Bending analysis of functionally graded curved beams with different properties in tension and compression

In this study, we obtained analytical solutions for functionally graded curved beams with different properties in tension and compression, in which the moduli of elasticity in tension and compression are assumed as two different exponential functions. First, by determining the unknown neutral layer, we established a simplified mechanical model concerning tension and compression subzone and derived the one-dimensional solution (i.e., the solution in the scope of mechanics of materials). Given that the one-dimensional solution is a relatively simplified one, thus a comprehensive understanding of this problem is still needed. For this purpose, we established the consistency equation expressed in terms of stress function under two-dimensional theory of elasticity. Combining boundary conditions of inner and outer edges with continuity conditions of the neutral layer, we applied power series method for the solution of stress components under pure bending. The variations of radial and circumferential stresses in different cases of bimodular functionally graded parameters are comprehensively analyzed with numerical examples. Results indicate that the position of the neutral layer is generally related to the elastic modulus and the functionally graded coefficients of the materials. Moreover, the maximum tensile or compressive bending stress may not take place at the outer or inner edges of the curved beam but inside the beam, which should be given more attention in the analysis and design of functionally graded curved beams with different properties in tension and compression.