One of the most important steps in the design of thin-walled structures is the evaluation of their stability. During loading, especially under compressive stress, the structure can suddenly shift from a stable state, which can lead to its collapse. In engineering practice, the analyses are performed either with analytical formulas defined by standards or with numerically, e.g. using the finite element method if the composition is more complex. In most cases, it is assumed that the material is linearly elastic. In such a case, the analysis is performed using Hooke’s law, which uses a constant stiffness, expressed by a modulus of elasticity, to describe the material. Nowadays, polymeric materials are often used instead of metals, for which the assumption of linear elasticity does not apply. The stiffness of such materials can either decrease or increase during deformation. The aim of this thesis is to develop a computer program to numerically evaluate the stability of a nonlinear elastic beam using the finite element method. Due to the need to cope with large deformations, a corotational formulation of the finite elements was chosen. The deformation behavior of the beam was determined based on the Bernoulli beam theory. Iterative calculations were carried out using the arc length method and generalized Ludwick's law was used for the material law, which describes the nonlinear behavior of the material.
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