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This book provides modern investigation into the bifurcation phenomena of physical and structural problems. Systematic methods - based on asymptotic, stochastic, and group-theoretic standpoints - are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.
List of contents
Introduction to Bifurcation Behavior.- Critical Point and Local Behavior.- Imperfection Sensitivity Laws.- Critical Initial Imperfections (I).- Stochasticity of Initial Imperfections (I).- Experimentally-observed Bifurcation Diagrams.- Group-theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-equivariant Systems.- Critical Initial Imperfections (II).- Stochasticity of Initial Imperfections (II).- Description of Bifurcation Behaviors.- Bifurcation of Cylindrical Sand Specimens.- Echelon-mode Formation.- Bifurcation of Steel Specimens.- Miscellaneous Aspects ofBifurcation Phenomena.- References.- Index.
