Abstract
A drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic-polynomial higher-order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect effect of thickness variations. As a result of compounding the proposed beam model in linear Lagrangian strains and variational of energy, the system of equations is obtained. The Galerkin method is here expanded for several edge conditions to obtain elastic critical buckling values. First, the importance of the higher-order beam theory, as well as stretching effect, is assessed in assorted tabulated comparisons. Next, with validations based on the existing and open literature, the proposed shape function is evaluated to consider the desired accuracy. Some comparative graphs by means of well-known shape functions are plotted. These comparisons reveal a very good compliance. In the final section of the paper, based on an inappropriate mixture of the SUS304 and Si3C4 as the first type of FGM beam (Beam-I) and, Al and Al2O3 as the second type (Beam-II), the results are pictured while the beam is kept in four states, clamped–clamped (C–C), pinned–pinned (S–S), clamped-pinned (C–S) and in particular cantilever (C–F). We found that the defect impresses markedly an FGM beam with boundary conditions with lower degrees of freedom.
Highlights
Graded materials (FGMs) are those whose mechanical properties change gently and continuously from one surface to another according to a given function
It is worth mentioning to say that the difference between higher‐order shear deformation theory (HSDT) and HPET can be further ascertained by C–C
Ceramic: Silicon Carbide (Si3C4) E1 = 348GPa, ν1 = 0.24 Metal:Stainless Steel-Grade 304 (AISI 304) E2 = 200GPa, ν2 = 0.29 Alumina: (Al2O3) E1 = 380GPa, ν1 = 0.3 Aluminium: (Al) E2 = 70GPa, ν2 = 0.3 In Figs. 5a–d, we examine the role of the incomplete functionally graded materials (FGM) beams in a thick manner and in the two states and patterns mentioned before for two types of FGM beams
Summary
Graded materials (FGMs) are those whose mechanical properties change gently and continuously from one surface to another according to a given function. Beam shear deformation theories have yielded good results in analysis of comparatively thick beams, they are far from accurate answers yet because of the neglect of transverse strains and stretching effects across the thickness. To fix this problem and maximize the accuracy, quasi‐3D elasticity came [8,9,10,11,12]. These theories work well only for isotropic thick materials and cannot be a general quasi‐3d elasticity model appropriate for all materials such as laminated composites This theory complements previous theories and considers both the effects of shear and transverse deformation along the thickness in the form of a higher‐order beam theory
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