Question

Considering the problem of (linear) bending of beams according to the Euler-Bernoulli beam theory, if the beam is in equilibrium, then solving the equations governing the equilibrium of the Euler-Bernoulli beam is equivalent to minimizing the total potential energy.

(a) True

(b) False

This question was posed to me in class test.

I need to ask this question from Governing Equations topic in section Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Correct option is (a) True

Explanation: Consider the problem of (linear) bending of beams according to the Euler-Bernoulli beam theory. The principle of minimum total potential energy states that if the beam is in equilibrium, then the total potential energy associated with the equilibrium configuration is the minimum; i.e., the equilibrium displacements make the total potential energy a minimum. Thus, solving the equations governing the equilibrium of the Euler-Bernoulli beam is equivalent to minimizing the total potential energy.