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 planeproblems 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 fouredges built-in as the basic system and then find displacement expressions of the actualsystem by using the reciprocal theorem between the basic system and actual system withvarious edge conditions.When only displacement edge conditions exist,obtaining displacement expressions bymeans of the method of reciprocal theorem is actual.But in other conditions,when staticforce edge conditions or mixed ones exist,the obtained displacements are admissible.Inorder to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient andgeneral one for the solution of plane problems of elasticity of the rectangular plates withvarious edge conditions.Evidently,it is a new method.