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Interpolated boundary conditions in plate bending problems using \(C^1\)-curved finite elements. (English) Zbl 0918.73126

Summary: The purpose of this paper is to construct high order \(C^1\)-curved finite elements which are useful for the approximate solutions of plate bending problems with clamp or simply support boundary conditions over nonpolygon domains. This kind of finite elements is defined over the exact domain of the problem, and the corresponding approximate solution is also obtained over the original domain. Moreover, the effect of the numerical quadrature schemes is studied.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
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[1] Strang, G.; Fix, G. J., An Analysis of Finite Element Method (1973), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0278.65116
[2] Chernuka, M. W.; Cowper, G. R.; Lindberg, G. M.; Olson, M. D., Finite element analysis of plates with curved edges, Internat. J. Numer. Methods Engrg., 4, 49-65 (1972) · Zbl 0253.73053
[3] Douglas, J.; Dupont, T.; Percell, P.; Scott, R., A family of \(C^1\)-finite elements with approximation properties for various Galerkin methods for 2nd and 4th order problems, Rev. Fr. Automat. Inform. Rech. Oper. Anal. Numer., 13, 227-256 (1979) · Zbl 0419.65068
[4] Bernadou, M., \(C^1\)-curved finite elements with numerical integrations for thin plate and thin shell problems, Comput. Methods. Appl. Mech. Engrg., 102, 255-292 (1993), Part I · Zbl 0767.73066
[5] Bernadou, M., \(C^1\)-curved finite elements with numerical integrations for thin plate and thin shell problems, Comput. Methods. Appl. Mech. Engrg., 102, 389-421 (1993), Part II · Zbl 0767.73067
[6] Mansfield, L. E., Approximation of the boundary in the finite element solution of fourth order problems, SIAM J. Numer. Anal., 15, 568-579 (1978) · Zbl 0391.65047
[7] Mansfield, L. E., A Clough-Tocher type element useful for fourth order problems over non-polygonal domains, Math. Comput., 32, 135-142 (1978) · Zbl 0382.65060
[8] Morgan, J.; Scott, R., A nodal basis for \(C^1\) piecewise polynomials of degree ⩾- 5, Math. Comput., 29, 736-741 (1975) · Zbl 0307.65074
[9] Gao, Q.; Li, L., A note on \(C^1\)-curved finite element, Comput. Methods. Appl. Mech. Engrg., 129, 107-114 (1996) · Zbl 0866.73073
[10] Babuska, I.; Pitkaranta, J., The plate paradox for hard and soft support, SIAM J. Math. Anal., 21, 551-576 (1990) · Zbl 0704.73052
[11] Ciarlet, P. G., Finite Element Method for Elliptic Problems (1978), Academic Press: Academic Press New York · Zbl 0383.65058
[12] Ciarlet, P. G.; Raviart, P.-A., Interpolation theory over curved elements with applications of finite elements methods, Comput. Methods. Appl. Mech. Engrg., 1, 217-249 (1972) · Zbl 0261.65079
[13] Boisserie, J. M., A new \(C^1\) finite element: full heptic, Internat. J. Numer. Methods Engrg., 28, 667-677 (1989) · Zbl 0676.73051
[14] Zlamal, M., The finite element method in domains with curved boundaries, Internat. J. Numer. Methods Engrg., 5, 367-373 (1973) · Zbl 0254.65073
[15] Zlamal, M., Curved elements in the finite element method, SIAM J. Numer. Anal., 10, 229-240 (1973), Part I · Zbl 0285.65067
[16] Zlamal, M., Curved elements in the finite element method, SIAM J. Numer. Anal., 11, 347-362 (1974), Part II · Zbl 0277.65064
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