VARIATIONAL METHOD FOR DERIVATION OF EQUATIONS OF MIXED TYPE FOR SHELLS OF A GENERAL TYPE

Vladimir Karpov

Abstract


In this work, derivation of equations of a mixed type for shallow shell constructions of an arbitrary type is carried out by means of the variational method. Such equations are more simplified equations of the shell theory, as compared to equations in displacements, but in case of some types of fixing of shell edges (for example, in case of pin-edge and movable fixing) they are more convenient. The mathematical model of shell deformation is based on the Kirchhoff–Love hypotheses, geometrical nonlinearity is taken into consideration.

The full functional of shell energy is used for derivation of equilibrium equations and the third equation of strain compatibility in the middle surface of a shell, its minimum condition (the first variation of the functional has to be equal to zero) giving place to these equations. The stress function is entered in the middle surface of the shell in such a way as to make the first two equilibrium equations vanish identically. Thus, the third equilibrium equation and the equation of strain compatibility give the equation of a mixed type in relation to the deflection function and the stress function in the middle surface.

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References


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DOI: https://doi.org/10.23968/2500-0055-2016-1-2-43-48

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