We analyze the structure of the Föppl-von Kármán shell equations of linear elastic shell theory using surface geometry and classical invariant theory. This equation describes the buckling of a thin shell subjected to a compressive load. In particular, we analyze the role of polarized Hessian covariant, also known as second transvectant, in linear elastic shell theory and its connection to minim...

This paper is concerned with the elastic buckling of pumpkin-shaped balloon structures. Pumpkin balloons, currently being used in the NASA Ultra-Long Duration Ballooning (ULDB) Program, consist of stiff meridional tendons that constrain a thin, highly curved plastic surface. The present study exploits the high degree of symmetry of this design by adopting a newly developed, closed form expressi...

An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic response of slender columns and braces under axial cyclic loading without unduly heavy discretization. It consists of three fiber segments, two at the member ends and one at mid-span, with two elastic segments sandwiched in between. The segments are ...

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study ...

A summary is first presented of the conceptual difficulties and paradoxes surrounding plastic bifurcation buckling analysis. Briefly discussed are nonconservativeness, loading rate during buckling, and the discrepancy of buckling predictions with use of .I2 flow theory vs JZ deformation theory. The axisymmetric prebuckling analysis, including large deflections, elastic-plastic material behavior...

This paper presents an overview of the mechanical properties of carbon nanotubes, starting from the linear elastic parameters, nonlinear elastic instabilities and buckling, and the inelastic relaxation, yield strength and fracture mechanisms. A summary of experimental findings is followed by more detailed discussion of theoretical and computational models for the entire range of the deformation...

The transformation of the straight embryonic heart tube into a helically wound loop is named cardiac looping. Such looping is regarded as an essential process in cardiac morphogenesis since it brings the building blocks of the developing heart into an approximation of their definitive topographical relationships. During the past two decades, a large number of genes have been identified which pl...

Oriented block copolymers exhibit a buckling instability when submitted to a tensile test perpendicular to the lamellae direction. In this paper we study this behavior using a coarse grained molecular dynamics simulation approach. Coarse grained models of lamellar copolymers with alternate glassy rubbery layers are generated using the Radical Like Polymerization method, and their mechanical res...

This paper explores the mechanism of bending with kinking of a long single-walled carbon nanotube under pure bending with moderate bending angles. The prebuckling response was modeled using the existing continuum mechanics theory accounting for the ovalization of the cross section. The post-buckling behavior was characterized by the development of an elastic kink mechanism, considering the van ...