Localization and Solitary Waves in Solid Mechanics

by Champneys, A. R.; Hunt, G. W.; Thompson, J. M. T.

• ISBN13: 9789810239152
• ISBN10: 9810239157
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.

Table of Contents

Introduction	1	(28)
Overview	1	(6)
Structural localization	7	(4)
Mathematical framework	11	(6)
Numerical methods	17	(1)
Rod mechanics	18	(11)
Bibliography	25	(4)
The strut on an elastic foundation	29	(40)
An overview of homoclinic modes for the strut on an elastic foundation	31	(23)
Wadee, M.K.
Instability of localized buckling modes in a one-dimensional strut model	54	(15)
Sandstede, B.
Numerics and discretization	69	(40)
Static solitary waves as limits of discretization: a plausible argument	71	(18)
Domokos, G.
Finite element modelling of spatially chaotic structures	89	(20)
Hunt, G.W.
Lawther, R.
Providencia E Costa, P.
Twisted rods	109	(146)
From helix to localized writhing in the torsional post-buckling of elastic rods	111	(22)
Thompson, J.M.T.
Champneys, A.R.
Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods	133	(24)
Van Der Heijden, G.H.M.
Thompson, J.M.T.
Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature	157	(24)
Champneys, A.R.
Van Der Heijden, G.H.M.
Thompson, J.M.T.
Elastic rods, rigid bodies, quaternions and the last quadrature	181	(20)
Kehrbaum, S.
Maddocks, J.H.
The writhing of circular cross-section rods: undersea cables to DNA supercoils	201	(34)
Stump, D.M.
Fraser W.B.
Gates, K.E.
Nonlinear dynamics of filaments. IV---spontaneous looping of twisted elastic rods	235	(20)
Goriely, A.
Tabor, M.
Cylindrical shells	255	(44)
Localized buckling in long axially loaded cylindrical shells	257	(14)
Hunt, G.W.
Lucena Neto, E.
Computation of localized post buckling in long axially compressed cylindrical shells	271	(14)
Lord, G.J.
Champneys, A.R.
Hunt, G.W.
Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells	285	(14)
Hunt, G.W.
Lord, G.L.
Champneys, A.R.
Other buckling problems	299	(50)
Localization and mode interaction in sandwich structures	301	(20)
Hunt, G.W.
Wadee, M.A.
Homoclinic and heteroclinic solutions of upheaval buckling	321	(11)
Hunt, G.W.
Blackmore, A.
Folding processes and solitary waves in structural geology	332	(17)
Hunt, G.W.
Muhlhaus, H.-B.
Whiting, A.I.M.
Solitary waves	349	(2)
On the dynamics of flexure and stretch in the theory of elastic rods	351	(28)
Coleman, B.D.
Dill, E.H.
Swiggon, D.
Travelling waves in a nonlinearly suspended beam: some computational results and four open questions	379
Chen, Y.
McKenna, P.J.