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

Abstract The finite element method based on the total Lagrangian description of the motion and the Hellinger–Reissner principle with independent strain is applied to investigate the non-linear static and dynamic responses of spherical laminated shells under external pressure. The non-linear dynamic problem is solved by employing the implicit time integration method. The critical load of thin spherical laminated panels is investigated by examining the static and dynamic responses. The critical dynamic load is determined by the phase-plane and the Budiansky–Roth criteria. The effect of the artificial coefficient of Rayleigh damping on the dynamic response is considered. The dynamic response with damping included converges to the static response. The damping coefficient greatly affects a highly non-linear dynamic response. For a thin spherical panel with the snapping phenomena, the critical dynamic load is lower than the static one.

[1]  Aouni A. Lakis,et al.  Non-linear free vibration analysis of laminated orthotropic cylindrical shells , 1998 .

[2]  Z. Ye.  THE NON-LINEAR VIBRATION AND DYNAMIC INSTABILITY OF THIN SHALLOW SHELLS , 1997 .

[3]  Ahmed K. Noor,et al.  Nonlinear shell analysis via mixed isoparametric elements , 1977 .

[4]  George J. Simitses,et al.  Instability of Dynamically-Loaded Structures , 1987 .

[5]  Ahmed K. Noor,et al.  Shear-Flexible Finite-Element Models of Laminated Composite Plates and Shells. , 1975 .

[6]  K. Liew,et al.  A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory , 1995 .

[7]  Romil Tanov,et al.  Numerical Simulation of Cylindrical Laminated Shells Under Impulsive Lateral Pressure , 1999 .

[8]  Vijaya Kumar,et al.  Geometrically non-linear dynamic analysis of laminated shells using Bézier functions , 1997 .

[9]  Anthony N. Palazotto,et al.  On the finite element analysis of non-linear vibration for cylindrical shells with high-order shear deformation theory , 1991 .

[10]  S. W. Lee,et al.  An assumed strain finite element model for large deflection composite shells , 1989 .

[11]  M. Shariyat,et al.  Dynamic buckling and post-buckling of imperfect orthotropic cylindrical shells under mechanical and thermal loads, based on the three-dimensional theory of elasticity , 1999 .

[12]  K. Chandrashekhara,et al.  Geometrically non-linear transient analysis of laminated, doubly curved shells , 1985 .

[13]  S. W. Lee,et al.  A nine node finite element for analysis of geometrically non-linear shells , 1988 .

[14]  Ahmed K. Noor,et al.  Geometrically nonlinear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elements , 1987 .

[15]  George J. Simitses,et al.  Dynamic Stability of Suddenly Loaded Structures , 1989 .

[16]  K. Sawamiphakdi,et al.  Large deformation analysis of laminated shells by ftnife element method , 1981 .

[17]  J. N. Reddy,et al.  Analysis of laminated composite shells using a degenerated 3‐D element , 1984 .

[18]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .