The Application of a Complex 3-Dimensional Elasticity Solution Representation for the Analysis of a Thick Rectangular Plate

Recently a complex representation of the stresses and displacements for the three-dimensional field equations of elasticity was developed such that the complex formulas of Muskhelishvili [1] for plane strain are included as special cases [2], [3], [4]. The solution is given in terms of six arbitrary complex valued functions. The complex variables in the formulation contain parameters, which can be considered as discrete parameter values or parameter functions. In this paper the use of the complex formulation for the case of discrete parameter values is illustrated within the example of a thick rectangular plate, where the boundary conditions on the side faces are chosen to be the vanishing deflection, normal stress and tangential displacements. Assuming these three-dimensional boundary conditions for the evaluation of the according conditions of a two-dimensional Reissner-model gives a set of boundary conditions which was treated by Salerno and Goldberg [9]. The Reissner-results are used for the sake of comparison with the three-dimensional solution.