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3 2024

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Bending of a sandwich beam with an individual functionally graded core

Magnucki Krzysztof, Sowiński Krzysztof

Journal of Theoretical and Applied Mechanics

2024

Vol. 62 nr 1

3--17

This paper is devoted to a clamped sandwich beam with an individual functionally graded core under a uniformly distributed load. A non-linear shear deformation theory is developed with consideration of the classical shear stress formula for beams. Two differential equations of the equilibrium of the beam are obtained based on the principle of stationary total potential energy. The shear effect function and the relative deflection line of the beam are determined. Moreover, a numerical FEM model (Ansys system) of this beam is elaborated. Detailed calculations of exemplary beams are realised using two methods, analytical and numerical FEM.

Bending of a homogeneous beam with a monosymmetric cross section – shear effect

Magnucki Krzysztof, Magnucka-Blandzi Ewa, Witkowski Dawid, Stefańska Natalia

Engineering Transactions

2024

Vol. 72, iss. 3

285--307

This paper is devoted to the study of a homogeneous clamped beam with a monosymmetric cross section under uniformly distributed load or three-point bending. A nonlinear shear deformation theory of a plane beam cross section based on the classical shear stress formula known as the Zhuravsky shear stress is developed. The values of shear coefficients and maximum deflections of exemplary beams are analytically determined. Moreover, numerical FEM computations for these beams are carried out. The results of the research from both methods are shown in figures, specified in tables, and compared. The percentage relative differences between the analytical and numerical results prove that the proposed original shear deformation theory accurately describes the shear deformation problem of a beam’s planar crosssection.

Bending of a five-layered composite beam with consideration of two analytical models

Magnucki Krzysztof

Archive of Mechanical Engineering

2024

LXXI, nr 1

27--46

The subject of the work is a five-layered composite beam with clamped ends subjected to a uniformly distributed load along its length. Two analytical models of this beam are developed with consideration of the shear effect. The first model is formulated on the basis of the classical zig-zag theory. Whereas, the second model is developed using an individual nonlinear shear deformation theory with consideration of the classical shear stress formula (called Zhuravsky shear stress). The system of two differential equations of equilibrium for each beam model is obtained based on the principle of stationary total potential energy. These systems of equations are exactly analytically solved. The shear effect function and the maximum deflection are determined for each of these two beam models. Detailed calculations are carried out for exemplary beams of selected dimensionless sizes and material constants. The main goal of the research is to develop two analytical models of this beam, determine the shear effect function, the shear coefficient, and the maximum deflection in the elastic range for each model, as well as to perform a comparative analysis.