Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

2016 ◽  
Vol 23 (5) ◽  
pp. 1253-1263 ◽  
Author(s):  
Kang Peng ◽  
Xu-yan Yin ◽  
Guang-zhi Yin ◽  
Jiang Xu ◽  
Gun Huang ◽  
...  
Keyword(s):  
Kirchhoff Plate ◽  
Winkler Foundation ◽  
Plate Model ◽  
Crown Pillar ◽  
Galerkin Solution ◽  
Kirchhoff Plate Model

scholarly journals DG approach to large bending plate deformations with isometry constraint

2021 ◽  
pp. 1-43
Author(s):  
Andrea Bonito ◽  
Ricardo H. Nochetto ◽  
Dimitrios Ntogkas
Keyword(s):  
Discontinuous Galerkin ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Gradient Flow ◽  
Kirchhoff Plate ◽  
Geometrically Nonlinear ◽  
Plate Model ◽  
Global Minimizers ◽  
Dg Method ◽  
Kirchhoff Plate Model

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove [Formula: see text]-convergence of the discrete energies and discrete global minimizers. We document the flexibility and accuracy of the dG method with several numerical experiments.

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