A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Abstract

A new fifth-order shear and normal deformation theory (FOSNDT) is developed for the static bending and elastic buckling analysis of functionally graded beams. The properties of functionally graded material are assumed to vary through the thickness direction according to power-law distribution (P-FGM). The most important feature of the present theory is that it includes the effects of transverse shear and normal deformations. Axial and transverse displacements involve polynomial shape functions to include the effects of transverse shear and normal deformations. A polynomial shape function expanded up to fifth-order in terms of the thickness coordinate is used to account for the effects of transverse shear and normal deformations. The kinematics of the present theory is based on six independent field variables. The theory satisfies the traction free boundary conditions at top and bottom surfaces of the beam without using problem dependent shear correction factor. The closed-form solutions of simply supported FG beams are obtained using Navier's solution procedure and non-dimensional results are compared with those obtained by using classical beam theory, first order shear deformation theory and other higher order shear deformation theories. It is concluded that the present theory is accurate and efficient in predicting the bending and buckling responses of functionally graded beams.

Analysis of functionally graded plates resting on elastic foundation and subjected to non-linear hygro-thermo-mechanical loading

“…The displacement field shown in Eq. 3is employed by the authors in their earlier published articles for the analysis of FG beams and plates under mechanical load [22,23]. One can also refer the articles by Naik and Sayyad [24][25][26] has addressed the bending analysis of laminated beams and plates using the same displacement field.…”

“…A good number of research papers are available in the literature on the bending analysis of simply supported FG plates subjected to mechanical loads [9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, Ghumare and Sayyad [22,23] and Naik and Sayyad [24][25][26] have developed a new fifth-order shear and normal deformation theory for the analysis of functionally graded and laminated composite beams and plates. The stability analysis of FG plates subjected to linear and non-linear thermal loadings using various refined theories also reported by many researchers [27][28][29][30][31][32][33][34][35][36][37][38].…”

A conjugate modal force strategy for instability analysis of thin-walled structures: an unconstrained vector positional finite element approach

“…Some interesting works using classical Finite Element Method (FEM) and solving stability problems may be cited (Mororo et al, 2015;Pastor and Roure, 2009;Ren et al, 2006). Among them, applications related to the stability of thin-walled structures are present, for example, in Anbarasu and Sukumar (2014), Ghumare and Sayyad (2017) and Soares et al (2019). These works verify the presence of limit points and bifurcations along the equilibrium path.…”

A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory

“…Based on different higher-order beam theories, Simsek [18] analyzed the fundamental frequency of FGM beams. Ghumare et al [19] developed a new fifth-order shear and normal deformation theory to analyze static bending and elastic buckling of P-FGM beams. Li et al [20] used higher-order theory for static and dynamic analyses of functionally graded beams.…”