A mechanically based approach to non-local beam theories |
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Authors: | Mario Di Paola Alba Sofi |
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Affiliation: | a Dipartimento di Ingegneria Strutturale, Aerospaziale e Geotecnica (DISAG), Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy b Dipartimento di Meccanica e Materiali (MECMAT), Università “Mediterranea” di Reggio Calabria, Via Graziella, Località Feo di Vito, 89124 Reggio Calabria, Italy c Dipartimento Patrimonio Architettonico ed Urbanistico (PAU), Università “Mediterranea” di Reggio Calabria, Via Melissari, Feo di Vito, 89124 Reggio Calabria, Italy |
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Abstract: | 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. |
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Keywords: | Non-local elasticity Long-range interactions Timoshenko beam theory Total elastic potential energy functional |
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