116
J. Chen et al.
13. Wang, C., Hun, P., Xia, Y.: A 4-node quasi-conforming Reissner-Mindlin shell element by
using Timoshenko’s beam function. Finite Elem. Anal. Des. 61, 12–22 (2012)
14. Kulikov, G.M., Plotnikova, S.V.: A family of ANS four-node exact geometry shell elements
in general convected curvilinear coordinates. Int. J. Numer. Meth. Eng. 83, 1376–1406 (2010)
15. Katili, I., Batoz, J.L., Maknun, I.J., Hamdouni, A., Millet, O.: The development of DKMQ
plate bending element for thick and thin shell analysis based on the Reissner/Mindlin shell
theory. Finite Elem. Anal. Des. 100, 12–27 (2015)
16. Hahn, Y., Kikuchi, N.: Mixed shell element for seven-parameter formulation. Int. J. Numer.
Meth. Eng. 64(1), 95–124 (2005)
17. Li, J.Z., Hung, K.C., Cen, Z.Z.: Shell element of relative degree of freedom and its application
on buckling analysis of thin-walled structure. Thin Wall. Struct. 40(10), 865–876 (2002)
18. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method-In Solid Mechanics, 5th edn.
Butterworth Heinemann, Oxford (2000)
19. Benson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.R.: Isogeometric shell analysis: the
Reissner-Mindlin shell. Comput. Method Appl. M. 199, 276–289 (2010)
20. Dornisch, W., Klinkel, S., Simeon, B.: Isogeometric Reissner-Mindlin shell analysis with
exactly calculated director vectors. Comput. Method Appl. M. 253, 491–504 (2013)
21. Kiendl, J., Bletzinger, K.U., Linhard, J.: Isogeometric shell analysis with Kirchhoff-Love
elements. Comput. Method Appl. M. 198, 3902–3914 (2009)
22. Oesterle, B., Ramm, E., Bischoff, M.: A shear deformable, rotation-free isogeometric shell
formulation. Comput. Method Appl. M. 307, 235–255 (2016)
23. Kikis, G., Dornisch, W., Klinkel, S.: Isogeometric Reissner-Mindlin shell analysis-employing
different control meshes for displacements and rotations. Adv. Appl. Math. Mech. 16, 209–210
(2016)
24. Riffnaller-Schiefer, A., Augsdörfer, U.H., Fellner, D.W.: Isogeometric shell analysis with
NURBS compatible subdivision surfaces. Appl. Math. Comput. 272, 139–147 (2015)
25. Lei, Z., Gillot, F., Jezeque, L.: Modal synthesis with the isogeometric Kirchhoff-Love shell
elements. Int. J. Appl. Mech. 9, 146–159 (2017)
26. Xiao, X., Bandara, K., Cirak, F.: Isogeometric shape optimisation of shell structures using
multiresolution subdivision surfaces. J. Phys.: Conf. Ser. 734, 032142 (2016)
27. Kuo-Mo, H.: Nonlinear analysis of general shell structures by flat triangular shell element.
Comput. Struct. 25, 665–675 (1987)
28. Cai, Y., Han, L., Tian, L., Zhang, L.: Meshless method based on Shepard function and Partition
of Unity for two-dimensional crack problems. Eng. Anal. Bound. Elem. 65, 126–135 (2016)
29. Cai, Y., Zhu, H.: A locking-free nine-DOF triangular plate element with incompatible
approximation. Int. J. Numer. Meth. Eng. 109, 915–935 (2017)
30. Cowper, G.R.: Gaussian quadrature formulas for triangles. Int. J. Numer. Meth. Eng. 7, 405–
408 (1973)
31. MacNeal, R.H., Harder, R.L.: A proposed standard set of problems to test finite element
accuracy. Finite Elem. Anal. Des. 1, 3–20 (1985)
32. Guan, Y., Tang, L.: A quasi-conforming nine-node degenerated shell finite element. Finite
Elem. Anal. Des. 11, 165–176 (1992)
