Equilibrium solution of two – dimensional non-homogeneous equations in the theory of elastic mixtures

Abstract

The problem of plane elasticity for a doubly connected body with inner and outer boundaries in a regular polygonal form with a common centre and parallel sides has been studied. The sides of the polygon were exposed to external forces. The nature of the force term was determined by application of complex variable theory. Kolosov’s method of solution was applied to obtain the biharmonic equation of the forcing term. The forces on the particle were studied under 2-dimensions from which the compatibility and equilibrium equations were derived. The compatibility and equilibrium equations were used to derive the force–stress relations. The results shows that there is a significant relationship between the angle of the force term on the plane of the particle and the stress state of the particle, which conforms with existing experimental results.