Mixed finite element formulations of strain-gradient elasticity problems

被引:184
作者
Amanatidou, E [1 ]
Aravas, N [1 ]
机构
[1] Univ Thessaly, Dept Mech & Ind Engn, Volos 38334, Greece
关键词
strain-gradient elasticity; finite elements; mixed formulation;
D O I
10.1016/S0045-7825(01)00353-X
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Theories on intrinsic or material length scales find applications in the modeling of size-dependent phenomena. In elasticity, length scales enter the constitutive equations through the elastic strain energy function, which, in this case, depends not only on the strain tensor but also on gradients of the rotation and strain tensors. In the present paper, the strain-gradient elasticity theories developed by Mindlin and co-workers in the 1960s are treated in detail. In such theories, when the problem is formulated in terms of displacements, the governing partial differential equation is of fourth order. If traditional finite elements are used for the numerical solution of such problems, then C-1 displacement continuity is required. An alternative "mixed" finite element formulation is developed, in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an "integral-sense". A variational formulation is developed which can be used for both linear and non-linear strain-gradient elasticity theories. The resulting finite elements require only C-0 continuity and are simple to formulate. The proposed technique is applied to a number of problems and comparisons with available exact solutions are made. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:1723 / 1751
页数:29
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