A Variational Approach for the Mixed Problem in the Elastostatics of Bodies with Dipolar Structure |
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Authors: | Marin?Marin Email author" target="_blank">Vicen?iu?R?dulescuEmail author |
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Institution: | 1.Department of Mathematics and Computer Science,Transilvania University of Bra?ov,Brasov,Romania;2.Faculty of Applied Mathematics,AGH University of Science and Technology,Kraków,Poland;3.Department of Mathematics,University of Craiova,Craiova,Romania;4.Institute of Mathematics, Physics and Mechanics,Ljubljana,Slovenia |
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Abstract: | 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. |
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