Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells

International Journal of Non-Linear Mechanics - Tập 69 - Trang 109-128 - 2015
Marco Amabili1
1Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Canada H3A 0C3

Tài liệu tham khảo

Amabili, 2008

Amabili, 2009, Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates, J.SoundVib., 320, 649, 10.1016/j.jsv.2008.08.006

Reddy, 2004

Reddy, 1984, Exact solutions of moderately thick laminated shells, J. Eng. Mech., 110, 794, 10.1061/(ASCE)0733-9399(1984)110:5(794)

Amabili, 2010, A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells, Int. J. Non-linear Mech., 45, 409, 10.1016/j.ijnonlinmec.2009.12.013

Carrera, 1999, Transverse normal stress effects in multilayered plates, J. Appl. Mech., 66, 1004, 10.1115/1.2791769

Carrera, 2011, Effects of thickness stretching in functionally graded plates and shells, Composites B, 42, 123, 10.1016/j.compositesb.2010.10.005

Büchter, 1994, Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept, Int. J. Numer. Methods Eng., 37, 2551, 10.1002/nme.1620371504

Bischoff, 1997, Shear deformable shell elements for large strains and rotations, Int. J. Numer. Methods Eng., 40, 4427, 10.1002/(SICI)1097-0207(19971215)40:23<4427::AID-NME268>3.0.CO;2-9

Bischoff, 2000, On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation, Int. J. Solids Struct., 37, 6933, 10.1016/S0020-7683(99)00321-2

Parisch, 1995, A continuum-based shell theory for non-linear applications, Int. J. Numer. Methods Eng., 38, 1855, 10.1002/nme.1620381105

Sansour, 2002, An energy-momentum integration scheme and enhanced strain finite element for the non-linear dynamics of shells, Int. J. Non-linear Mech., 37, 951, 10.1016/S0020-7462(01)00108-1

Arciniega, 2007, Large deformation analysis of functionally graded shells, Int. J. SolidsStruct., 44, 2036, 10.1016/j.ijsolstr.2006.08.035

Amabili, 2013, A new nonlinear higher-order shear deformation theory with thickness variation for large-amplitude vibrations of laminated doubly curved shells, J. Sound Vib., 332, 4620, 10.1016/j.jsv.2013.03.024

Alijani, 2014, Non-linear static bending and forced vibrations of rectangular plates retaining non-linearities in rotations and thickness deformation, Int. J. Non-linear Mech., 67, 394, 10.1016/j.ijnonlinmec.2014.10.003

Novozhilov, 1953

Novozhilov, 1964

Amabili, 2003, Comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach, J. Sound Vib., 264, 1091, 10.1016/S0022-460X(02)01385-8

Amabili, 2012, Nonlinear vibrations of angle-ply laminated circular cylindrical shells: Skewed modes, Compos. Struct., 94, 3697, 10.1016/j.compstruct.2012.05.019

Doedel, 1998

Alijani, 2014, Non-linear vibrations of shells: a literature review from 2003 to 2013, Int. J. Non-linear Mech., 58, 233, 10.1016/j.ijnonlinmec.2013.09.012