- #1
bugatti79
- 794
- 1
Folks,
The total potential energy functional for an isolated finite element timoshenko beam is given as
## \displaystyle \Pi_e(w, \Psi)=\int_{x_e}^{x_{e+1}} \left[ \frac{EI}{2} \left (\frac{d \Psi}{dx}\right )^2 + \frac{ G A K_s}{2} \left ( \frac {dw}{dx} + \Psi \right )^2 +...\right]dx +...##
Where the first term in the integral is the bending energy of the element. The author states that a constant state of ##\Psi(x)## is not admissible because the bending energy of the element would be zero leading to the numerical problem of shear locking.
Not sure I understand this concept. It is just a term that will go to 0 on the first derivative but the rest of the integral can still be evaluated. Why is it not admissible?
The total potential energy functional for an isolated finite element timoshenko beam is given as
## \displaystyle \Pi_e(w, \Psi)=\int_{x_e}^{x_{e+1}} \left[ \frac{EI}{2} \left (\frac{d \Psi}{dx}\right )^2 + \frac{ G A K_s}{2} \left ( \frac {dw}{dx} + \Psi \right )^2 +...\right]dx +...##
Where the first term in the integral is the bending energy of the element. The author states that a constant state of ##\Psi(x)## is not admissible because the bending energy of the element would be zero leading to the numerical problem of shear locking.
Not sure I understand this concept. It is just a term that will go to 0 on the first derivative but the rest of the integral can still be evaluated. Why is it not admissible?