TCSS5AD Continuum mechanics for solids and fluids | Duration : 30 hours | ECTS Credits : 3.5 | Semester : S5 | |
Person in charge : Emmanuel Plaut, Professor, emmanuel.plaut@mines-nancy.univ-lorraine.fr | ||||
Keywords : Vectorial analysis, multi-variables functions, general mechanics
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Prerequisites : The fundamentals of continuum mechanics applied to elastic solids et Newtonian fluids | ||||
Objective:
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Program and Content : • Elements of tensor calculus (independent study, if lack of time): algebra and tensor analysis: intrinsic definitions: calculations in curvilinear coordinates. • Continuum model – Elementary kinematics: model boundaries: Lagrangian and Eulerian motion descriptions: characteristic lines. • Advanced kinematics: study of deformations, Lagrangian and Eulerian studies, introduction to appropriate tensors. • Balances of mass and motion – Constraints: introduction to the Cauchy stress tensor: Mohr representation. • Elastic solids: law of linear elastic isotropic: linearised elasticity problems: displacement methods: Navier equation: constraints method. • Kinetic energy balance – Elastic solids: potential elastic energy: conservative nature of the dynamics of elastic solids. • Newtonian fluids: incompressible Newtonian fluid behavior law, Navier-Stokes equation, model of perfect fluid, kinetic energy balance: viscous dissipation, charge losses. • Dimensional analysis and similarity: Vaschy – Buckingham theorem and principles: applications, especially with charge losses in pipe flow.
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Abilities: | ||||
Levels | Description and operational verbs | |||
Know |
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understand | ||||
Apply | ||||
Analyse | ||||
Summarise | ||||
Assess |
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