Article
MSC:
35A35,
35J20,
35Q99,
65N30,
74B99,
74H99 | MR 0391539 | Zbl 0355.65087 | DOI: 10.21136/AM.1976.103620
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Summary:
A new variational formulation of the displacement boundary value problem in linear plane elastostatics is established on the basis of a nonclassical spliting of the system of differential operators and the Friedrichs transform.
The variational problem is proved to be correct and an application is shown, which yields a mixed finite element model. Two components of the approximate vector-field converge to the real displacements and the third to the shear stress.
References:
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[2] Haslinger J., Hlaváček I.: Curved elements in a mixed finite element method close to the equilibrium model. Aplikace matematiky 20 (1975), 233 - 252. MR 0383790
[3] Timoshenko S., Goodier J. N.: Theory of Elasticity. 2nd ed., New York 1951. MR 0045547 | Zbl 0045.26402
[4] Watwood V. B., Jr., Hartz B. J.: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems. Int. J. Solids Structures 4, (1968), 857-873. DOI 10.1016/0020-7683(68)90083-8
[5] Fraeijs de Veubeke B.: Displacement and equilibrium models in the finite element method. In Stress Analysis, ed. Zienkiewicz O. C. and Holister G., Wiley (1965), 145-197.
[6] Courant R., Hilbert D.: Methods of Mathematical Physics. Vol. 1, Interscience, New York, 1953. MR 0065391 | Zbl 0053.02805
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