Relaxation and Block-Relaxation Procedures for the Dual Formulation of the Signorini-Coulomb Frictional Contact

2009 ◽  
Author(s):  
P. Bisegna ◽  
F. Lebon ◽  
F. Maceri
Keyword(s):  
Frictional Contact ◽  
Dual Formulation ◽  
Block Relaxation

scholarly journals Dual-Dual Formulation for a Contact Problem with Friction

2013 ◽  
Vol 16 (1) ◽  
pp. 1-16
Author(s):  
Michael Andres ◽  
Matthias Maischak ◽  
Ernst P. Stephan
Keyword(s):  
Variational Inequality ◽  
Saddle Point ◽  
Friction Force ◽  
Minimization Problem ◽  
Frictional Contact ◽  
Contact Problems ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Rotation Tensor ◽  
Dual Formulation

AbstractA variational inequality formulation is derived for some frictional contact problems from linear elasticity. The formulation exhibits a two-fold saddle point structure and is of dual-dual type, involving the stress tensor as primary unknown as well as the friction force on the contact surface by means of a Lagrange multiplier. The approach starts with the minimization of the conjugate elastic potential. Applying Fenchel's duality theory to this dual minimization problem, the connection to the primal minimization problem and a dual saddle point problem is achieved. The saddle point problem possesses the displacement field and the rotation tensor as further unknowns. Introducing the friction force yields the dual-dual saddle point problem. The equivalence and unique solvability of both problems is shown with the help of the variational inequality formulations corresponding to the saddle point formulations, respectively.

Local block relaxation method for the solution of equations of gasdynamics

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1377-1384
Author(s):  
Carlo de Nicola ◽  
Renato Tognaccini ◽  
Vittorio Puoti
Keyword(s):  
Relaxation Method ◽  
Solution Of Equations ◽  
Block Relaxation ◽  
Local Block

scholarly journals A Note on the Decomposition Methods for Support Vector Regression

2002 ◽  
Vol 14 (6) ◽  
pp. 1267-1281 ◽  
Author(s):  
Shuo-Peng Liao ◽  
Hsuan-Tien Lin ◽  
Chih-Jen Lin
Keyword(s):  
Support Vector Regression ◽  
Decomposition Method ◽  
Decomposition Methods ◽  
Support Vector ◽  
Dual Formulation ◽  
Working Set ◽  
Number Of Iterations

The dual formulation of support vector regression involves two closely related sets of variables. When the decomposition method is used, many existing approaches use pairs of indices from these two sets as the working set. Basically, they select a base set first and then expand it so all indices are pairs. This makes the implementation different from that for support vector classification. In addition, a larger optimization subproblem has to be solved in each iteration. We provide theoretical proofs and conduct experiments to show that using the base set as the working set leads to similar convergence (number of iterations). Therefore, by using a smaller working set while keeping a similar number of iterations, the program can be simpler and more efficient.

scholarly journals Discrete element model for general polyhedra

2021 ◽  
Author(s):  
Alfredo Gay Neto ◽  
Peter Wriggers
Keyword(s):  
Frictional Contact ◽  
Virtual Work ◽  
Particle Surface ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Principle Of Virtual Work ◽  
Dynamics Model ◽  
Railway Ballast ◽  
Multibody Dynamics Model

AbstractWe present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast.

scholarly journals A Hybrid Material Point Method for Frictional Contact with Diverse Materials

2019 ◽  
Vol 2 (2) ◽  
pp. 1-24 ◽  
Author(s):  
Xuchen Han ◽  
Theodore F. Gast ◽  
Qi Guo ◽  
Stephanie Wang ◽  
Chenfanfu Jiang ◽  
...  
Keyword(s):  
Hybrid Material ◽  
Frictional Contact ◽  
Material Point Method ◽  
Material Point ◽  
Point Method
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