The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid–structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibilit...

Thin plate structures are more widely used in many engineering applications as one of the structural members. Generally, buckling strength of thin shell structures is the ultimate load carrying capacity of these structures. The presence of cracks in a thin shell structure can considerably affect its load carrying capacity. Hence, in this work, static buckling strength of a thin square plate wit...

The current rapid growth in the use of nanosized particles is fueled in part by our increased understanding of their physical properties and ability to manipulate them, which is essential for achieving optimal functionality. Here we report detailed quantitative measurements of the mechanical response of nanosized protein shells (viral capsids) to large-scale physical deformations and compare th...

A subproblem method with dual finite element magnetostatic and magnetodynamic formulations is developed to correct the inaccuracies near edges and corners coming from thin shell models, that replace thin volume regions by surfaces. The surface-to-volume correction problem is defined as one of the multiple subproblems applied to a complete problem, considering successive additions of inductors a...

The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution ...

Modal signals of transverse sensing of truncated conical shells with simply supported boundary condition at both ends are investigated. The embedded piezoelectric layer on the surface of conical shell is used as sensors and output voltages of them in considered modes are calculated. The Governing sensing signal displacement equations are derived based on the Kirchhoff theory, thin-shell assumpt...

We present a novel approach to probe elastic properties of polyelectrolyte multilayer microcapsules. The method is based on measurements of the capsule load-deformation curves with the atomic force microscope. The experiment suggests that at low applied load deformations of the capsule shell are elastic. Using elastic theory of membranes we relate force, deformation, elastic moduli, and charact...

Ophthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular pressure (IOP) measurements. It measures the force required to press a flat disc against the cornea to produce a flattened circular region of known area. The IOP is deduced from this force using the Imbert-Fick principle. However, there is scant analytical justification for this analysis. We presen...