Analysis of continuum by the integrated force method

The novel formulation termed the integrated force method (IFM) has been established for finite element discrete analysis. In this paper we have extended the IFM for the analysis of continuum taking circular plate as the example. The primary variables of the analysis are moments. All the continuum equations (equilibrium equations and compatibility conditions) in the field and on the boundary are obtained in moments from the stationary condition of the variational functional of the IFM. A new stress function required for the functional is defined. The variational functional yields the known equations along with the novel boundary condition identified as the boundary compatibility condition. The moment solution for the plate problem is obtained without any recourse to displacements either in the field or on the boundary. From moments, displacements are obtained by integration and boundary displacement continuity conditions. The IFM solution and boundary compatibility conditions are verified using Timoshenko's work and finite element displacement method.