The classical theories for thin-walled beams (Timoshenko, Vlasov) are based on the assumption that the beam’s cross section remains unchanged. Using that assumption, the displacement and stress analysis for bending and torsion of the beams are relatively simple. But, for thin-walled beams, and beams made of orthotropic materials, the cross-section distortion could be significant and it could influence stress distribution and its value. The influence of the distortion of the cross sections at the bending and torsion of the beams is of particular interest. The warping of the cross sections due to shear for the bending of isotropic beams is relatively well investigated. The warping is studied to determine its influence on the displacements more than on the stresses. At torsion, the warping of thin-walled cross section is included in the Vlasov’s theory of torsion; the warping due to shear is subject of the novel investigations. The studying of the thin-walled beams at the complex loading conditions, particularly made of the orthotropic materials, is subject of the most recent investigations, also. Within research activities related to the thin-walled beams, a special attention is devoted to the analysis of thin-walled curved beams. In addition to the coupling effects between displacements and internal forces components, the influence of the shear in the analysis of the short thin-walled curved beams with bi-symmetrical open cross-sections loaded with in and out-of-plane loads will be investigated also.

In the field of mathematical theory of plasticity, it is planned to continue research related to: development of constitutive models by which the plastic anisotropy evolution with on-going deformation process can be described (implementation of complex orthotropic stress functions and algorithmic consistent tangent module, consideration of plastic flow stability conditions),  application of alternative procedures in model calibration and application of developed models in prediction and optimization of various sheet metal forming processes (especially crimping process). Furthermore, research related to the characterization and modelling of elastic and plastic anisotropy of metal samples made by additive manufacturing will be conducted.