Triangular, nine-degrees-of-freedom, 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

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References | Additional Information

**[1]**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)**[2]**Garrett Birkhoff and Henry L. Garabedian,*Smooth surface interpolation*, J. Math. and Phys.**39**(1960), 258–268. MR**0119387****[3]**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)**[4]**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)**[5]**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)**[6]**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)**[7]**W. Prager,*Variational principles for elastic plates with relaxed continuity requirements*, Int. J. Solids Structures**4**, 837-844 (1968)**[8]**T. H. H. Pian,*Derivation of element stiffness matrices by assumed stress distribution*, AIAA J.**2**, 1333-1336 (1964)**[9]**J. A. Stricklin, W. E. Haisler, P. R. Tisdale and R. Gunderson,*A rapidly converging triangular plate element*, AIAA J.**7**, 180-181 (1969)**[10]**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)**[11]**I. Fried,*Shear in and plate bending elements*, Int. J. Solids Structures**9**, 449-460 (1973)**[12]**R. P. Nordgren,*A bound on the error in plate theory*, Quart. Appl. Math.**28**(1971), 587–595. MR**0280051**, https://doi.org/10.1090/S0033-569X-1971-0280051-4**[13]**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)**[14]**I. Fried,*Condition of finite element matrices generated from nonuniform meshes*, AIAA J.**10**, 219--221 (1972)**[15]**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)**[16]**I. Fried,*The and 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

DOI:
https://doi.org/10.1090/qam/99699

Article copyright:
© Copyright 1973
American Mathematical Society