Elasticity solutions for plane anisotropic functionally graded beams

By H. Ding, D. Huang, Wei-qiu Chen. 2007

138 citations recorded by the source corpus.

Abstract This paper considers the plane stress problem of generally anisotropic beams with elastic compliance parameters being arbitrary functions of the thickness coordinate. Firstly, the partial differential equation, which is satisfied by the Airy stress function for the plane problem of anisotropic functionally graded materials and involves the effect of body force, is derived. Secondly, a unified method is developed to obtain the stress function. The analytical expressions of axial force, bending moment, shear force and displacements are then deduced through integration. Thirdly, the stress function is employed to solve problems of anisotropic functionally graded plane beams, with the integral constants completely determined from boundary conditions. A series of elasticity solutions are thus obtained, including the solution for beams under tension and pure bending, the solution for cantilever beams subjected to shear force applied at the free end, the solution for cantilever beams or simply supported beams subjected to uniform load, the solution for fixed–fixed beams subjected to uniform load, and the one for beams subjected to body force, etc. These solutions can be easily degenerated into the elasticity solutions for homogeneous beams. Some of them are absolutely new to literature, and some coincide with the available solutions. It is also found that there are certain errors in several available solutions. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded anisotropic cantilever beam.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2611218b40c37973c2ffee5f8b2af1b6cc7719a9

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Modeling and analysis of functionally graded sandwich beams: a review (2019, background): “[34] is further extended by Huang et al.”
Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations (2008, methodology): “[31] derived a series of analytical solutions for anisotropic FGM beams with various end conditions using an Airy stress function in the generalized polynomial form.”
Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach (2014, background): “Ding et al. (2007) derived an elasticity solution for plane anisotropic FG beams with elastic compliance parameters being arbitrary functions of the thickness coordinate.”
Analysis of FGM Beams by Means of Classical and Advanced Theories (2010, methodology): “[35] generalised Silverman’s method (see Silverman [36]) in order to obtain a stress function for anisotropic functionally graded beams in a general manner.”
Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory (2013, methodology): “[4] derived a series of analytical solutions for anisotropic FGM beams with various end conditions using an Airy stress function in the generalized polynomial form.”