Mathematical Theory in Periodic Plane Elasticity

2000 ◽  
Author(s):  
Hai-Tao Cai ◽  
Jian-Ke Lu
Keyword(s):  
Mathematical Theory ◽  
Plane Elasticity ◽  
Periodic Plane

Sliding Contact of Elastically Dissimilar Periodic Profiles

2008 ◽  
Author(s):  
Joseph M. Block ◽  
Leon M. Keer
Keyword(s):  
Mathematical Theory ◽  
Coulomb Friction ◽  
Plane Elasticity ◽  
Sliding Contact ◽  
Straightforward Manner ◽  
Extensive Experience ◽  
New Approach ◽  
Partial Contact ◽  
Curved Structures ◽  
Periodic Problems

Various methods for solving the partial contact of surfaces with regularly periodic profiles—which might arise in analyses of asperity level contact, serrated surfaces or even curved structures—have previously been employed for elastic materials. A new approach based upon the summation of evenly spaced Flamant’s solution is used here to solve periodic problems in plane elasticity for sliding contact with Coulomb friction. The advantage is that solutions are derived in a straightforward manner without requiring extensive experience with advanced mathematical theory.

A Mathematical Theory of Hints

1995 ◽  
Author(s):  
Jürg Kohlas ◽  
Paul-André Monney
Keyword(s):  
Mathematical Theory

Evaluation Opportunities in Mechanized Theories

10.29007/7kx8 ◽  
2018 ◽  
Author(s):  
Joe Hurd
Keyword(s):  
Mathematical Theory ◽  
Theorem Prover ◽  
Mechanized Mathematics ◽  
Reasoning Tasks

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.

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