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

Abstract

There are many beam models to simulate the variable thickness functionally graded material (FGM) beam, each model has advantages and disadvantages in computer aided engineering of the mechanical behavior of this beam. In this work, a new model of beam is presented to study the mechanical static bending, free vibration, and buckling behavior of the variable thickness functionally graded material beams. The formulations are based on modified first order shear deformation theory and interpolating polynomials. This new beam model is free of shear-locking for both thick and thin beams, is easy to apply in computation, and has efficiency in simulating the variable thickness beams. The effects of some parameters, such as the power-law material index, degree of non-uniformity index, and the length-to-height ratio, on the mechanical behavior of the variable thickness FGM beam are considered.

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

“…at is the reason why numerous researchers focus on investigating the dynamic as well as static behaviors of the FGM structures, for example, beams [5][6][7][8][9][10], plates [11][12][13][14][15][16][17][18], shells [19][20][21], and other structures [22,23]. Many plate theories have been established and/or applied to investigate these structures, for example, classical plate theory (CPT), first-order shear deformation (FSDT), higherorder shear deformation theory (HSDT), and quasi-3D shear deformation theory.…”

A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler–Pasternak Foundations

“…In this study, the elastic foundation is modelled by the Winkler-Pasternak type that consists of two components which are a Winkler foundation with the stiffness of k w and a shear layer with the stiffness of k s . e material properties of the plates are assumed to vary continuously through the thickness of the plates as powerlaw functions [3,4].…”

“…In such type of material, the material properties vary continuously through the thickness of the structures. Because of their exotic properties, FGMs are widely applied in many fields of engineering and industry [1][2][3][4][5][6], for example, aeronautics, nuclear engineering, advanced civil engineering, and so on. More details of the application and investigation of FGMs can be read from a state-of-the-art review by Swaminathan et al [7].…”

Size-Dependent Free Vibration and Buckling of Three-Dimensional Graphene Foam Microshells Based on Modified Couple Stress Theory

“…If disregarding inertia terms and assuming Nxx0=−P, Equation (58) is reduced to the equilibrium equations of a static buckling problem of the 3D-GrF microshell:(boldK−P⋅Kg)⋅boldd={000} where P represents buckling load. Therefore, the critical (minimum) buckling load P cr and vibration frequencies of the 3D-GrF microshell are obtained by solving the above eigenvalue problems [55,56,57].…”