Factorization of equilibrium equation in Toupin-Mindlin strain-gradient elasticity in quaternion analysis. (English) Zbl 07867691
Summary: In this paper, we introduce a factorization of the equilibrium equation in the theory of Toupin-Mindlin strain-gradient elasticity in the framework of quaternion analysis by using the inframonogenic operator \(\mathcal{F}u = DuD\) and the Dirac operator of mixed sides \(D_au = \cos aDu + \sin auD\), where \(D\) is the Dirac operator in \(\mathbb{R}^3\). We construct some integral representation formulae for the displacement fields. In application, we obtain a decomposition formula of the displacement fields.
Keywords:
integral representation; inframonogenic operator; Dirac operator; displacement decompositionReferences:
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