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Foek Tjong Wong
Petra Christian University
Civil Engineering, Building, Construction & Architecture

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Free-Vibration and Buckling Analyses of Beams using Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique Foek Tjong Wong; Nelvin Tanoyo; Tonny C. Gosaria
Civil Engineering Dimension Vol. 26 No. 1 (2024): MARCH 2024
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/ced.26.1.21-31

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.
Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements Foek Tjong Wong; Henokh G. Tjahyono; Sugiyono Hartono; Timothy A. Setiabudi
Civil Engineering Dimension Vol. 27 No. 1 (2025): MARCH 2025
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/ced.27.1.22-32

Abstract

This paper presents an approach for constructing field-consistent Timoshenko beam elements using least-squares smoothed (LSS) shape functions. The variational basis for shear strain redistribution is thoroughly explained, leading to the derivation of LSS shape functions for linear, quadratic, and cubic Timoshenko beam elements. These elements are then applied to linear static analysis, bifurcation buckling analysis, and free vibration analysis of prismatic and tapered beams. Numerical tests demonstrate that the LSS-based beam elements effectively eliminate shear locking and provide accurate, reliable results. Their performance is comparable to the discrete shear gap technique but with a simpler implementation procedure. The LSS shape function approach offers a practical and efficient alternative for achieving field consistency in Timoshenko beam elements, with potential applications in enhanced finite element methods (FEMs) such as isogeometric FEM and Kriging-based FEM.
Co-Authors Henokh G. Tjahyono Nelvin Tanoyo Sugiyono Hartono Timothy A. Setiabudi Tonny C. Gosaria