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Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finite element method

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Abstract

The contribution provided in this paper is to investigate the dynamic and buckling response of bidirectional graded material beams (BDFB) with transverse cracks, considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence is integrated for accurate results. The material properties of the beam are supposed to be dependent on the gradation pattern through the width and thickness directions via power-law form. Lagrange’s principle is employed in order to extract the governing equations of motion. The stiffness of the cracked beam element is computed based on the shrinking of the beam’s cross section. The Differential quadrature finite elements method is used as an effective and accurate tool to determine the buckling loads and natural frequencies of the BDFG beam. The numerical results are evaluated with those from earlier studies. Finally, several studies examples were done to examine the impact of the power-law gradation index, crack depth, and position for various boundary conditions on the critical buckling of the beam and natural frequencies. These investigations highlight the advantages of the bidirectional FG beam over the unidirectional FG and pure metallic beams under the presence of a crack.

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  1. IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid (UABT), Tlemcen, Algeria

    Ahmed Saimi, Ismail Bensaid & Ahmed Fellah

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  1. Ahmed Saimi
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Saimi, A., Bensaid, I. & Fellah, A. Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finite element method. Arch Appl Mech 93, 3131–3151 (2023). https://doi.org/10.1007/s00419-023-02429-w

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