Free-vibration and buckling analyses of beams using Kriging-based Timoshenko beam elements with the discrete shear gap technique

Wibowo, Mariana and Octavia, Jeanny and Joanna, Vanessa (2024) Free-vibration and buckling analyses of beams using Kriging-based Timoshenko beam elements with the discrete shear gap technique. [UNSPECIFIED]

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Abstract

A family of locking-free Kriging-based Timoshenko beam elements with a new implementation of the discrete shear gap technique was recently developed (referred to as K-beam-DSG1 elements). Performance of the K-beam-DSG1 elements has been shown to be very satisfactory in the linear static analysis of beams for a wide variety of thicknesses. This paper presents further development of the K-beam-DSG1 elements to free vibration and bifurcation buckling analyses of prismatic and non-prismatic beams. Consistent Kriging-based mass matrices are used for free vibration analysis and similarly, consistent Kriging-based geometric stiffness matrices are used for buckling analysis. The results show that for most of the cases, the K-beam-DGS1 elements yield remarkably accurate natural frequencies and critical compressive loads using a reasonable number of elements to discretize the beam. For an axially functionally graded fixed-fixed supported beam, however, the elements fail to predict the critical load accurately.

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