An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

Autor:	Krzysztof Magnucki, Ewa Magnucka-Blandzi, Jerzy Lewiński
Rok vydání:	2020
Předmět:	Physics Differential equation Mechanical Engineering Computational Mechanics 02 engineering and technology Function (mathematics) Mechanics Bending Deformation (meteorology) 021001 nanoscience & nanotechnology Potential energy Finite element method Shear (sheet metal) 020303 mechanical engineering & transports 0203 mechanical engineering Solid mechanics Physics::Accelerator Physics 0210 nano-technology
Zdroj:	Acta Mechanica. 231:4381-4395
ISSN:	1619-6937 0001-5970
DOI:	10.1007/s00707-020-02763-y
Popis:	The paper is devoted to simply supported beams under three-point bending. Their mechanical properties symmetrically vary in the depth direction. The individual shear deformation theory for beams of such features is proposed. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear coefficients and deflections of example beams are calculated. The solution is compared with other analytical results obtained with the use of another deformation function. Moreover, the bending problem of these beams is also numerically studied using the finite element method. Results of analytical and numerical studies are presented in Figures and Tables.
Databáze:	OpenAIRE
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