Modelisation elastoplastique des coques minces par un element courbe a variables nodales globales - Ghazlan, Ghassan; Lemaire, Maurice (European Journal of Computational Mechanics, 1992)
The purpose of this text is to present a geometrically (large displacements) and materially (plasticity) nonlinear analysis of thin plates and shells modelized by a curved triangular element based on Marguerre’s theory. For computational efficiency an updated lagrangian description is used, referring the kinematical and mechanical field variables to local corotated coordinate frames. The curved shape of the shell is taken into account by Marguerre’s theory. The constitutive equations are given in terms of increments ofmidsurface strains and curvatures and corresponding generalized stress ( Eidsheim-Larsenapproximation), thus avoiding the integration over the shell thickness and taking into account the propagation of plastic zones through the thickness. Integral approach is used to evaluate stress increments satisfying elastoplastic conditions, thus avoiding in some cases successive approximation process. The nonlinear response is determined using the Newton-Raphson method in conjunction with a scaling sphere, thus permitting an automatic piloting of the whole response in geometrically and materially nonlinear problems. An efficient solution with a small number of elements is obtained using Marguerre’s therory coupled to EidsheimLarsen criterion which allowed progressive propagation of plastic zone without successive approximation process.