Abstract
Static analysis of Functionally Graded (FG) beams is studied by the Complementary Functions Method (CFM). The material properties, Young’s modulus, of the straight beams, are graded in the thickness direction based on a power law distribution while the Poisson’s ratio is supposed to be constant. Governing equations of the considered problem are obtained with the aid of minimum total potential energy principle based on Timoshenko’s beam theory (FSDT). The main purpose of this paper is the infusion of the CFM to the static analysis of FG straight beams. The effectiveness and accuracy of the proposed method are confirmed by comparing its numerical results with those available in the literature. Application of this efficient method provides accurate results of static response for FGM beams with different variations of material properties in the thickness of the beam.
Highlights
FGM beams are extensively applied in many practical applications of engineering
Solutions are obtained for several loading cases. They assumed the variation of the material properties in the thickness direction of the beam. [3] carried out the finite element (FE) for static equilibrium equations of Functionally Graded (FG) beams
The main aim of this study is to suggest an accurate and effective numerical approach for the bending analysis of FG straight beams
Summary
FGM beams are extensively applied in many practical applications of engineering. straight beams made by using FG materials are mainly used in the construction of modern engineering structures. A shear deformable finite element (FE) was developed by [1] for static and dynamic analysis of beams with FGM layers [4] presented a unified approach to study the static and dynamic analysis of FG beams by including the effects of shear deformation. [6] derived the governing equation for static and dynamic responses of FG beams by considering the influence of shear deformation. Several deformation theories for static and dynamic response of FG beams were presented by [8] They examined the effects of the material gradient index on the bending behavior of the considered structures. The equations which govern the static response of the considered structure are obtained with the aid of minimum total potential energy based on the Timoshenko’s beam theory.
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