Abstract
In this paper, the diagonalized consistent mass matrix is found for the triangular ring element in axisymmetrical problems. The results of this work eliminate the feeling of uncertainty and arbitrariness of lumped mass method on the one hand and the difficulty of computation due to non-diagonalized character of consistent mass method on the other. This paper gives also the foundations of the finite element analysis of elastic-plastic axisymmtrical impact problems.
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References
Zienkiewicz, O.C.,The Finite Element Method (Third Edition) (1977), pp. 533–540, McGraw-Hill, New York.
Myklestad, N.O.,Vibration Analysis, McGraw-Hill, New York (1944).
Johnson, G.R.,Analysis of Elastic-plastic Impact Involving Severe Distorsion, Journal of Applied Mechanics, Vol. 93, No. 3, Trans. ASME., Series E, Vol. 98, Sept. (1976), pp. 439–444.
Johnson, G.R.,High Velocity Impact Calculations in Three Dimensions, Journal of Applied Mechanics, Vol. 44, No. 1, Trans. ASME. Vol. 99, Series E. Mar., (1977), pp. 95–100.
Chien, W.Z.Dynamic Finite Element with Diagonalized Consistent Mass Matrix and Elastic-plastic Impact Calculation. Applied Mathematics and Mechanics, Vol. 3, No. 3, May, (1982).
Chien, W.Z.,Mechanics of Penetration and Perforation, Lecture Notes of Applied Mathematics and Mechanics Symposium held at Wuhan sponsored by the Editorial Board of Applied Mathematics and Mechanics. Oct. 5–25, (1981). (in Chinese)
Boresi, A.F.,Elasticity in Engineering Mechanics, Prentice-Hall, Englewood Cliffs, N.J., (1965).
Von Neumann, J., and Richtmyer, R.D.,A Method for the Numerical Calculation of Hydrodynamic Shocks, Journal of Applied Physics, Vol. 21, (1950), pp. 232–237.
Walsh, J.M., et. al.,Shock Wave Compressions of Twenty-seven Metals, Equations of State of Metals, Physical Review, Vol. 10, No. 27, Oct. (1957), pp. 196–216.
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Wei-zang, C. Diagonalized consistent mass matrix and the dynamical finite element analysis of elastic-plastic impact in axisymmetrical problems. Appl Math Mech 3, 469–489 (1982). https://doi.org/10.1007/BF01908223
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DOI: https://doi.org/10.1007/BF01908223