created finite diff ipynb

README.md

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+# Numerically integrate Euler-Bernoulli equation
+$EI\frac{d^4w}{dx^4}=0$
+
+Boundary Conditions:
+
+1. $w(0)=0$ 
+
+2. $w'(0)=0$
+
+3. $w''(L)=0$
+
+4. $EIw'''(L) = -F$
+
+Using constants
+- L=400 mm
+- E=200e3 MPa
+- t=3 mm
+- w=12 mm
+
+**Demonstrate qualitative convergence between 4, 24, and 44 nodes. The beam
+shape looks similar between each solution**
+
+**Demonstrate quantitative convergence of tip displacement under given load.**
+
+The relative error is calculated based upon finite-difference calculations
+
+$e_{rel}=\frac{\delta_{new}-\delta_{old}}{\delta_{new}}$
+
+The absolute error is compared to the analytical solution of $EIw''''=0$ for a
+cantilever beam
+
+$\delta_{an}=\frac{FL^3}{3EI}$
+
+$e_{abs}=\frac{\delta_{new}-\delta_{an}}{\delta_{an}}$