On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity

In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist,obtaining displacement expressions by means of the method of reciprocal theorem is actual.But in other conditions,when static force edge conditions or mixed ones exist,the obtained displacements are admissible.In order to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions.Evidently,it is a new method.