J. Chen et al.
13. Wang, C., Hun, P., Xia, Y.: A 4-node quasi-conforming Reissner-Mindlin shell element by
using Timoshenko’s beam function. Finite Elem. Anal. Des. 61, 12–22 (2012)
14. Kulikov, G.M., Plotnikova, S.V.: A family of ANS four-node exact geometry shell elements
in general convected curvilinear coordinates. Int. J. Numer. Meth. Eng. 83, 1376–1406 (2010)
15. Katili, I., Batoz, J.L., Maknun, I.J., Hamdouni, A., Millet, O.: The development of DKMQ
plate bending element for thick and thin shell analysis based on the Reissner/Mindlin shell
theory. Finite Elem. Anal. Des. 100, 12–27 (2015)
16. Hahn, Y., Kikuchi, N.: Mixed shell element for seven-parameter formulation. Int. J. Numer.
Meth. Eng. 64(1), 95–124 (2005)
17. Li, J.Z., Hung, K.C., Cen, Z.Z.: Shell element of relative degree of freedom and its application
on buckling analysis of thin-walled structure. Thin Wall. Struct. 40(10), 865–876 (2002)
18. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method-In Solid Mechanics, 5th edn.
Butterworth Heinemann, Oxford (2000)
19. Benson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.R.: Isogeometric shell analysis: the
Reissner-Mindlin shell. Comput. Method Appl. M. 199, 276–289 (2010)
20. Dornisch, W., Klinkel, S., Simeon, B.: Isogeometric Reissner-Mindlin shell analysis with
exactly calculated director vectors. Comput. Method Appl. M. 253, 491–504 (2013)
21. Kiendl, J., Bletzinger, K.U., Linhard, J.: Isogeometric shell analysis with Kirchhoff-Love
elements. Comput. Method Appl. M. 198, 3902–3914 (2009)
22. Oesterle, B., Ramm, E., Bischoff, M.: A shear deformable, rotation-free isogeometric shell
formulation. Comput. Method Appl. M. 307, 235–255 (2016)
23. Kikis, G., Dornisch, W., Klinkel, S.: Isogeometric Reissner-Mindlin shell analysis-employing
different control meshes for displacements and rotations. Adv. Appl. Math. Mech. 16, 209–210
(2016)
24. Riffnaller-Schiefer, A., Augsdörfer, U.H., Fellner, D.W.: Isogeometric shell analysis with
NURBS compatible subdivision surfaces. Appl. Math. Comput. 272, 139–147 (2015)
25. Lei, Z., Gillot, F., Jezeque, L.: Modal synthesis with the isogeometric Kirchhoff-Love shell
elements. Int. J. Appl. Mech. 9, 146–159 (2017)
26. Xiao, X., Bandara, K., Cirak, F.: Isogeometric shape optimisation of shell structures using
multiresolution subdivision surfaces. J. Phys.: Conf. Ser. 734, 032142 (2016)
27. Kuo-Mo, H.: Nonlinear analysis of general shell structures by flat triangular shell element.
Comput. Struct. 25, 665–675 (1987)
28. Cai, Y., Han, L., Tian, L., Zhang, L.: Meshless method based on Shepard function and Partition
of Unity for two-dimensional crack problems. Eng. Anal. Bound. Elem. 65, 126–135 (2016)
29. Cai, Y., Zhu, H.: A locking-free nine-DOF triangular plate element with incompatible
approximation. Int. J. Numer. Meth. Eng. 109, 915–935 (2017)
30. Cowper, G.R.: Gaussian quadrature formulas for triangles. Int. J. Numer. Meth. Eng. 7, 405–
408 (1973)
31. MacNeal, R.H., Harder, R.L.: A proposed standard set of problems to test finite element
accuracy. Finite Elem. Anal. Des. 1, 3–20 (1985)
32. Guan, Y., Tang, L.: A quasi-conforming nine-node degenerated shell finite element. Finite
Elem. Anal. Des. 11, 165–176 (1992)