On the decay of exponential type for the solutions in a dipolar elastic body
Marín Marín, R. Ellahi, Sorin Vlase, M. M. Bhatti
Abstract
Our study is concerned with a generalization of the principle of Saint-Venant in the context of the theory of elastic bodies with a dipolar structure. It is an extension of the form of this principle proposed by Toupin in the case of classical linear elasticity. We consider a straight cylinder which is occupied by an dipolar elastic body that is only loaded at one end and our main finding proves that the internal energy in a portion of this cylinder, that is located at a given distance regarding the end that is loaded, is exponentially decreasing, regarding the respective distance.
Topics & Concepts
Elasticity (physics)DipoleCylinderExponential functionContext (archaeology)GeneralizationLinear elasticityElastic energyExponential growthMathematical analysisMathematicsClassical mechanicsPhysicsGeometryThermodynamicsQuantum mechanicsFinite element methodBiologyPaleontologyThermoelastic and Magnetoelastic PhenomenaElasticity and Wave PropagationElasticity and Material Modeling