A New Locking-Free Thick/Thin Shell Element
115
and easier numerical implementation compared to some other shell elements, of
which the displacement conformity is satisfied by including high-order derivatives
of displacement in the nodal DOFs.
3) Since the DOFs do not depend on the shape and nodes of the element and have no
clear mechanical meaning, the connection and coupling analysis of the SEIA with
other types of elements (truss, beam and solid) is quite convenient, even in different
coordinate systems, which is practical in engineering numerical calculation.
4) Given the conciseness of the element expressions and the simplicity of the matrix
calculation, the SEIA has a broad application prospect in the dynamic analysis and
the nonlinear analysis of the shell, which will be the next step of the author’s research.
5) The SEIA has no restrictions on the element shape, thus it is easy to implement the
h-p adaptive analysis, which lays the foundation for the crack propagation analysis
and the transformation from the continuous analysis to the discontinuous analysis.
They will also be explored in the author’s future work.
Acknowledgements. The authors gratefully acknowledge the support of National Natural Science Foundation of China (NSFC 51778473) and Ministry of Science and Technology of the
People’s Republic of China (SLDRCE19-B-40).
References
1. Xiang, J., Chen, X., Yang, L., He, Z.: A class of wavelet-based flat shell elements using
B-spline wavelet on the interval and its applications. Comput. Model. Eng. Sci. 23(1), 1–12
(2008)
2. Kulikov, G.M., Plotnikova, S.V.: Finite rotation geometrically exact four-node solid-shell
element with seven displacement degrees of freedom. Comput. Model. Eng. Sci. 28(1), 15–38
(2008)
3. Bao, Y., Feng, D., Ma, N., Zhu, H., Rabczuk, T.: Experimental and numerical study on structural performance of reinforced concrete box sewer with localized extreme defect. Undergr.
Space 3, 166–179 (2018)
4. Bloodworth, A., Su, J.: Numerical analysis and capacity evaluation of composite sprayed
concrete lined tunnels. Undergr. Space 3, 87–108 (2018)
5. Bathe, K.J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)
6. Kraus, H.: Thin Elastic Shells. Wiley, New York (1967)
7. Jarak, T., Sori´ c, J.: On shear locking in MLPG solid-shell approach. Comput. Model. Eng.
Sci. 81(2), 157–193 (2011)
8. Lee, K., Lee, S.W.: An assumed strain solid shell element formulation with transversely
quadratic displacement. Comput. Model. Eng. Sci. 34(3), 253–272 (2008)
9. Talbot, M., Dhatt, G.: Three discrete Kirchhoff elements for shell analysis with large
geometrical nonlinearities and bifurcations. Eng. Comput. 4, 15–22 (1987)
10. Rafetseder, K., Zulehner, W.: A new mixed approach to Kirchhoff-Love shells. Comput.
Method Appl. M. 346, 440–445 (2018)
11. Hughes, T.J.R.: Review: The Finite Element Method: Linear Static and Dynamic Finite
Element Analysis. Prentice-Hall, Inc., Englewood Cliffs (1987)
12. Bathe, K., Dvorkin, E.N.: A four-node plate bending element based on Mindlin/Reissner plate
theory and a mixed interpolation. Int. J. Numer. Meth. Eng. 21, 367–383 (1985)
115
and easier numerical implementation compared to some other shell elements, of
which the displacement conformity is satisfied by including high-order derivatives
of displacement in the nodal DOFs.
3) Since the DOFs do not depend on the shape and nodes of the element and have no
clear mechanical meaning, the connection and coupling analysis of the SEIA with
other types of elements (truss, beam and solid) is quite convenient, even in different
coordinate systems, which is practical in engineering numerical calculation.
4) Given the conciseness of the element expressions and the simplicity of the matrix
calculation, the SEIA has a broad application prospect in the dynamic analysis and
the nonlinear analysis of the shell, which will be the next step of the author’s research.
5) The SEIA has no restrictions on the element shape, thus it is easy to implement the
h-p adaptive analysis, which lays the foundation for the crack propagation analysis
and the transformation from the continuous analysis to the discontinuous analysis.
They will also be explored in the author’s future work.
Acknowledgements. The authors gratefully acknowledge the support of National Natural Science Foundation of China (NSFC 51778473) and Ministry of Science and Technology of the
People’s Republic of China (SLDRCE19-B-40).
References
1. Xiang, J., Chen, X., Yang, L., He, Z.: A class of wavelet-based flat shell elements using
B-spline wavelet on the interval and its applications. Comput. Model. Eng. Sci. 23(1), 1–12
(2008)
2. Kulikov, G.M., Plotnikova, S.V.: Finite rotation geometrically exact four-node solid-shell
element with seven displacement degrees of freedom. Comput. Model. Eng. Sci. 28(1), 15–38
(2008)
3. Bao, Y., Feng, D., Ma, N., Zhu, H., Rabczuk, T.: Experimental and numerical study on structural performance of reinforced concrete box sewer with localized extreme defect. Undergr.
Space 3, 166–179 (2018)
4. Bloodworth, A., Su, J.: Numerical analysis and capacity evaluation of composite sprayed
concrete lined tunnels. Undergr. Space 3, 87–108 (2018)
5. Bathe, K.J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs (1996)
6. Kraus, H.: Thin Elastic Shells. Wiley, New York (1967)
7. Jarak, T., Sori´ c, J.: On shear locking in MLPG solid-shell approach. Comput. Model. Eng.
Sci. 81(2), 157–193 (2011)
8. Lee, K., Lee, S.W.: An assumed strain solid shell element formulation with transversely
quadratic displacement. Comput. Model. Eng. Sci. 34(3), 253–272 (2008)
9. Talbot, M., Dhatt, G.: Three discrete Kirchhoff elements for shell analysis with large
geometrical nonlinearities and bifurcations. Eng. Comput. 4, 15–22 (1987)
10. Rafetseder, K., Zulehner, W.: A new mixed approach to Kirchhoff-Love shells. Comput.
Method Appl. M. 346, 440–445 (2018)
11. Hughes, T.J.R.: Review: The Finite Element Method: Linear Static and Dynamic Finite
Element Analysis. Prentice-Hall, Inc., Englewood Cliffs (1987)
12. Bathe, K., Dvorkin, E.N.: A four-node plate bending element based on Mindlin/Reissner plate
theory and a mixed interpolation. Int. J. Numer. Meth. Eng. 21, 367–383 (1985)