Chaos in Structural Mechanics

This monograph is devoted to construction of novel theoretical approaches of m- eling non-homogeneous structural members as well as to development of new and economically ef?cient (simultaneously keeping the required high engineering ac- racy)computationalalgorithmsofnonlineardynamics(statics)ofstronglynonlinear behavior of either purely continuous mechanical objects (beams plates shells) or hybrid continuous/lumped interacting mechanical systems. In general the results presented in this monograph cannot be found in the - isting literature even with the published papers of the authors and their coauthors. We take a challenging and originally developed approach based on the integrated mathematical-numerical treatment of various continuous and lumped/continuous mechanical structural members putting emphasis on mathematical and physical modeling as well as on the carefully prepared and applied novel numerical - gorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the ?elds of bifurcation chaos control and s- bility of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs) and may have a positive impact on interdisciplinary ?elds of n- linear mechanics physics and applied mathematics. We show for the ?rst time in a book the complexity and fascinating nonlinear behavior of continual mechanical objects which cannot be found in widely reported bifurcational and chaotic dyn- ics of lumped mechanical systems i. e. those governed by nonlinear ODEs.