期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 47, 期 5, 页码 539-548出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2009.09.029
关键词
Non-local elasticity; Long-range interactions; Non-local elastic potential energy; Non-local state variables; Variational theorems
类别
资金
- Italian Minister of Educations and University (MIUR)
The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Moreover, the Euler-Lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations. Numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approach. (C) 2009 Published by Elsevier Ltd.
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