In this doctoral thesis we focused on wrinkling of thin shells on elastic substrates. Wrinkling belongs among the highly non-linear stability problems and as a result, such systems are very hard to solve. Not many researchers work in the field of wrinkling, therefore this field has still very high research potential. We approached the problem with finite element method. The kinematic behavior of the shell was assumed to be according to the Kirchhoff-Love shell theory. This theory is only accurate when the shells are very thin. We developed all shell finite elements on our own. The theory of other finite elements was taken from the appropriate literature. The computer codes of finite elements were implemented with the help of Mathematica program and its add-on AceGen and AceFem. We developed several different shell finite elements which differ one to another by the type of interpolations, number of degrees of freedom and material models. Elastic substrates were initially modeled with Winkler's foundation and later with 3D finite elements. Results of several different numerical simulations were at the end compared to the measurements. The goal was to check which simulation model is the most appropriate for modeling of the wrinkling phenomena.
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