Variational analysis of gradient elastic flexural plates under static loading

被引:113
作者
Papargyri-Beskou, S. [3 ]
Giannakopoulos, A. E. [4 ]
Beskos, D. E. [1 ,2 ]
机构
[1] Univ Patras, Dept Civil Engn, GR-26500 Patras, Greece
[2] Acad Athens, Off Theoret & Appl Mech, GR-11527 Athens, Greece
[3] Aristotle Univ Thessaloniki, Dept Civil Engn, GR-54006 Thessaloniki, Greece
[4] Univ Thessaly, Dept Civil Engn, GR-38334 Volos, Greece
关键词
Flexural plates; Gradient elasticity; Variational methods; Static analysis; Classical and non-classical boundary conditions; STRUCTURAL-ANALYSIS; MICROPOLAR PLATES; DYNAMIC-ANALYSIS; BEAM; STABILITY; TENSION; BAR;
D O I
10.1016/j.ijsolstr.2010.06.003
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2755 / 2766
页数:12
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