Shearing of a functionally graded block

Abstract

Mechanics of Solid and Materials study the propagation of shearing in materials. Under the analysis of linear elastic materials, both the stress and displacement fields along the depth direction will be of concern. Analysing the different shapes of a block, we identify how the stress and displacement fields varies upon simple shearing. In addition to that, noticing the trend of the stress and displacement field along the shearing area could be important as well. The motivation of this fyp report is to determine the displacement and stress fields within a functionally graded block subjected to simple shearing. Due to the governing equations having non-linear and linear equation, it can be complicated to solve thus a computational software, Wolfram Mathematica, will be used to produce graph to help in this analysis. This fyp report explores the displacement and stress field of different sizes of a functionally graded block of dimension, Lx, Ly and Lz under generalised shearing of a fix prescribed linear displacement, u1 (Ly). The result from the graph simulations will be shown in this report