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RESEARCH PRODUCT
A mechanically based approach to non-local beam theories
Alba SofiMassimiliano ZingalesMario Di PaolaGiuseppe Faillasubject
Timoshenko beam theoryPhysicsBody forceNon-local elasticityCauchy stress tensorMechanical EngineeringElastic energyTotal elastic potential energy functionalCondensed Matter PhysicsContact forceLong-range interactionTimoshenko beam theoryClassical mechanicsMechanics of MaterialsMechanics of MaterialGeneral Materials ScienceMaterials Science (all)Boundary value problemVolume elementBeam (structure)Civil and Structural Engineeringdescription
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, the mechanical boundary conditions are found coincident with the corresponding mechanical boundary conditions of classical elasticity theory. Numerical applications are also reported. © 2011 Elsevier Ltd. All rights reserved.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 | International Journal of Mechanical Sciences |