On the Generation of Harmonics by the Non-Linear Buckling of an Elastic Beam

The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear coordinates along the deflected position, namely, the arc length and angle of inclination. The present paper starts with the exact equation in a third form, that is, (iii) using Cartesian coordinates along and normal to the undeflected position like (i), but allowing exactly the non-linear effects of a large slope like (ii). This third form of the equation of the elastica shows that the exact non-linear shape is a superposition of linear harmonics; thus, the non-linear effects of a large slope are equivalent to the generation of harmonics of a linear solution for a small slope. In conclusion, it is shown that: (i) the critical buckling load is the same in the linear and non-linear cases because it is determined by the fundamental mode; (ii) the buckled shape of the elastica is different in the linear and non-linear cases because non-linearity adds harmonics to the fundamental mode. The non-linear shape of the elastica, for cases when powers of the slope cannot be neglected, is illustrated for the first four buckling modes of cantilever, pinned, and clamped beams with different lengths and amplitudes.

Ipsilateral penetrating rotational autokeratoplasty: case report and literature review

Purpose. To assess the features and results of post-traumatic reconstruction of the anterior part of the eye in a child with ipsilateral rotational autokeratoplasty (IRAK). Clinical case. Patient I. 5.5 years old, on the right eye performed a reconstructive surgery of the anterior part of the eye with IRAK, including synechiotomy, iridoplasty, phacoaspiration of traumatic cataract and implantation of an intraocular lens. The analysis of literature data has been carried out The restoration of the transparency of the optical axis and increase in visual functions were obtained – the diameter of the autokeratograft was 8.0 mm with a rotation angle 110°. The most preferred for IRAK are central post-traumatic corneal scars, which have a linear shape with significant areas of the transparent corneal periphery preservation. Conclusion. IRAK does not require donor material, it is recommended for limited central corneal sports, eliminates the risk of graft rejection due to incompatibility, and does not require the usage of systemic corticosteroids and immunosuppressants. IRAK is highly effective in childhood when it is necessary to perform combined reconstructive interventions such as «open sky» on the cornea, iris and lens. Key words: ipsilateral rotational autokeratoplasty, post-traumatic scars, ophthalmology reconstruction surgery.

A Mechanical Analysis of Chemically Stimulated Linear Shape Memory Polymer Actuation

In the present work, we study the role of programming strain (50% and 100%), end loads (0, 0.5, 1.0, and 1.5 MPa), and chemical environments (acetone, ethanol, and water) on the exploitable stroke of linear shape memory polymer (SMP) actuators made from ESTANE ETE 75DT3 (SMP-E). Dynamic mechanical thermal analysis (DMTA) shows how the uptake of solvents results in a decrease in the glass temperature of the molecular switch component of SMP-E. A novel in situ technique allows studying chemically triggered shape recovery as a function of time. It is found that the velocity of actuation decreases in the order acetone > ethanol > water, while the exploitable strokes show the inverse tendency and increases in the order water > ethanol > acetone. The results are interpreted on the basis of the underlying chemical (how solvents affect thermophysical properties) and micromechanical processes (the phenomenological spring dashpot model of Lethersich type rationalizes the behavior). The study provides initial data which can be used for micromechanical modeling of chemically triggered actuation of SMPs. The results are discussed in the light of underlying chemical and mechanical elementary processes, and areas in need of further work are highlighted.