A variational justification of the assumed natural strain formulation of finite elements—I. Variational principles

Willam, 1969, Finite element analysis of cellular structures Ashwell, 1976, Strain elements, with applications to arches, rings and cylindrical shells Bathe, 1985, A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, Int. J. Numer. Meth. Engng, 21, 367, 10.1002/nme.1620210213 Hughes, 1981, Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element, J. appl. Mech., 48, 587, 10.1115/1.3157679 Huang, 1986, A new nine-node degenerated shell element with enhanced membrane and shear interpolation, Int. J. Numer. Meth. Engng, 22, 73, 10.1002/nme.1620220107 Park, 1986, A curved C0 shell element based on assumed natural-coordinate strains, J. appl. Mech., 108, 278, 10.1115/1.3171752 Simo, 1986, On the variational foundations of assumed strain methods, J. appl. Mech., 53, 51, 10.1115/1.3171737 Gurtin, 1972, The linear theory of elasticity, Vol. VIa/2 Jones, 1964, A generalization of the direct stiffness method of structural analysis, AIAA Jnl, 2, 821, 10.2514/3.2437 Finlayson, 1972 Pian, 1982, Alternative ways for formulation of hybrid stress elements, Int. J. Numer. Meth. Engng, 18, 1679, 10.1002/nme.1620181107 Pian, 1983, On the suppression of zero energy deformation modes, Int. J. Numer. Meth. Engng, 19, 1741, 10.1002/nme.1620191202 Hughes, 1987 de Veubeke, 1965, Displacement and equilibrium models in the finite element method