The Problem of Additional Load of Minimum Work in a Thin Plate

Abstract. A rectangular plate is simply supported along its boundary. A flexural couple is exerted on one of its sides, while the others remain unloaded. The question is posed, assuming the ability to produce couples along the side opposite the already loaded one, of determining the values of these latter couples, which would minimize the elastic strain energy of the system. The solution is obtained in explicit form by representing the transverse displacement in the form of a Fourier series and directly calculating the minimum of the strain energy.