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The mixed FEM for analysis of quantum-dot systems based on gradient theory

Sladek Jan, Sladek Vladimir, Repka Miroslav, Hrcek Slavomir

Computer Methods in Materials Science

2018

Vol. 18, No. 3

81--89

The QD nanostructures are analyzed under a thermal load. The dimensions of the QDs are of the same order as the material length scale. Therefore, the gradient elasticity theory should be applied to account for the size-dependent behavior of such nano-sized QDs. Since governing equations contain higher order derivatives than in conventional approaches the C1-elements are required for approximation of primary fields in the FEM. The mixed FEM are developed here, where C0 continuous interpolation is applied independently for displacement and displacement gradients. The kinematic constraints between strains and displacements are satisfied by collocation at some cleverly chosen internal points in elements. A unit cell of Indium Arsenide QD in a finite sized Gallium Arsenide (GaAs) substrate is analysed.