Non-linear static and dynamic instability of complete spherical shells using mixed finite element formulation

Noor, 1977, Nonlinear shell analysis via mixed isoparametric elements, Comput. Struct., 7, 615, 10.1016/0045-7949(77)90004-9 Chang, 1981, Large deformation analysis of laminated shells by finite element method, Comput. Struct., 13, 331, 10.1016/0045-7949(81)90141-3 Chao, 1984, Analysis of laminated composite shells using a degenerated 3-D element, Int. J. Numer. Methods Eng., 20, 1991, 10.1002/nme.1620201104 Saigal, 1986, Geometrically non-linear finite element analysis of imperfect laminated shells, J. Comput. Math., 20, 197 Rhiu, 1988, A nine node finite element for analysis of geometrically nonlinear shells, Int. J. Numer. Methods Eng., 26, 1945, 10.1002/nme.1620260905 Yeom, 1989, An assumed strain finite element model for large deflection composite shells, Int. J. Numer. Methods Eng., 28, 1749, 10.1002/nme.1620280804 To, 2001, Geometrically non-linear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elements, Finite Element Anal. Des., 37, 1, 10.1016/S0168-874X(00)00015-9 Reddy, 1985, Geometrically non-linear transient analysis of laminated, doubly curved shells, Int. J. Non-Linear Mech., 20, 79, 10.1016/0020-7462(85)90002-2 Simitses, 1987, Instability of dynamically-loaded structures, Appl. Mech. Rev., 40, 1407, 10.1115/1.3149542 Simitses, 1990 Tsai, 1991, On the finite element analysis of non-linear vibration for cylindrical shells with high-order shear deformation theory, Int. J. Non-Linear Mech., 26, 379, 10.1016/0020-7462(91)90067-4 Kumar, 1997, Geometrically non-linear dynamic analysis of laminated shells using Bezier functions, Int. J. Non-Linear Mech., 32, 425, 10.1016/S0020-7462(96)00068-6 Lakis, 1998, Non-linear free vibration analysis of laminated orthotropic cylindrical shells, Int. J. Mech. Sci., 40, 27, 10.1016/S0020-7403(97)00029-5 Ye, 1997, The non-linear vibration and dynamic instability of thin shallow shells, J. Sound Vib., 202, 303, 10.1006/jsvi.1996.0827 Mao, 1998, Post-critical behaviors of orthotropic circular cylindrical shells under time dependent axial compression, J. Sound Vib., 210, 307, 10.1006/jsvi.1997.1151 Shariyat, 1999, Dynamic buckling and post-buckling of imperfect orthotropic cylindrical shells under mechanical and thermal loads, based on the three-dimensional theory of elasticity, Trans. ASME J. Appl. Mech., 66, 476, 10.1115/1.2791072 Tabiei, 1999, Numerical simulation of cylindrical laminated shells under impulsive lateral pressure, AIAA J., 37, 629, 10.2514/2.763 B. Budiansky, R.S. Roth, Axisymetrical dynamic buckling of clamped shallow spherical shells, NASA TN-D-1510, 1962, p. 597. A.K. Noor, M.D. Mathers, Shear-flexible finite element models of laminated composite plates and shells, NASA TN-D-8044, 1975, p. 94. Reddy, 1984, Exact solution of moderately thick laminated shells, Trans. ASME J. Appl. Mech., 110, 794 Liew, 1995, A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory, Comput. Methods Appl. Mech. Eng., 127, 145, 10.1016/0045-7825(95)00837-1 Bathe, 1982