Multiscale Analysis of Functional Gradient Beam under Uniform Load
To consider the material properties of functional gradient beam structure change along the thickness. In this paper, the wavelet multi-scale method is used to solve beam differential equations with initial or boundary conditions. An operational matrix of integration based on the wavelet is established and the procedure for applying the matrix to solve the differential equations is formulated, and gets the stress of the beam when the material properties of gradient beam take arbitrary function. The results show that the proposed way is quite reasonable while comparing to the exact solution.
K. L. Ren et al., "Multiscale Analysis of Functional Gradient Beam under Uniform Load", Advanced Materials Research, Vols. 261-263, pp. 858-862, 2011