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2 Journal of Theoretical and Applied Mechanics

2 2024

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Elastic buckling of a rectangular sandwich plate with an individual functionally graded core

Magnucki Krzysztof, Magnucka-Blandzi Ewa, Sowiński Krzysztof

Journal of Theoretical and Applied Mechanics

2024

Vol. 62 nr 1

171--185

This paper is devoted to a thin-walled sandwich plate with an individual functionally graded core. The nonlinear shear deformation theory of a straight normal line is applied. A system of three differential equations of equilibrium of this plate is obtained, based on the principle of stationary potential energy, which is reduced to two differential equations and solved analytically. The critical load of the rectangular sandwich plate is determined. A detailed analytical study is carried out for selected exemplary plates. Moreover, a numerical FEM model of this plate is developed. The results of these calculations are compared with each other.

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.