By S. S. Antman (auth.)

Starting in 1996, a series of articles seemed within the magazine of Nonlinear technology devoted to the reminiscence of 1 of its unique editors, Juan-Carlos Simo, utilized Me chanics, Stanford collage. unfortunately, Juan-Carlos passed on to the great beyond at an early age in 1994. We misplaced an excellent colleague and an excellent individual. those articles are accumulated within the current quantity. lots of them are up to date and corrected specifically for this celebration. those essays are in parts of medical curiosity of Juan-Carlos, together with mechanics (particles, inflexible our bodies, fluids, elasticity, plastic ity, etc.), geometry, utilized dynamics, and, after all, computation. His pursuits have been tremendous broad-he didn't see barriers among computation, arithmetic, me chanics, and dynamics, and, in that experience, he preferably mirrored the spirit of the magazine and lots of of the main intriguing components of present medical curiosity. Juan-Carlos was once a type of pick out and talented those who may well move interdisci plinary limitations with tremendous top of the range and efficient interactions of lasting price. His contributions, starting from concrete engineering difficulties to primary mathematical theorems in geometric mechanics, are striking. In present meetings in addition to in clinical books and articles, and over quite a lot of matters, one usually hears how his principles in addition to particular effects are usually used and quoted-this is one indication of simply how profound and primary his paintings has impacted the community.

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**Extra resources for Mechanics: From Theory to Computation: Essays in Honor of Juan-Carlos Simo**

**Example text**

The limit equation is x E 5'. 3). Example 2. 6) 40 Z. P. E. 7). Example 3. (ai¢j + aj¢J is the linearized strain tensor, A, It the Lame constants. Here we used al := aJaxl, a2 := aJaxz, and a3 := aJay. Note that these equations describe a linearized Saint Venant-Kirchhoff model. 9). As in previous examples, we take an approximation by a constrained-director model where;P = (CPI, CPz, CP3), ill are vector-valued functions on JR3. I

Camassa, R. and D. Holm [1993] An integrable shallow water equation with peaked solitons, Phys. Rev. , 71, 1661-1664. Ciarlet, P. G. [1980], A justification of the von Karman equations. Arch. Rat!. Mech. Anal. 73, 349-389. Ciarlet, P. G. [1994] Mathematical shell theory: recent developments and open problems, in Duration and Change: Fifty years at Oberwolfach, M. Artin, H. Kraft, and R. , Springer-Verlag, New York, 159-176. Ciarlet, P. G. and V. Lods [1994] Analyse asymptotique des coques lineairement elastiques.

I'JQ[ IE (I. H = f Q -E -E a¢ a¢ )) d-xdy ? ¢+g x,y,¢,-,-,E 2 ax ay a¢ a¢)) ? "2¢·¢+gisotro PiC x,y,¢, ax,E ay d-xdy. 2) In particular, if g is quadratic plus higher order terms in a¢/ay, then it satisfies the hypotheses needed to get an unconstrained limiting model. The Hamiltonian for the limiting model is then given in terms of the variable cp and the scaled variable iii = I" W by H shell = ( _acp))? '[(1( .. ) / JQ cp. cp + W + gshell x, cp, w, ax d-x, "2 JW . 3) where gshell acp _) _ acp) ( ( x,cp,W, ax =gisotropic x,D,cp, ax'w .