Axially loaded pretwisted nonlinear thin plates: A strain gradient analogy

Abstract eng:
In the present work a pre-twisted thin plate subjected to axial loading is analysed. The analysis is conducted within the framework of linear elasticity assuming that the plate undergoes large deformations associated with small strains, i.e. the generalised Hookes law is utilised. The problem is attacked under different conceptual perspectives. First, a classical structural theory is employed where the effect of warping of the non-circular cross section of the plate is introduced. Adopting an energy variational statement the governing partial differential equation is explicitly derived. Secondly, the problem is formulated in terms of second gradient elasticity theory involving only one material length parameter , in addition to the two classical Lame constants. It is shown, by the analogy, that the material length parameter can be expressed on physical ground through the geometrical aspects of the plate and the loading providing a thorough insight of the role of micro-structure.

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