Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Corner Instabilities in Slender Elastic Cylinders:
Analytical Solutions and Formation Mechanism

by
Dr Hui-Hui Dai
Department of Mathematics
City University of Hong Kong

Date: March 14, 2007 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: Stabilities and instabilities are important topics in finite elasticity and structures. Here, we study one kind of instability, the corner instability. Such an instability is widespread.  For example, if one compresses a block of sponge, the post-buckling state will have the profile with a corner. As far as we know, there is not any analytical study on this kind of instability, and the reason is probably that mathematically this is a very difficult problem: one needs to study the bifurcations of complicated nonlinear PDE's and show which bifurcations lead to "singular" solutions. Here, we present a novel approach to tackle the challenging problem of the corner formation in an elastic cylinder under compression and reveal the mechanism of its formation. Through a method of compound series-asymptotic expansions, we manage to derive a singular dynamical system (the vector field has a singularity at one point) together with boundary conditions to model this type of problems. We then carry out a phase-plane analysis for this system. It turns out that there is a vertical singular line, which causes a variety of bifurcation phenomena. In particular, a singular solution with a discontinuity in the first-order derivative can arise, which represents the formation of a corner. From the analytical results obtained, we reveal that it is the interaction of the material nonlinearity and geometrical size which causes the formation of a corner.  This is a joint work with my student Fan-Fan Wang.

             

** All interested are welcome **

For enquiry: 2788-9816

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