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| In our contribution we want to mathematically correct formulate and analyze several optimal control problems for the nonlinear beam which was introduced in 1996 by David Y. Gao. The beam model is given by a static nonlinear fourth-order differential equation with some boundary conditions. The beam is here subjected to a vertical load and possibly to an axial load as well. A cost functional we will construct in such a way that the lower its value is, the better model we obtain. We will study the existence and eventually the uniqueness for the solution of our control problems. Another task is to derive optimality conditions. Next we want to study the finite element approximation of the considered problems as exact solutions are not available. Finally we proceed to a numerical realization of our problems. Some results including numerical examples are offered to illustrate justification of our previous considerations. |
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