DO Question 7 (20 marks) The static deflection of a membrane can be described by the Poisson equation as follows: (av av + where T is the tension applied to the membrane and f(x,y) is the vertical load on the membrane. T * 2 * ) = f(x,y) = 2 ?) (i) Calculate the deflection v(x,y) of a fully fixed (v = 0 on the boundaries) membrane of dimensions 10+D m (x direction) x 5m (y direction) loaded by a uniform tension T = 20000 + 1000H N and subjected to the uniform load f(x,y) = 10000 N. Use a finite-difference method with 6 interior points. (10 marks) Show your workings (please attach below a scan of your hand-calculations showing the setting up of the problem): Copy and paste your MATLAB code below: (5 marks) (ii) Create the surface (MATLAB function surf) plot of v(x,y) and paste it below: (5 marks) ModuleCode_SEM1_2021/2022 Page 9 of 9