Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure

• Published in: Composite structures Vol. 252; p. 112593
• Main Authors: Fouaidi, Mustapha, Jamal, Mohammad, Belouaggadia, Naoual
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.11.2020
• Subjects: Asymptotic Numerical Method; Continuation procedure; Functionally Graded Porous beams; Meshless technique; Multiquadric Radial Basis Function; Nonlinear bending analysis; Taylor series expansion; Taylor series expansion; Meshless technique; Asymptotic Numerical Method; Multiquadric Radial Basis Function; Continuation procedure; Functionally Graded Porous beams; Nonlinear bending analysis
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2020.112593

•Nonlinear bending behavior of functionally graded porous beams is investigated.•First-order shear deformation elastic beam theory is used.•The Asymptotic Numerical Method is employed to linearize governing equations.•The globally supported Multiquadric Radial Basis Function method is adopted to built meshless shape functions.•Results are compared with available solutions. In this paper, the nonlinear bending analysis of Functionally Graded Porous (FGP) beams is investigated using an efficient numerical algorithm associating a meshless collocation technique uses the Multiquadric Radial Basis Function (MQRBF) approximation method and a higher-order Taylor series-based continuation procedure. Material properties of the FGP beams are described by adopting a modified power-law function taking into account the effect of porosities. Based on the First Order Shear Deformation Theory (FSDT) of beams with the von-Kármán kinematic hypothesis, the strong form of nonlinear equations is established. For an efficient application of the proposed numerical approach, a quadratic matrix strong form of the problem is presented. The resulting nonlinear equations are solved numerically with the proposed algorithm which leaned on the following three steps: a higher-order Taylor series expansion to transform the quadratic nonlinear equations into a sequence of linear ones, a meshless collocation technique based on MQRBF approximation method to solve numerically the resulting linear equations and a continuation procedure to get the whole solution branch. To demonstrate the robustness of the developed algorithm, convergence and validation studies have been carried out. Furthermore, the effects of power-law index, porosity volume fraction, Young’s modulus ratio, loads and boundary conditions are investigated.