Under the actions of internal pressure and electric voltage, a spherical dielectric elastomer balloon usually keeps a sphere during its deformation, which has also been assumed in many previous studies. In this article, using linear perturbation analysis, we demonstrate that a spherical dielectric elastomer balloon may bifurcate to a nonspherical shape under certain electromechanical loading conditions.
Consider the set of monic fourth-order real polynomials transformed so that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four.
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid- and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.
This treatise provides a broad overview of the definitions of
fundamental quantities and methods of analysis for the use of solid materials
in structural components. The presentation is limited to the linear elastic
range of material behavior where there is a one to one relationship between
load and displacement. Fundamental
methods of analysis and typical results for structures made of elastic solid materials
subjected to axial, bending, torsion, thermal, and internal pressure loading;
This monograph gives a complete overview on the subject of nonconservative stability from the modern point of view. Relevant mathematical concepts are presented, as well as rigorous stability results and numerous classical and contemporary examples from mechanics and physics.
I wrote these notes about 10 years ago to supplement a course of lectures at Ecole Polytechnique. There might be errors in the notes, but I hope they can help you learn this fascinating subject of lasting value.
We have recently studied the atomic scale structural stability of
freestanding wavy gold (Au) nanofilms using molecular dynamics
simulations. In recent years, wavy or patterned structurs have shown great promise for applications in various emerging technologies including fuel cells
engineering, tissue engineering, biomedical engineering, creation
of counterfeit-resistant documents , nanolithography in microelectronics, optoelectronics, nanomachinesand many others. It is out of question that the success of these novel applications lies on one crucial factor – the
Koiter's PhD thesis, dated 1945, gave the birth of post-buckling analysis, and quantified the notion of imperfection sensitivity. He wrote the thesis in Dutch. An excellent English translation is free online.