Displacement Potential Approach for the Solution of 3-D Body of Orthotropic Composite Materials

Abstract

In this paper, a displacement potential formulation of 3-D orthotropic composite material is derived following the philosophy of theory of elasticity. All stress and displacement components are expressed in terms of a single function, y. In this approach, if the displacement components are substituted in equilibrium equations, among them two equilibrium equations are satisfied, the other one transforms into the governing equation in terms of a single function, y . The stress components are expressed in terms of a single function, y substituting displacement components into stress displacement relationships of 3-D body of orthotropic composite materials. The present displacement potential approach can be used for any mixed boundary value problem when the existing approach is hardly applicable in mixed boundary value problems. Using the present formulations, one can obtain the elastic field of 3-D body of isotropic and anisotropic materials. Application of the present approach using Finite difference technique is shown and it is observed that the computational work reduced by the present approach is nearly 96%.