Axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise have been studied numerically. Effects of geometric nonlinearities have been incorporated into the problem formulation. The problem is challenging because the buckled configuration is unknown a priori. By assuming that the amplitude of plate’s vibration and the additional strains ind...

Axisymmetric deformations of a uniformly heated pre-buckled and post-buckled thin circular plate reinforced with shape memory alloy (SMA) fibers placed in the radial direction only are studied. Effects of von Kármán’s nonlinearities are incorporated in the problem formulation. The matrix is assumed to be linear thermoelastic and the thermo-mechanical response of the SMA is modeled by one-dimens...

We carry out axisymmetric, finite deformation finite element analyses of the uniaxial compression of cylindrical bundles of vertically aligned carbon nanotubes (VACNTs) firmly attached to a Si substrate. A compressible elastic–viscoplastic constitutive relation with a piecewise, linear hardening–softening–hardening flow strength is used to model the material. Calculations are performed for VACN...

Scleral buckling is a surgical technique to treat rhegmatogenous retinal detachment (RRD). Vision may be affected by the scleral buckle. Since the buckle is pushed into the sclera towards the detached retina, it may change the shape and the focal length of the eyeball. A paradigm mathematical model of human eyeball is set up to examine how the focal length of the eye is affected under the actio...

For shallow caps under an axisymmetric external pressure distribution which is inward (with a representative magnitude pO) in a neighborhood of the pole and outward away from the pole, it has been shown previously that a finite axisymmetric dimple state of deformation is possible if p0 is at least of the order of the classical buckling pressure for a complete spherical shell, Pi, and that, asym...

This paper is concerned with the airway closure problem and investigates the quasi-steady deformation characteristics of strongly collapsed (buckled) airways occluded by liquid bridges of high surface tension. The airway wall is modeled as a thin-walled elastic shell, which deforms in response to an external pressure and to the compression due to the surface tension of the liquid bridge. The go...

In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under general finite strain are derived using variational approach. The solved the compound matrix method two cases of axisymmetric growth conditions – purely radial, and combined radial circumferential growth. effect on buc...