NUMERICAL STABILITY OF MASS LUMPING SCHEMES FOR ...

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Numerical stability• Fried, I.: Discretization and round-off errors in the finite element analysis of elliptic boundaryvalue problems and eigenproblems. Ph.D thesis, MIT, 1971.• Dokainish, M.A., Subbaraj, K.: A survey of direct time-integration methods in computationalstructural dynamics - I. Explicit methods. Computers and Structures, 32(6), pp1371–1386, 1989.Stability condition∆t ≤ ∆t cr = 2ω maxEstimation of the maximum eigenvaluesup ω(H/λ) ≤ ω max ≤H/λ∈(0;0.5)max ω max(m)m=1,nelem
Critical Courant numberbounding eienvalueslumping optimizationCo crit0.50.4dispersion analysiseigenfrequenciesCo crit0.50.40.30.3consistent mass matrix0.20.20.10.100 0.05 0.1 0.15 0.2 0.25x00 0.05 0.1 0.15 0.2 0.25xRemark 1: Critical Courant number for the consistent mass matrix is 0.25.Remark 2: Critical Courant number for x = 0.23 is 0.21.
Page 2 and 3: Contents• Finite element dispersi
Page 4: Finite element method• Belytschko
Page 7: frequency ωH/c 1 =0.5
Page 11 and 12: Contents• Finite element dispersi
Page 14 and 15: Mass matrix lumpingRow sum and Hint
Page 16 and 17: Optimum mass distribution(central d
Page 20: Conclusions• Threshold values of

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