157 research outputs found
On the Derivation of Hooke’s Law for Plane State Conditions
We discuss the derivation of Hooke’s law for plane stress and plane strain states from its general three-dimensional representation. This means that we consider the anisotropic case to ensure a certain generality of our representation. Thereby, two approaches are examined, namely the tensorial representation involving fourth-order tensors over a three-dimensional vector space, and the Voigt-Mandel-Notation involving second-order tensors over a six-dimensional vector space. The latter reduces to a vector-matrix notation common in engineering applications. It turns out that both approaches have their merits: The tensorial approach is easier to handle symbolically, the matrix approach is easier to handle numerically. Both procedures are applicable for arbitrary material symmetries. Finally, we answer the question why a material under the assumptions of a plane stress state behaves softer and why it behaves stiffer under a plane strain state compared to the three-dimensional state
Occurrence of carbapenemase-producing Klebsiella pneumoniae and Escherichia coli in the European survey of carbapenemase-producing Enterobacteriaceae (EuSCAPE): a prospective, multinational study
Beitrag Schwingungen [in: Dubbel-Taschenbuch für den Maschinenbau. 21., neu bearb. und erw. Aufl.]
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