A Practical Variant of the Semismooth Newton Method for Frictionless Contact Problems
TLDR
In this article, a simple solution scheme for frictionless contact problems of linear elastic bodies is proposed, which is a variant of the semismooth Newton method and can be applied to large-scale contact problems.Abstract:
In this paper, a simple solution scheme for frictionless contact problems of linear elastic bodies is proposed. The proposed method is a variant of the semismooth Newton method. The frictionless contact problem, which is discretized using the finite element method with lower-order elements and a node-to-node contact model, is considered, although the proposed method can be extended to a node-to-segment or segment-to-segment contact model. The present method can be implemented by slightly modifying a computer program for the semismooth Newton method. In the iterative loop of the proposed method, a symmetric linear structural problem with multi-point constraints is solved. Therefore, the proposed method can be applied to large-scale contact problems. Good convergence of the proposed method compared to the semismooth Newton method is demonstrated in some examples.read more
Citations
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A Numerical Algorithm for Block-Diagonal Decomposition of Matrix ⁄-Algebras ⁄
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References
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Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
Reference EntryDOI
Computational Contact Mechanics
Peter Wriggers,Giorgio Zavarise +1 more
TL;DR: The mathematical structure of the contact formulation for finite element methods is derived on the basis of a continuum description of contact, and several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed.
Journal ArticleDOI
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
TL;DR: The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept, which leads to new local convergence results of the primal-dual active set strategy.
BookDOI
Interior point algorithms: theory and analysis
TL;DR: This paper presents a meta-analyses of Linear Programming Algorithms and its applications to Convex Optimization, focusing on the areas of linear programming and nonconvex optimization.
Book
Computational Contact and Impact Mechanics
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and they are subject to change without notice, all errors and omissions excepted.