Search results for "Total elastic potential energy functional"

A mechanically based approach to non-local beam theories

2011

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, t…