Error through the constitutive relation for beam and C-0 plate finite elements: static and vibration analyses

Applications of the so-called 'error through the constitutive relation' are presented for the static and modal analyses of beams and plates. The error associated to the performed computation is estimated from the lack of veri fication. by two admissible fields, of the constitutive relation. One is an admissible stress resultant field and the other is the generalised strain given by the finite element analysis. Admissible stress resultants are deri ved from the finite element stress solution following two main ideas. First ly, loads and moments ensuring the element equilibrium are calculated local ly using an 'on average' equilibrium property of the finite element stress solution. Secondly, the stress resultants are determined within a set large enough to allow an optimisation in the way of rendering the error estimati on more accurate. For the normal mode analyses, an error estimation is made for each eigenvector associated to a frequency within a given range. An au tomatic procedure is described in case of beam structures that ensures a gi ven accuracy for all modes in a given frequency range. A set of examples is presented wherein the estimated error is compared to the error obtained fr om the analytical solution. Theses examples show that the beam and plate an alyses are areas well adapted to the method. (C) 1999 Elsevier Science S.A. All rights reserved.