Engineering Transactions, 26, 4, pp. 619-643, 1978

Numerical Analysis of Compatible Finite Elements of Different Order in Two-Dimensional Problems of Elasticity

F. Braga
Instituto di Sienza delle Construzioni, Universita di Roma, Roma
Italy

G. Rega
Instituto di Sienza delle Construzioni, Universita di Roma, Roma
Italy

F. Vestroni
Instituto di Sienza delle Construzioni, Universita di Roma, Roma
Italy

A large number of compatible finite element models for plane elasticity problems has been presented in the last decade. On the contrary, the number of studies so far carried out regarding the elements is small. This paper is mainly concerned with the evaluation of the efficiency of different comparison of the behaviour of compatible triangular elements of different order. Such a comparison regards mainly the results associated with LST and QST elements for different values of the number of degrees of freedom in the analysis of problems for which analytical solutions are available. Attention is focused separately on displacement and stress fields by analysing the convergence of the elements as well as the global and local approximation. A numerical analysis is also performed in order to compare the efficiency of two methods suited for encompassing lack of uniqueness of stress nodal values, as usually encountered in the compatible formulation, i.e. the simple average and the method based on the theory of conjugate approximations.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

B. FRAEIJS DE VEUBEKE, Displacement and equilibrium models in the finite element method, Stress analysis, O.C. ZIENKIEWICZ, G. S. HOLISTER [ed.], J. Wiley and son, 1965.

J. L. TOCHER and B. J. HARTZ, Higher-order finite element for plane stress, ASCE, J. Eng. Mech. Div. 93, EM4, 149-174, August 1967; discussion by I. HOLAND and P.G. BERGAN, ASCE, J. Eng. Mech. Div., 94, EM2, 698-702, April 1968.

P. C. DUNNE, Complete polynomial displacement fields for finite element method, Trans. Roy. Aero. Soc., 72, 245, 1968: discussion by B. M. IRONS, J. G. ERGATOUDIS, O. C. ZIENKIEWICZ, Trans. Roy. Aero, Soc., 72, 709-711, 1968.

E. R. DE ARANTES OLIVEIRA, Theoretical foundation of the finite element method, Int. J. Solids Struct., 4, 929-952, 1968.

R.S. DUNHAM and K.S. PISTER, A finite element application of the Hellingger-Reissner variational theorem, Proc. Conf. Matrix Meth. Struct. Mech., Wright-Patterson Air Force Base, Ohio 1968.

T. H. H. PIAN and P. TONG, Basis of finite element methods for solid continua, Intern. J. Num. Meth., 1, 3-28, 1969.

A. HRENNIKOFF, Precision of finite element method in plane stress, Pub, Int. Assn. Bridge Struct. Eng., 29-II, 125-137, 1969.

0.C. ZUNKIEWICZ et al., Isoparametric and associated element families for two and three-dimensional analysis, in: Finite element methods in stress analysis, I. HOLAND and K. BELL [ed.], Techn. Univ. of Norway, Tapir Press, Trondheim, Norway 1969.

I. HOLAND, The finite element method in plane stress analysis, ibidem.

P. A. IVERSEN, Some aspects of the finite element method in two-dimensional problems, ibidem.

C. BREBBIA, Plane stress-plane strain, in: Finite element techniques in structural mechanics, H. TOTTENHAM and C. BREBBIA [ed.], Univ. of Southampton, England, 1970.

J. T. ODEN and H. J. BRAUCHLI, On the calculation of consistent stress distributions in finite element approximations, Int. J. Num. Meth. Eng., 3, 317-325, 1971.

J. T. ODEN and J.N. REDDY, Note on an approximate method for computing consistent conjugate stresses in elastic finite elements, Intern. J. Num. Meth. Eng., 6, 55-61, 1973.

P. PEDERSON, Some properties of linear triangles and optimal finite element models, Intern, Num. Meth. Eng., 7, 415-430, 1973.

D. J. TURCKE and G. M. McNEICE, Guidelines for selecting finite element grids based on an optimization study, Computers and Structures, 4, 499-519, 1974.

G. E. RAMEY, Some effects of system idealisations, singularities and mesh patterns on finite element solutions, Computers and Structures, 4, 1173-1184, 1974.

F. BRAGA, G. REGA, F. VESTRONI, CST, LST and QST elements in the analysis of two-dimensional elastic problems. The FINEL 1 program (in Italian), Rep. No. 11-200, Ist. Scienza d'elle Costuzioni, Roma, 1976.