Limit Analysis and Inf-Sup Conditions on Convex Cones S. Sysala, J. Haslinger and S. Repin XV International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS 2019 E. O˜ nate, D.R.J. Owen, D. Peric, M. Chiumenti & Eduardo de Souza Neto (Eds) LIMIT ANALYSIS AND INF-SUP CONDITIONS ON CONVEX CONES STANISLAV SYSALA * , JAROSLAV HASLINGER * , SERGEY REPIN †,‡ * Institute of Geonics of the Czech Academy of Sciences, (IGN) Department of Applied Mathematics and Computer Sciences & Department IT4Innovations, Studentska 1768, 708 00 Ostrava, Czech Republic e-mails: stanislav.sysala@ugn.cas.cz, hasling@karlin.mff.cuni.cz, web page: http://www.ugn.cas.cz † St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27 Fontanka, 191023 St.Petersburg, Russia e-mail: repin@pdmi.ras.ru - web page: http://www.pdmi.ras.ru ‡ University of Jyv¨askyl¨ a, Mattilanniemi 2, 40100 Jyv¨askyl¨ a, Finland e-mail: sergey.s.repin@jyu.fi - web page: https://www.jyu.fi Key words: perfect plasticity, limit analysis, conic optimization, inf-sup condition, finite element method, mesh adaptivity Abstract. This paper is focused on analysis and reliable computations of limit loads in perfect plasticity. We recapitulate our recent results arising from a continuous setting of the so-called limit analysis problem. This problem is interpreted as a convex opti- mization subject to conic constraints. A related inf-sup condition on a convex cone is introduced and its importance for theoretical and numerical purposes is explained. Fur- ther, we introduce a penalization method for solving the kinematic limit analysis problem. The penalized problem may be solved by standard finite elements due to available con- vergence analysis using a simple local mesh adaptivity. This solution concept improves the simplest incremental method of limit analysis based on a load parametrization of an elastic-perfectly plastic problem. 1 INTRODUCTION Stability of a structure is analyzed in many engineering areas. From this analysis, one can get various safety parameters that depend on the applied loads. One can also estimate failure zones describing collapse of the structure. Limit analysis is one of the main methods in stability assessment and is based on a parametrization of the load by a scalar factor. The related safety parameter is defined as a limit (ultimate) value of this factor. Beyond this value, the structure collapses. The limit load factor can be 133