Truss Modular Beams with Deformation Energy depending on Higher Displacement Gradients  

Oleh:

Alibert, Jean-Jacques ; Seppecher, Pierre ; Dell'Isola, Francesco

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Mathematics and Mechanics of Solids vol. 8 no. 1 (Feb. 2003), page 51-73.
Topik: Second gradient theory; third gradient theory; homogenization; r-convergence; finite differences; modular truss beam; pantograph
Fulltext: 51MMS81.pdf (599.73KB)

Isi artikel

Until now, no third gradient theory has been proposed to describe the homogenized energy associated with a microscopic structure. In this paper, we prove that this is possible using pantographic-type structures. Their deformation energies involve combinations of nodal displacements having the form of second-order or third-order finite differences. We establish the r-convergence of these energies to second and third gradient functionals. Some mechanical examples are provided so as to illustrate the special features of these homogenized models.

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