Limit and shakedown analysis based on solid shell models XIV International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIV E. O˜ nate, D.R.J. Owen, D. Peric & M. Chiumenti (Eds) LMIT AND SHAKEDOWN ANALYSIS BASED ON SOLID SHELL MODELS LEONARDO LEONETTI * , GIOVANNI GARCEA. * DOMENICO MAGISANO * FRANCESCO LIGUORI * * Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica Universit della Calabria 87036 Rende (Cosenza), Italy web page: http://www.labmec.unical.it/ Key words: Computational Plasticity, Shakedown, Optimization, Solid Shells Abstract. The paper treats the formulation of the shakedown problem and, as special case, of the limit analysis problem, using solid shell models and ES-FEM discratization technology. In this proposal the Discrete shear gap method is applied to alleviate the shear locking phenomenon. 1 INTRODUCTION Shakedown analysis plays an important role in assessing the safety of structures in presence of many independent load combinations [1] against plastic collapse, loss in func- tionality due to excessive deformation (ratcheting) or collapse due to low cycle fatigue. Nowadays, due to the growing attention of the scientific community, solid-shell elements have reached a high level of efficiency and accuracy. It has been shown that solid-shell finite elements give some advantages in linear and nonlinear context of analysis [2]. When compared to shell elements, solid-shell formulations present a simpler structure since only displacement degrees-of-freedom are employed. They can automatically account for 3D constitutive relations and are able to model through the thickness behaviours more ac- curately without the need to resort plane-stress assumptions, which often occurs in shell elements including rotation degrees-of-freedom. Solid-shell formulations also present im- portant advantages when considering double-sided contact situations and in treating large deformations, since no rotation degrees-of-freedom are involved. However in addition to the classical shear, membrane and volumetric lockings, in the solid-shell exhibits thickness and trapezoidal locking. The latter is typical only of low order FEM. Assumed Natural Strain, Enhanced Assumed Strain and mixed (hybrid) formulations have been proposed for resolving these locking phenomena. In the context of triangular grids, the Assumed Natural Strain doesn’t solve at all the shear locking [3] and a good alternative seems to be the so-called Discrete Shear Gap method [4]. Particularly for these models, to be competitive, it is better to improve the behaviour of lower-order finite elements due to its low computational cost when moderately fine meshes are required. To this aim linear 876