Nonlinear and transient finite element analysis of general reinforced concrete plates and shells.
The present work is concerned with the development of
finite element techniques for nonlinear transient dynamic
analysis of reinforced concrete plates and shells.
Computational models have been developed and coded, which are
applied to various engineering problems under static and
dynamic loading conditions.
The first part of the thesis deals with some aspects of
linear-elastic, geometric and material nonlinear finite element
formulations of general thin and thick shell analysis under
static or quasistatic loading. A generalized displacement
method is proposed to overcome the 'shear locking' problem for
the degenerated thick shell element when used in the context of
thin shell structures. The basic concept and mathematical
formulation of the generalized displacement method are detailed
and its application is illustrated by numerical examples. The
method is also extended to the geometrically nonlinear analysis
of thin shells based on both Updated and Total Lagrangian
An elasto-viscoplastic analysis of anisotropic plates and
shells is developed by means of the finite element displacement
method. A discrete layered approach is adopted to represent
different material properties and gradual plastification
through the thickness. Viscoplastic yielding is based on the
Huber-Mixes criterion extended by Hill for anisotropic material
and special consideration is given to the evaluation of the
viscoplastic strain increment for anisotropic situations.
The second part of this thesis is concerned with
nonlinear dynamic transient analysis of reinforced concrete
shell structures. Direct integration methods are reviewed and
discussed. In particular, the general single step explicit,
implicit and implicit-explicit algorithms with predictor -
corrector forms are presented and corresponding stability
conditions are deduced by invoking the energy method.
The modelling of reinforced concrete behaviour in shell
structures under fast loading conditions is considered. Both a
strain rate sensitive elasto-viscoplastic model and a strain
rate sensitive elasto-plastic model are presented for
describing concrete nonlinearities due to multiaxial
compressive or tensile yielding under dynamic loads. The models
are used in conjuction with a tensile crack monitoring
algorithm to trace concrete crack opening and closing. Various
reinforced concrete plates and shells are analyzed and reported
in detail, with the results obtained being compared with those
from other sources.