Sn. Patnaik et al., COMPLETED BELTRAMI-MICHELL FORMULATION FOR ANALYZING MIXED BOUNDARY-VALUE-PROBLEMS IN ELASTICITY, AIAA journal, 34(1), 1996, pp. 143-148
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.