Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures
Tài liệu tham khảo
Ahmad, 1970, Analysis of thick and thin shell structures by curved finite elements, Int. J. Numer. Meth. Engrg., 2, 419, 10.1002/nme.1620020310
Simo, 1989, On a stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization, Comput. Methods Appl. Mech. Engrg., 72, 267, 10.1016/0045-7825(89)90002-9
Chinosi, 1998, Hierarchic finite elements for thin Naghdi shell model, Int. J. Solids Struct., 35, 1863, 10.1016/S0020-7683(97)83328-8
Cho, 2003, Development of geometrically exact new elements based on general curvilinear coordinates, Int. J. Numer. Meth. Engrg., 56, 81, 10.1002/nme.546
Chapelle, 2003, MITC elements for a classical shell model, Comput. Struct., 81, 523, 10.1016/S0045-7949(02)00408-X
Büchter, 1992, Shell theory vs. degeneration – a comparison in large rotation finite element analysis, Int. J. Numer. Meth. Engrg., 34, 39, 10.1002/nme.1620340105
Lee, 2005, Insight into finite element shell discretizations by use of the “basic shell mathematical model”, Comput. Struct., 83, 69, 10.1016/j.compstruc.2004.07.005
Hinton, 1986, A family of quadrilateral Mindlin plate elements with substitute shear strain fields, Comput. Struct., 23, 409, 10.1016/0045-7949(86)90232-4
Dvorkin, 1984, A continuum mechanics based four-node shell element for general nonlinear analysis, Engrg. Comput., 1, 77, 10.1108/eb023562
Simo, 1990, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Meth. Engrg., 29, 1595, 10.1002/nme.1620290802
Leino, 1994, On the membrane locking of h-p finite elements in a cylindrical shell problem, Int. J. Numer. Meth. Engrg., 37, 1053, 10.1002/nme.1620370611
Pitkäranta, 1995, Shell deformation states and the finite element method: a benchmark study of cylindrical shells, Comput. Methods Appl. Mech. Engrg., 128, 81, 10.1016/0045-7825(95)00870-X
Hakula, 1996, Scale resolution, locking, and high-order finite element modelling shells, Comput. Methods Appl. Mech. Engrg., 133, 157, 10.1016/0045-7825(95)00939-6
Pontaza, 2005, Least-square finite element formulation for shear deformable shells, Comput. Methods Appl. Mech. Engrg., 194, 2464, 10.1016/j.cma.2004.07.041
Büchter, 1992, 3D-extension of nonlinear shell equations based on the enhanced assumed strain concept
Sansour, 1995, A theory and finite element formulation of shells at finite deformations involving thickness change: circumventing the use of a rotation tensor, Arch. Appl. Mech., 65, 194, 10.1007/s004190050012
Simo, 1990, On a stress resultant geometrically exact shell model. Part IV: variable thickness shells with through-the-thickness stretching, Comput. Methods Appl. Mech. Engrg., 81, 53, 10.1016/0045-7825(90)90143-A
Braun, 1994, Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates, Comput. Mech., 15, 1, 10.1007/BF00350285
Büchter, 1994, Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept, Int. J. Numer. Meth. Engrg., 37, 2551, 10.1002/nme.1620371504
Bischoff, 1997, Shear deformable shell elements for large strains and rotations, Int. J. Numer. Meth. Engrg., 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
Brank, 2002, Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation, Comput. Struct., 80, 699, 10.1016/S0045-7949(02)00042-1
Krätzig, 1993, Best transverse shearing and stretching shell theory for nonlinear finite element simulations, Comput. Methods Appl. Mech. Engrg., 103, 135, 10.1016/0045-7825(93)90043-W
Betsch, 1998, On the parametrization of finite rotations in computational mechanics: a classification of concepts with application to smooth shells, Comput. Methods Appl. Mech. Engrg., 155, 273, 10.1016/S0045-7825(97)00158-8
Sansour, 2000, Families of 4-nodes and 9-nodes finite elements for a finite deformation shell theory. An assessment of hybrid stress, hybrid strain and enhanced strain elements, Comput. Mech., 24, 435, 10.1007/s004660050003
Balah, 2002, Finite element formulation of a third-order laminated finite rotation shell element, Comput. Struct., 80, 1975, 10.1016/S0045-7949(02)00222-5
Brank, 1995, On implementation of a four node shell element for thin multilayered elastic shells, Comput. Mech., 16, 341, 10.1007/BF00350723
Vu-Quoc, 2003, Optimal solid shells for nonlinear analyses of multilayered composites. I. Statics, Comput. Methods Appl. Mech. Engrg., 192, 975, 10.1016/S0045-7825(02)00435-8
Başar, 1993, Refined shear-deformation models for composite laminates with finite rotations, Int. J. Solids Struct., 30, 2611, 10.1016/0020-7683(93)90102-D
Arciniega, 2005, Consistent third-order shell theory with application to composite circular cylinders, AIAA J., 43, 2024, 10.2514/1.6593
Reddy, 2004, Shear deformation plate and shell theories: from Stavsky to present, Mech. Adv. Mater. Struct., 11, 535, 10.1080/15376490490452777
R.A. Arciniega, On a tensor-based finite element model for the analysis of shell structures, Ph.D. Dissertation, Department of Mechanical Engineering, Texas A&M University, 2005.
