Triangular, nine-degrees-of-freedom, $C^0$ plate bending element of quadratic accuracy
Authors:
Isaac Fried and Shok Keng Yang
Journal:
Quart. Appl. Math. 31 (1973), 303-312
DOI:
https://doi.org/10.1090/qam/99699
MathSciNet review:
QAM99699
Full-text PDF Free Access
References |
Additional Information
R. W. Clough and J. L. Tocher, Finite element stiffness matrices for analysis of plate bending, in Proceedings of the conference on matrix methods in structural mechanics, Wright-Patterson Air Force Base, TR-66-80 (1966)
- Garrett Birkhoff and Henry L. Garabedian, Smooth surface interpolation, J. Math. and Phys. 39 (1960), 258–268. MR 119387
G. P. Bazeley, Y. K. Cheung, B. M. Irons and O. C. Zienkiewicz, Triangular elements in plate bending—conforming and nonconforming solutions, in Proceedings of the conference on matrix methods in structural mechanics, Wright–Patterson Air Force Base, TR-66-80 (1966)
R. T. Severn and P. R. Taylor, The finite element method for flexure of slabs when stress distributions are assumed, Proc. Inst. Civ. Engnrs. 34, 153–167 (1966)
R. Dungar, R. T. Severn and P. R. Taylor, Vibration of plate and shell structure using triangular finite elements, J. Strain Anal. 2, 73–83 (1967)
D. J. Allman, Triangular finite elements for plate bending with constant and linearly varying bending moments, in Colloquium of the IUTAM on high-speed computing of elastic structures, University of Liege, Belgium (1970)
W. Prager, Variational principles for elastic plates with relaxed continuity requirements, Int. J. Solids Structures 4, 837–844 (1968)
T. H. H. Pian, Derivation of element stiffness matrices by assumed stress distribution, AIAA J. 2, 1333–1336 (1964)
J. A. Stricklin, W. E. Haisler, P. R. Tisdale and R. Gunderson, A rapidly converging triangular plate element, AIAA J. 7, 180–181 (1969)
G. A. Wempner, J. T. Oden and D. K. Kross, Finite element analysis of thin shells, J. Engineering Mech. Div. ASCE 94, 1273–1294 (1968)
I. Fried, Shear in ${C^0}$ and ${C^1}$ plate bending elements, Int. J. Solids Structures 9, 449–460 (1973)
- R. P. Nordgren, A bound on the error in plate theory, Quart. Appl. Math. 28 (1971), 587–595. MR 280051, DOI https://doi.org/10.1090/S0033-569X-1971-0280051-4
I. Fried, Discretization and round-off error in the finite element analysis of elliptic boundary value and eigenvalue problems, Ph.D. thesis, Massachusetts Institute of Technology (June 1971)
I. Fried, Condition of finite element matrices generated from nonuniform meshes, AIAA J. 10, 219—221 (1972)
I. Fried, Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number, J. Sound Vibration 22, 407–418 (1972)
I. Fried, The ${l_2}$ and ${l_\infty }$ condition numbers of the finite element stiffness and mass matrices and the pointwise convergence of the method, Conference on the Mathematics of Finite Elements and Applications, Brunel University, April 18–20, Academic Press, ed. J. R. Whiteman (1972)
R. W. Clough and J. L. Tocher, Finite element stiffness matrices for analysis of plate bending, in Proceedings of the conference on matrix methods in structural mechanics, Wright-Patterson Air Force Base, TR-66-80 (1966)
G. Birkhoff and H. L. Garabedian, Smooth surface interpolation, J. Math. Phys. 39, 353–368 (1960)
G. P. Bazeley, Y. K. Cheung, B. M. Irons and O. C. Zienkiewicz, Triangular elements in plate bending—conforming and nonconforming solutions, in Proceedings of the conference on matrix methods in structural mechanics, Wright–Patterson Air Force Base, TR-66-80 (1966)
R. T. Severn and P. R. Taylor, The finite element method for flexure of slabs when stress distributions are assumed, Proc. Inst. Civ. Engnrs. 34, 153–167 (1966)
R. Dungar, R. T. Severn and P. R. Taylor, Vibration of plate and shell structure using triangular finite elements, J. Strain Anal. 2, 73–83 (1967)
D. J. Allman, Triangular finite elements for plate bending with constant and linearly varying bending moments, in Colloquium of the IUTAM on high-speed computing of elastic structures, University of Liege, Belgium (1970)
W. Prager, Variational principles for elastic plates with relaxed continuity requirements, Int. J. Solids Structures 4, 837–844 (1968)
T. H. H. Pian, Derivation of element stiffness matrices by assumed stress distribution, AIAA J. 2, 1333–1336 (1964)
J. A. Stricklin, W. E. Haisler, P. R. Tisdale and R. Gunderson, A rapidly converging triangular plate element, AIAA J. 7, 180–181 (1969)
G. A. Wempner, J. T. Oden and D. K. Kross, Finite element analysis of thin shells, J. Engineering Mech. Div. ASCE 94, 1273–1294 (1968)
I. Fried, Shear in ${C^0}$ and ${C^1}$ plate bending elements, Int. J. Solids Structures 9, 449–460 (1973)
R. P. Nordgren, A bound on the error in plate theory, Quart. Appl. Math. 30, 587–595 (1972)
I. Fried, Discretization and round-off error in the finite element analysis of elliptic boundary value and eigenvalue problems, Ph.D. thesis, Massachusetts Institute of Technology (June 1971)
I. Fried, Condition of finite element matrices generated from nonuniform meshes, AIAA J. 10, 219—221 (1972)
I. Fried, Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number, J. Sound Vibration 22, 407–418 (1972)
I. Fried, The ${l_2}$ and ${l_\infty }$ condition numbers of the finite element stiffness and mass matrices and the pointwise convergence of the method, Conference on the Mathematics of Finite Elements and Applications, Brunel University, April 18–20, Academic Press, ed. J. R. Whiteman (1972)
Additional Information
Article copyright:
© Copyright 1973
American Mathematical Society
