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.
