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THIS PAPER IS DEVOTED TO AN ASYMMETRICAL SANDWICH BEAM with a functionally graded core with three different variants of boundary conditions. An analytical model of this beam, considering individual nonlinear shear deformation theory, is developed. Based on Hamilton's principle, two differential equations of motion for this beam are obtained. These equations are solved analytically, and as a consequence, the critical forces and basic natural frequencies for each beam support variant are determined. Detailed calculations are carried out for selected exemplary beam structures, and their results are compared with numerical FEM analysis. [ABSTRACT FROM AUTHOR]

Free flexural vibration of a simply supported sandwich beam on an elastic foundation is the main purpose of the presented investigation. An analytical model of multi-layered beam on elastic foundation has been prepared. The authors submitted an original beam-foundation interaction model which based on variable parameters of the foundation and their influence on the beam response. This explanation leads to the possibility of continuous characterization of the beam-foundation interplay. A nonlinear mathematical function for symmetrical properties of the foundation has been adopted. The frequency equation as a function of geometric and mechanical properties of the beam and the parameters of the elastic foundation was derived using the Galerkin method. The analytical investigation has been divided into two parts: the analysis of elastic foundation with constant and variable properties. The unconventional shape function and the function of deflection have been introduced and employed. Moreover, the finite element analysis has been performed. Sample analytical and numerical calculations have been performed, demonstrating a good concurrence between both models. The difference between analytical and numerical values of the fundamental natural frequency did not exceed 0:5%. [ABSTRACT FROM AUTHOR]

The subject of the numerical investigation is an ellipsoidal head with a central (axis-symmetrical) nozzle. The nozzle is loaded by axial load force. The ellipsoidal head is under axial-symmetrical compression load. The numerical FEM model is elaborated. The calculation will provide the critical loads and equilibrium paths for the sample head.. The investigation will measure the influence of the diameter of the nozzle on the critical state of the ellipsoidal head.

The subject of the paper is cold-formed thin-walled channel beams with open or closed profile of drop flanges. The geometric properties of two C-sections are described including warping functions and warping inertia moments. The analytical solutions of problems of global and local stability of thin-walled beams are presented. The theoretical solutions of elastic buckling problems of these beams are numerically found using FEM and are experimentally verified. The results of analytical and numerical investigations are compared and presented in the tables and figures. DOI: 10.1061/(ASCE)ST.1943-541X.0000184 CE Database subject headings: Beams; Buckling; Flanges; Finite element method. Author keywords: Thin-walled beam; Global and local buckling; Drop flanges; Channel beams.