COMPLETED BELTRAMI-MICHELL FORMULATION FOR ANALYZING MIXED BOUNDARY-VALUE-PROBLEMS IN ELASTICITY

In elasticity, the method of forces, wherein stress parameters are con sidered as the primary unknowns, is known as the Beltrami-Michell form ulation, The Beltrami-Michell formulation can only solve stress bounda ry value problems; it cannot handle the more prevalent displacement or mixed boundary value problems of elasticity. Therefore, this formulat ion, which has restricted application, could not become a true alterna tive to the Navier displacement method, which can solve all three type s of boundary value problems, The restrictions of the Beltrami-Michell formulation have been alleviated by augmenting the classical formulat ion with a novel set of conditions identified as the boundary compatib ility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulati on, The completed Beltrami-Michell formulation can solve general elast icity problems, with stress, displacement, and mixed boundary conditio ns in terms of stresses as the primary unknowns. The completed Beltram i-Michell formulation is derived from the stationary condition of the variational functional of the integrated force method, In the complete d Beltrami-Michell formulation, stresses for kinematically stable stru ctures can be obtained without any reference to displacements either i n the field or on the boundary, This paper presents the completed Belt rami-Michell formulation and its derivation from the variational funct ional of the integrated force method, Examples are presented to demons trate the applicability of the completed formulation for analyzing mix ed boundary value problems under thermomechanical loads. Selected exam ples include analysis of a composite cylindrical shell, wherein membra ne and bending response are coupled, and a composite circular plate.