Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Abstract

Prismatic fixed-end beams with circular cross-section are often used in engineering. Therefore, there is a need for a solution of an elastoplastic deflection of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam, which is suitable for practical use. The elastoplastic deflection beam theory does not provide a solution in a closed form for such a problem. Hence, a semi-analytical solution is proposed in this paper. Homogenous and isotropic beams with the bilinear elastoplastic strain hardening behaviour are covered in the proposed solution. The elastic deflection of a beam is determined by the Bernoulli–Euler formula. However, differential equation of beam bending in the plastic domain of material behaviour does not have a solution in a closed form. Therefore, an incremental procedure for determining the curvature of the plasticised region of the beam is suggested. The proposed semi-analytical solution is validated by comparing to the finite element analysis results of 16 different fixed-end beam models with varying geometric and material characteristics. Also, validation is done with experimental results of the bar damper device, available in the literature, which has been selected as a sample of a real engineering system where the proposed solution can be applied. A satisfying agreement between the proposed semi-analytical results and the subsequent numerical and experimental results is herein achieved, confirming the solution’s reliability. Finally, a parametric study is conducted using the proposed semi-analytical solution in order to determine the influence of geometrical parameters and material characteristics on the mechanical properties of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam.

Special issue: Advanced mathematical modeling in mechanical engineering

“…Few more articles are dedicated to specific construction engineering problems. 8,9 Zoric and Trajkovic-Milenkovic 8 develop a semi-analytical mathematical model for solving elastoplastic deflection of prismatic fixed-end beams with circular cross-sections loaded by lateral displacement at one end of the beam, suitable for different engineering applications. Homogenous and isotropic beams with bilinear elastoplastic strain hardening behavior are covered in the proposed solution.…”