Nonlinear finite elements/Homework 6/Solutions/Problem 1/Part 4

Problem 1: Part 4 edit

Why is the Euler-Bernoulli beam theory  ? Why is the Timoshenko beam theory  ?

In the Euler-Bernoulli theory, the rate of deformation in the   direction is given by


Since second-derivatives of   are involved, any approximate solution needs to be at least twice differentiable (or  ) to be acceptable. This is why this theory is called  .

On the other hand, in the Timoshenko theory, only first derivatives of the primary dependent variables appear. Therefore, once differentiable (or  ) shape functions are acceptable and the theory is called  .