Chadwick, 1999
Naghdi, 1972, Theory of shells and plates, vol. VIa/2
Pietraszkiewicz, 1979
Green, 1968
Naghdi, 1963, Foundations of elastic shell theory, vol. 4
Başar, 2000
Reddy, 2004
Reddy, 2002
Truesdell, 1965, The nonlinear field theories, vol. III/2
Reddy, 2004
Başar, 1993, Finite-rotation theories for composite laminates, Acta Mech., 98, 159, 10.1007/BF01174300
Reddy, 2000, Analysis of functionally graded plates, Int. J. Numer. Meth. Engrg., 47, 663, 10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
Praveen, 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, Int. J. Solids Struct., 35, 4457, 10.1016/S0020-7683(97)00253-9
Reddy, 1998, Thermomechanical analysis of functionally cylinders and plates, J. Thermal Stresses, 21, 593, 10.1080/01495739808956165
D.D. Fox, A geometrically exact shell theory, Ph.D. Dissertation, Applied Mechanics Division, Stanford University, 1990.
Hughes, 1978, Consistent linearization in mechanics of solids and structures, Comput. Struct., 8, 391, 10.1016/0045-7949(78)90183-9
Marsden, 1983
Bonet, 1997
Liu, 2002
Reddy, 2005
Bathe, 1996
Sze, 2004, Popular benchmark problems for geometric nonlinear analysis of shells, Fin. Elem. Anal. Des., 40, 1151, 10.1016/j.finel.2003.11.001
Simo, 1990, On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory, Comput. Methods Appl. Mech. Engrg., 79, 21, 10.1016/0045-7825(90)90094-3
Chróścielewski, 1992, Genuinely resultant shell finite elements accounting for geometric and material nonlinearity, Int. J. Numer. Meth. Engrg., 35, 63, 10.1002/nme.1620350105
Massin, 2002, Nine node and seven node thick shell elements with large displacements and rotations, Comput. Struct., 80, 835, 10.1016/S0045-7949(02)00050-0
Timoshenko, 1936
Sanders, 1963, Nonlinear theories for thin shells, Q. Appl. Math., 21, 21, 10.1090/qam/147023
Librescu, 1987, Refined geometrically nonlinear theories of anisotropic laminated shells, Q. Appl. Math., 45, 1, 10.1090/qam/885164
Park, 1995, An efficient assumed strain element model with six DOF per node for geometrically nonlinear shells, Int. J. Numer. Meth. Engrg., 38, 4101, 10.1002/nme.1620382403
Sansour, 1992, An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation, Int. J. Numer. Meth. Engrg., 34, 73, 10.1002/nme.1620340107
Stander, 1989, An assessment of assumed strain methods in finite rotation shell analysis, Engrg. Comput., 6, 58, 10.1108/eb023760
Wagner, 1994, A simple finite rotation formulation for composite shell elements, Engrg. Comput., 11, 145, 10.1108/02644409410799209