Cusped elastic beams under the action of stresses and concentrated forces

Abstract

A dynamical problem in the (0, 0) approximation of elastic cusped prismatic beams is investigated when stresses are applied at the face surfaces and the ends of the beam. Two types of cusped ends are considered when the beam cross-section turns into either a point or a straight line segment. Correspondingly, at the cusped end either a force concentrated at the point or forces concentrated along the straight line segment is applied. We prove the exists and uniqueness theorems in appropriate weighted Sobolev spaces.

Keywords:

• concentrated forces
• cusped prismatic beams
• degenerate hyperbolic equations
• PDEs with the order degeneration
• initial boundary value problems
• existence and uniqueness theorems

AMS Subject Classifications::

• 74K10
• 74B99
• 35L80

Acknowledgements

The research described in this publication was made possible in part by Award No. GEP1-3339-TB-06 of the Georgian Research and Development Foundation (GRDF) and the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF)