Hybrid and Mixed Methods for Plate Bending Problems

1976 ◽  
pp. 73-88
Author(s):  
F. Brezzi
Keyword(s):  
Mixed Methods ◽  
Plate Bending ◽  
Bending Problems

scholarly journals A Hybrid High-Order method for Kirchhoff–Love plate bending problems

2018 ◽  
Vol 52 (2) ◽  
pp. 393-421 ◽  
Author(s):  
Francesco Bonaldi ◽  
Daniele A. Di Pietro ◽  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Sharp Estimate ◽  
High Order ◽  
Plate Bending ◽  
Mechanical Modeling ◽  
High Order Method ◽  
Local Polynomial ◽  
Bending Behavior ◽  
Bending Problems ◽  
Norm Of The Error ◽  
Theoretical Results

We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff–Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree k ≥ 1 are used as unknowns, we prove convergence in hk+1 (with h denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the energy projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in hk+3 is also derived for the L2-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization.

Spline Boundary Element Method for Plate Bending Problems

1986 ◽  
pp. 427-436 ◽  
Author(s):  
Y.C. WANG ◽  
L.Z. JIANG ◽  
J. LI ◽  
Z.H. WANG
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Plate Bending ◽  
Bending Problems ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document