Weighted residuals as a basis of a general solution method in elasticity. (English) Zbl 0536.73014

Bigi, Dante; Cicala, Placido

Meccanica 19, 34-37 (1984).

Summary: It is shown that the general integral form of the elastic equilibrium equations obtainable through the weighted residuals agrees with the variational formulation given by the extremum conditions of the Washizu functional allowing a complete relaxation of the interelement continuity requirements.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
49M15	Newton-type methods

Keywords:

general integral form; elastic equilibrium equations; weighted residuals; extremum conditions of the Washizu functional

References:

[1]	Bigi D.,Sul metodo dei residui in elasticita, Atti Accademia delle Scienze di Torino, 1983, in pubblicazione.
[2]	Tong P.,A New Finite Element Model for Solid Continua, AFOSR-TR-1860, M.I.T. ASRL.TR-144-2, (1968).
[3]	Pian T.H.H.,Hybrid Models, Numerical and Computer Methods in Structural Mechanics, p. 59 Acad. Press, London 1973. · Zbl 0303.49027
[4]	Pian T.H.H., Tong P.,Basis of Finite Elements Methods for Solid Continua, Int. J. for Numer. Methods in Eng., vol. 1 p. 3–28, 1969. · Zbl 0252.73052 · doi:10.1002/nme.1620010103
[5]	Spilker R.L., Munir N.I.,Elastic-plastic Analysis of plates by the hybrid-stress model and initial-stress approach, Int. J. for Numer. Methods in Eng., 17, p. 1791–1810, 1981. · Zbl 0466.73095 · doi:10.1002/nme.1620171205
[6]	Pian T.H.H.,Finite element methods by variational principles with relaxed continuity requirements-Variational Methods in Engineer., Proc. Intern. Conf. Southampton, p. 3/1–3/24, 1972. · Zbl 0274.65033