Two non-probabilistic set-theoretical models for dynamic response and buckling failure measures of bars with unknown-but-bounded initial imperfections

Alefeid, 1983 Ben-Haim, 1989, Non-probabilistic models of uncertainty in the nonlinear buckling of shells with general imperfections: theoretical estimates of the knockdown factor, ASME Journal of Applied Mechanics, 56, 403, 10.1115/1.3176097 Ben-Haim, 1990 Deif, 1991 Elishakoff, 1978, Axial impact buckling of a column with random initial imperfections, ASME Journal of Applied Mechanics, 45, 361, 10.1115/1.3424302 Elishakoff, 1978, Impact buckling of thin bar via Monte Carlo method, ASME Journal of Applied Mechanics, 45, 586, 10.1115/1.3424366 Koning, C., Taub, J., 1934. Impact buckling of thin bars in the elastic range hinged at both ends. NACA TM 748 (translation from German) Lindberg, 1965, Impact buckling of a thin bar, ASME Journal of Applied Mechanics, 32, 312, 10.1115/1.3625801 Lindberg, 1991, Dynamic response and buckling failure measures for structures with bounded and random imperfections, ASME Journal of Applied Mechanics, 58, 1092, 10.1115/1.2897690 Malyshev, 1966, Stability of columns under impact compression, Izvestiya Akademii Nauk SSSR Mekhanika, Tverdogo Tela, 1, 137 Moore, 1979 Pantelides, 2001, Comparison of fuzzy set and convex model theories in structural design, Mechanical Systems and Processing, 15, 499, 10.1006/mssp.2000.1379 Qiu, 1995, Natural frequencies of structures with uncertain but non-random parameters, Journal of Optimization Theory and Applications, 86, 669, 10.1007/BF02192164 Qiu, 1998, Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis, Computer Methods in Applied Mechanics and Engineering, 152, 361, 10.1016/S0045-7825(96)01211-X Qiu, 2001, Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach, Mathematics and Computers in Simulation, 56, 35, 10.1016/S0378-4754(00)00200-7 Qiu, 2001, An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices, Communications in Numerical Methods in Engineering, 17, 239, 10.1002/cnm.401 Qiu, 1996, The bound set of possible eigenvalues of structures with uncertain but non-random parameters, Chaos, Solitions & Fractals, 7, 1845, 10.1016/S0960-0779(96)00041-0 Rao, 1997, Analysis of uncertain structural systems using interval analysis, AIAA Journal, 35, 727, 10.2514/2.164