Answer Happy

Problem 2. A thin rectangular plate consists of an inhomogeneous material in which Young's modulus E as function of position is given by E = Ee where Eo and B are known constants and Poisson's ratio v is constant. A given displacement vo in the x2 direction is applied to the upper and lower edges. (i) What are the boundary conditions on edges AB and BC? (ii) Find the stress, strain and displacement state in the plate. (Hint: Solve the problem by starting with a reasonable displacement field guess -e.g. u, linear with x₁). (iii) If the material fails according to a Tresca condition what is the maximum allowable vo before failure occurs? How would this value change if plane strain was applicable? 2b A D A 2a 4 B C V V 0 0 E1 E Eo a E2