The Mechanics of Ribbons and Möbius Bands by Roger Fosdick, Eliot Fried

By Roger Fosdick, Eliot Fried

Recent advancements in biology and nanotechnology have influenced a quickly growing to be curiosity within the mechanics of skinny, versatile ribbons and Mobius bands.

This edited quantity comprises English translations of 4 seminal papers in this subject, all initially written in German; of those, Michael A. Sadowsky released the 1st in 1929, via others in 1930, and Walter Wunderlich released the final in 1962.

The quantity additionally includes invited, peer-reviewed, unique learn articles on similar topics.

Previously released within the magazine of Elasticity, quantity 119, factor 1-2, 2015.

Show description

Read or Download The Mechanics of Ribbons and Möbius Bands PDF

Best mechanics books

Mechanics of Microstructured Solids: Cellular Materials, Fibre Reinforced Solids and Soft Tissues

This distinctive quantity of the sequence Lecture Notes in utilized and Computational Mechanics is a compendium of reviewed articles provided on the eleventh EUROMECH-MECAMAT convention entitled "Mechanics of microstructured solids: mobile fabrics, fibre bolstered solids and delicate tissues", which happened in Torino (Italy) in March 10-14, 2008, on the Museo neighborhood delle Scienze.

Holographic Interferometry in Experimental Mechanics

This monograph bargains with various purposes of holographic interferome­ test in experimental sturdy mechanics. Holographic interferometry has skilled a improvement of two decades. It has loved luck and suffered a few disappointments often as a result of early overestimation of its power. at the moment, improvement of holo­ photo interferometry is progressing essentially as a method for quantita­ tive measurements.

Optical Methods in Experimental Solid Mechanics

The ebook covers the theories and physics of complex new optical measuring tools and difficulties of experimental functionality, fresh achievements within the easy interferometric tools holography, speckle-interferometry, shearography in addition to linear/non-linear photoelasticity and photoviscoelasticity, Moiré- and grid-techniques.

Extra info for The Mechanics of Ribbons and Möbius Bands

Example text

Aside from approximation results regarding convergence of minimizers of (3) to minimizers of (2), important open questions include the possibility of centerlines with inflection points. An anticipated difficulty to be overcome is the lack of a polynomial growth bound, from below, for the integrand of the Sadowsky functional (2). There may be some temptation to view the results gathered here as being relevant to the work of Friesecke, James and Müller [7]. In that work, the elastic energy of a deformed rectangle is defined on the space of surfaces parameterized by functions u ∈ W 2,2 ([0, ] × [−w, w]; R3 ) satisfying ux · uy = |ux |2 − 1 = |uy |2 − 1 = 0.

2(a)), while the normal projection on the yz plane (“elevation”) takes the form of a pure oval (see Fig. 2(b)), which can be approximated by the ellipse y2 + z2 = 1, c2 4 with c = . 5 (10) The power series expansion of m as a function of x in a neighborhood of the vertex C will begin as follows: y = λx 3 + · · · , z=c 1− λ2 6 x + ··· . 2 (11) We now raise the central projection of the midline m from its singular point C(0, 0, c) onto the xy plane—the “stereographic projection” of the elliptical cylinder (10), if you will: ξ= Reprinted from the journal cx , c−z η= 26 cy .

The theorem has the following important corollary. Corollary 1 On the set X +,p = κm >0 X κm ,p , the Sadowsky functional is the Γ -limit of the elastic energy Fε (·, I ) with respect to the sequential weak topology and with respect to the strong topology on W 3,p (I ; R3 ). Proof Let u ∈ X +,p . Then u ∈ X κm ,p for some κm > 0. That the limsup condition (20) is satisfied follows from the Γ convergence of Fε (·, I ) to F (·, I ) in X κm ,p . Let {uj } be a sequence in X +,p such that uj → u either strongly or weakly.

Download PDF sample

Rated 4.65 of 5 – based on 39 votes