scholarly journals Well-posedness of systems of 1-D hyperbolic partial differential equations

2018 ◽  
Vol 19 (1) ◽  
pp. 91-109 ◽  
Author(s):  
Birgit Jacob ◽  
Julia T. Kaiser
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Well Posedness ◽  
Partial Differential

DRAPING WOVEN SHEETS

2021 ◽  
pp. 1-31
Author(s):  
P. D. HOWELL ◽  
H. OCKENDON ◽  
J. R. OCKENDON
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Carbon Fibre ◽  
Continuum Limit ◽  
Woven Fabric ◽  
Hyperbolic Partial Differential Equations ◽  
Well Posedness ◽  
Partial Differential ◽  
Rigid Rods ◽  
The Continuum

Abstract Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations whose characteristics are the fibres in the fabric. The analysis of this system gives useful information about the drapability of obstacles of many shapes and also poses interesting theoretical questions concerning well-posedness, smoothness and computability of the solutions.

Draping woven sheets

2021 ◽  
Vol 62 ◽  
pp. 355-385
Author(s):  
P. D. Howell ◽  
H. Ockendon ◽  
J. R. Ockendon
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Carbon Fibre ◽  
Continuum Limit ◽  
Woven Fabric ◽  
Hyperbolic Partial Differential Equations ◽  
Well Posedness ◽  
Partial Differential ◽  
Rigid Rods ◽  
The Continuum

Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations whose characteristics are the fibres in the fabric. The analysis of this system gives useful information about the drapability of obstacles of many shapes and also poses interesting theoretical questions concerning well-posedness, smoothness and computability of the solutions. doi:10.1017/S144618112000019X

Sign in / Sign up

Export Citation Format

Share Document