence of Dynamic and Second-Order Geometric Effects, Tech. Rep., ISTC, Politecnico di Milano, 1973.
[33] M. Capurso,Displacement Bounding Principles in the Dynamics of Elastoplastic Continua, to appeare in ”Jour. Struct. Mech.”.
[34] V. P. Tamuzh,On a Minimum Principle in Dynamics of Rigid-Plastic Bodies, Prikl. Math. Mek., Vol. 26, p. 1067, 1962. · Zbl 0115.19103
[35] M. Capurso,A Quadratic Programming Approach to the Impulsive Loading of Rigid-Plastic Structures, Meccanica, vol. 7, No. 1, p. 45, 1972. · Zbl 0236.73052 · doi:10.1007/BF02133604
[36] L. H. N. Lee, Chi-Mou Ni,A Minimum Principle in Dynamics of Elastic-Plastic Continua at Finite Deformation, Arch. Mech., 25, 3, p. 457, 1973. · Zbl 0262.73042
[37] M. Capurso,On the External Properties of the Solution in Dynamics of Rigid-Viscoplastic Bodies allowing for Large Displacement Effects, Meccanica, vol. 7, No. 4, p. 236, 1972. · Zbl 0258.73025 · doi:10.1007/BF02133722
[38] E. A. Witmer, H. A. Balmer, J. W. Leech, T. H. H. Pian,Large Dynamic Deformation of Beams, Circular Rings, Circular Plates and Shells, AIAA Jour, No. 1, p. 1848, 1963. · Zbl 0114.16406
[39] J. W. Leech, E. A. Witmer, T. H. H. Pian,Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells, AIAA Jour., Vol. 6, p. 2352, 1968. · Zbl 0181.52801 · doi:10.2514/3.4994
[40] S. Nagarajan, E. P. Popov,Elastic-Plastic Dynamic Analysis of Aximmetric Solids, Comp. and Struct., vol. 4, p. 1117, 1974. · doi:10.1016/0045-7949(74)90028-5
[41] S. E. Benzley, J. R. Hutchinson, S. W. Key,A Dynamic Shell Theory Coupling Thickness Stress Wave Effects with Gross Structural Response, Jour. Appl. Mech., vol. 40, p. 371, 1973.
[42] S. B. Menkes, H. J. Opat,Broken Beams, Exp. Mech., vol. 13, n. 11, p. 480, 1973. · doi:10.1007/BF02322734
[43] R. W. Cottle,On a Problem in Linear Inequalities, J. Lond. Math. Soc., 43, p. 378, 1968. · Zbl 0181.04001 · doi:10.1112/jlms/s1-43.1.378
[44] G. B. Dantzig, E. Eisenberg, R. W. Cottle,Symmetric Dual Nonlinear Programs, Oper. Research Center, U. of California, Berkley, RR 30, Dec. 1972. · Zbl 0136.14001
[45] R. W. Cottle, G. B. Dantzig,Complementary Pivot Theory of Mathematical Programming, Lin. Alg. and its Appl. 1, p. 103, 1968. · Zbl 0155.28403 · doi:10.1016/0024-3795(68)90052-9
[46] A. A. Cannarozzi, F. Laudiero, Sul calcolo delle strutture rigido-plastiche soggette a carichi dinamici, Proc. II Nat. (Italian) Congr. AIMETA, vol. II, p. 395, Naples, 1974.
[47] A. A. Cannarozzi, F. Laudiero,On Plastic Dynamic Flexure of Plates, Tech. Rep. I.S.C.B. n. 13, Bologna, 1975. · Zbl 0373.73044
[48] W. Kahan,Numerical Linear Algebra, Canad. Math. Bull., 9, p. 757, 1966. · Zbl 0236.65025 · doi:10.4153/CMB-1966-083-2
[49] P. G. Hodge, Jr.,Plastic Analysis of Structures, Mc Graw-Hill Book Comp., New York, 1959. · Zbl 0113.17903
[50] N. Jones,A Literature Review of the Dynamic Plastic Response of Structures, M.I.T. Rep. 74-9, Cambridge, 1974.
[51] P. Perzyna,Fundamental Problems in Viscoplasticity, inAdvances in Applied Mechanics, vol. IX, Academic Press, London, 1966.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.