Variational methods for constructing approximate solutions to some problems of continuum mechanics

In order to find approximate solutions to continuum mechanics problems admitting a variational statement we use an approach that is based on restricting the class of functions in which we seek the extremum of the action. We demonstrate the method on some examples of the forced oscillations problem for a nonlinear elastic membrane (a string in particular), the problem of fluid flow through a porous obstacle, and the problem of stationary waves on the surface of a heavy fluid.