Semi-Analytical Solution for Elastoplastic Deflection of Non-Prismatic Cantilever Beams with Circular Cross-Section

Abstract

A solution for the elastoplastic deflection of cantilever beams with linearly variable circular cross-section loaded by shear force at the free end, which is suitable for practical use, has not yet been developed. A semi-analytical solution for such a problem is proposed in this paper. The solution involves beams made of homogenous and isotropic materials with bilinear elastoplastic strain hardening behavior. The Bernoulli–Euler formula is used for determining the elastic deflection. However, for the plastic domain of material behavior, the differential equation of beam bending does not have a solution in closed form. Therefore, an incremental procedure for determining the curvature of the plastified region of the beam is suggested. Deflection of the cantilever beam is calculated via integration of the approximated function of the beam curvature. The proposed semi-analytical solution is validated using experimental results of the seismic energy dissipation device components which have been selected as a sample of a real engineering system. Also, validation is done via finite element analysis of six different cantilever beam models with varying geometric and material characteristics. A satisfying agreement between the proposed semi-analytical results and the subsequent experimental and numerical results is herein achieved, confirming its reliability.

High-Order Fiber Bragg Grating Corrosion Sensor Based on the Detection of a Local Surface Expansion

“…Tis evolution of strain caused by vertical displacement of in two-point clamped circular beam represents a reasonable approximation of the conditions encountered in the proposed sensor. Furthermore, longitudinal strain evolution in two-point clamped cross-section beams was also well researched, modeled and verifed by numerous simulations in the past [59][60][61][62][63][64]. Simulations carried out within this investigation showed dependency of the geometry of the clamps, i.e., diferent shapes (angles and height) and clamping materials can signifcantly afect the longitudinal strain distributions.…”

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.…”

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

“…By substituting equation (7) into equation (6), the bending moment of the plasticised cross-section for the incremental analysis of deflection of the prismatic fixed-end beam can be defined as follows 19 :…”

“…By separating the integral into the elastic and plastic part of the cross-section, and by taking into account the hypothesis that plane sections remain plane, the bending moment of the plasticised cross-section can be calculated as 19 :…”