The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation

• Published in: Engineering with computers Vol. 38; no. Suppl 4; pp. 3217 - 3235
• Main Authors: Hou, Fengxia, Wu, Shengbin, Moradi, Zohre, Shafiei, Navvab
• Format: Journal Article
• Language: English
• Published: London Springer London 01.10.2022; Springer Nature B.V
• Subjects: Beam theory (structures); Bending; Boundary conditions; Buckling; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer simulation; Computer-Aided Engineering (CAD; Control; Cross-sections; Deflection; Equations of motion; Exact solutions; Functionally gradient materials; Generalized differential quadrature method; Math. Applications in Chemistry; Mathematical and Computational Engineering; Microbeams; Nonlinear equations; Original Article; Perturbation methods; Porosity; Quadratures; Scale effect; Systems Theory; Bending analysis; Non-uniform cross-section; Imperfect functionally graded material; Truncated conical tube; Buckling analysis; Nonlinear analysis
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-021-01456-x

In this paper, the bending and buckling analysis of microbeam with the uniform and non-uniform cylindrical cross-section was examined based on the classical beam theory and the modified couple stress theory to model the micro-structures effects. The nonlinear effect of the Von-Kármán theory is regarded to study the large-deflection effect on the buckling of microtubes. The conservation energy principle is used to derive the nonlinear equation of motion and the boundary conditions. The effect of several applicable cross-sections, including the linear, exponential, and convex function, on the static behavior of cylindrical beam is investigated, which is made by the porosity-dependent axially functionally graded material. The homotopy perturbation technique as a semi-analytical solution, coupled with the generalized differential quadrature method, is employed to obtain the nonlinear results. Eventually, the influence of various parameters such as the porosity, volume fraction index, bending load, nonlinear deflection, length-scale effect on the bending deflection, and buckling of microbeam with both clamped and pinned supported are analyzed in details.