A Variational Approach for the Mixed Problem in the Elastostatics of Bodies with Dipolar Structure
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In this study, we address the mixed initial boundary value problem in the elastostatics of dipolar bodies. Using the equilibrium equations, we build the operator of dipolar elasticity and prove that this operator is positively defined even in the general case of an elastic inhomogeneous and anisotropic dipolar solid. This helps us to prove the existence of a generalized solution for first boundary value problem and also the uniqueness of the solution. Moreover, relying on this property of the operator of dipolar elasticity to be positively defined, we can apply the known variational method proposed by Mikhlin.
KeywordsDipolar bodies first boundary value problem operator of dipolar elasticity generalized solution variational method
Mathematics Subject ClassificationPrimary 70G75 Secondary 53A45 58E30 74A20
The authors are grateful to the anonymous reviewer for the careful reading of the initial version of this paper and for numerous suggestions that improved the present work. V.D. Rădulescu acknowledges the support through the Project MTM2017-85449-P of the DGISPI (Spain).
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