A new Kirchhoff plate model based on a modified couple stress theory
By George C. Tsiatas. 2009
475 citations recorded by the source corpus.
In this paper a new Kirchhoff plate model is developed for the static analysis of isotropic micro-plates with arbitrary shape based on a modified couple stress theory containing only one material length scale parameter which can capture the size effect. The proposed model is capable of handling plates with complex geometries and boundary conditions. From a detailed variational procedure the governing equilibrium equation of the micro-plate and the most general boundary conditions are derived, in terms of the deflection, using the principle of minimum potential energy. The resulting boundary value problem is of the fourth order (instead of existing gradient theories which is of the sixth order) and it is solved using the Method of Fundamental Solutions (MFS) which is a boundary-type meshless method. Several plates of various shapes, aspect and Poisson’s ratios are analyzed to illustrate the applicability of the developed micro-plate model and to reveal the differences between the current model and the classical plate model. Moreover, useful conclusions are drawn from the micron-scale response of this new Kirchhoff plate model.
Subfields: Materials Chemistry, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/61147ee826af79c3cae77e13223fc8695783c0b9
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In Materials Chemistry
In Mechanics of Materials
Citations in the corpus
- Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory (2012, methodology): “After this, modified couple stress, non-local elasticity, and strain gradient elasticity theories have been widely applied to static and dynamic analysis of beams [18–28], plates [29,30] and other type structures [31–33].”
- Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory (2013, background): “small-size of the microplate [23, 24, 26, 34].”
- A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory (2013, methodology): “Comparison of the resulted EKM solution with the meshless method (Tsiatas, 2009) for boundary condition (a) case (i) and (b) case (ii). A. Ashoori Movassagh, M.J. Mahmoodi / European Journal of Mechanics A/Solids 40 (2013) 50e59 57”
- Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory (2015, methodology): “In order to verify the couple stress formulation, themaximumnormalized deflections of an SSSSmicroplate under sinusoidal load predicted by the present method are compared with the results of Tsiatas [23,43].”