Y. Leng, Tianyi Hu, Sthavishtha R. Bhopalam, Héctor Mauricio Serna-Gómez
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Numerical solutions of a gradient-elastic Kirchhoff plate model on convex and concave geometries using isogeometric analysis
In this work, we study numerical solutions of a gradient-elastic Kirchhoff plate model on convex and concave geometries. For a convex plate, we first show the well-posedness of the model. Then, we split the sixth-order partial differential equation (PDE) into a system of three second-order PDEs. The solution of the resulting system coincides with that of the original PDE. This is verified with convergence studies performed by solving the sixth-order PDE directly (direct method) using isogeometric analysis (IGA) and the system of second-order PDEs (split method) using both IGA and C0 finite elements. Next, we study a concave pie-shaped plate, which has one re-entrant point. The well-posedness of the model on the concave domain is proved. Numerical solutions obtained using the split method differ significantly from that of the direct method. The split method may even lead to nonphysical solutions. We conclude that for gradient-elastic Kirchhoff plates with concave corners, it is necessary to use the direct method with IGA.
期刊介绍:
The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.