Write A Matlab Code Which Is Able To Implement The Numerical Differentation Method By Using Forward Divided Difference 1 (98.33 KiB) Viewed 27 times
Write a Matlab code which is able to implement the "Numerical Differentation Method by using Forward Divided Difference" for data set for any problem. Test your code for an engineering problem below. "Submit a file which includes your code by using "Numerical Differentation Method by using Forward Divided Difference" A rectangular plate under a uniform stress, G. To find the stresses and the stress concentration factor, one needs to find the derivatives of these displacements. In Table 1, the radial displacements u are given along the y-axis. The radius of the hole is 1.0 cm. AH Be X a Figure 2. Rectangular plate with circular hole of radius a under uniform stress. To find the stress concentration around a hole in a plate under a uniform stress, Please, write a code in MATLAB by using Forward Divided Difference program in order to calculate the radial and tangential displacements at different points in the plate. Also, calculate the following items in the same code in MATLAB; du a) At x = 0, if the radial strain &, is given by &, = -, find the radial strain at r = 1.1 cm using the forward divided difference method. b) If the tangential strain at r=1.1cm, 0 = 90° is given to you as &q=0.0029733, find the E hoop stress, ,, at r=1.1cm, 0 = 90° if σ₂ = -(&, + v), where 1-v² E = 200GPa and v=0.3. Jo
Table 1. Radial displacement as a function of location. r (cm) u (cm) 1.0 -0.0010000 1.1 -0.0010689 1.2 -0.0011088 1.3 -0.0011326 1.4 -0.0011474 1.5 -0.0011574 1.6 -0.0011650 1.7 -0.0011718 1.8 -0.0011785 1.9 -0.0011857 Hint: If the plate now has changed in the cross-section, the normal stresses will increase as a result of these changes. To find the derivatives of functions that are given at discrete points, several methods are available like Forward Difference Forward Difference Approximation of the First Derivative f(x) 1 X x + Ax X Figure 2. Graphical representation of forward difference approximation of first derivative.
So given n+1 data points (x, y). (x₁,₁). (x₂,₂)(x,y), the value of f'(x) for x₁ ≤x≤ x₁, i = 0,.....n-1, is given by f'(x) = S(x₁+₁)-1(x₂) Xil-Xi
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