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In this thesis we analyze the buckling behavior of an infinitely long, thin, uniform, inextensible, elastic plate that has a steady current flowing along its length. We are concerned with the derivation of the nonlinear equations of motion using nonlinear continuum mechanics, and subsequent analysis of the buckling behavior of the plate under electromagnetic self-forces. In particular, we concentrate on how the body-forces that result from the applied current determine the buckled configurations. We derive both analytical and numerical results, and in the process develop a novel boundary value problem solver for integro-differential equations in addition to a predictor-corrector algorithm to continue solutions with respect to the control parameters. We take a relatively complex problem in magneto-solid mechanics and elasticity theory and form a realistic model that sheds light on the bifurcation and buckling behavior resulting from the electromagnetic-field- induced self-forces that are derived in their full, exact form using Biot-Savart Law. / Ph. D.

In this thesis, a hybrid-stress finite element is developed for nonuniform Timoshenko beams. The element stiffness matrix is obtained by assuming a stress field only. Since element boundaries are simply the element nodes, a displacement assumption is not necessary. Geometric and mass stiffness matrices are obtained via equilibrium and kinematics of deformation equations which are derived in the beam arbitrary cross-section. Utilizing this method eliminates the displacement assumption for the geometric and mass stiffness matrices. The element has six degrees of freedom at each node. Axial, flexural and torsional effects are considered. The torsional and distortional warping effects are omitted. Deformations due to shear is also taken into account. Finally, some sample problems are solved with the element and results are compared with the solutions in the literature and commercial finite element programs (i.e. MSC/NASTRAN&reg / ).

The current trend in the design of steel structures leads, due to the saving of the material, to the frequent use of thin-walled cold formed steel sections. Thin cold-formed steel profiles are often manufactured with web holes. A specific example of thin-walled steel profiles are Sigma beams used in additionally installed built-in floors systems in warehouses. The aim of doctoral thesis is the analysis, assessment and experimental verification of the technical solution of thin-walled steel beams with web openings loaded in bending with respect to lateral torsional buckling. The objective is to develop knowledge about the real properties of steel members of considered structural arrangement in order to specify the methods of analysis and design in industrial practice. The theoretical analysis describes the behavior of the beams by means of solving the differential equations of the equilibrium on deformed element of thin walled member under bending. In case of beams with web holes is used the solution in the form of introduction of substitute cross-section properties, which are defined as the weighted average of the properties of full and weakened section. The numerical analysis is focused on the use of commonly available software in order to predict the bending resistance of beams with web opening with respect to lateral torsional buckling. Since the software used in practice solves only the prismatic beams without option to model the web openings, it is in frame of numerical analysis verified the model of beam with reduced thickness of web constantly over the whole beam length in the zone of perforation. The experimental analysis is firstly focusing on the verification of real bending and torsion stiffness of the beams, based on which are being derived the values of basic cross-sectional properties. Subsequently the experimental verification of real bending resistance with respect to the lateral torsional buckling is being performed.