import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
matplotlib.RcParams._get = dict.get
Evaluate strain energy using SymPy#
import sympy as sym
L, x, q, GA_C, EI = sym.symbols('L, x, q, GA_C, EI')
M = -q * (L-x)**2 / 2
E_c_M = sym.integrate(M**2/EI/2,(x,0,L))
display(E_c_M)
\[\displaystyle \frac{L^{5} q^{2}}{40 EI}\]
V = (L-x)*q
E_c_V = sym.integrate(V**2/GA_C/2,(x,0,L))
display(E_c_V)
\[\displaystyle \frac{L^{3} q^{2}}{6 GA_{C}}\]