Civil Engineering Reference
In-Depth Information
incrementation has been chosen, the increment will be attempted again with
smaller time increments.
Steel and steel-concrete composite bridges may be checked for safety
against dynamic loads, as an example bridges constructed in regions that
are subjected to earthquakes. In this case, dynamic finite element analyses
should be performed. Although this topic is not specifically written for
detailing dynamic analyses, brief highlights of the different dynamic analyses
are highlighted in this topic. ABAQUS [1.29] offers several methods for per-
forming dynamic analysis of problems in which inertia effects are considered.
Direct integration of the system must be used when nonlinear dynamic
response is being studied. Implicit direct integration is provided in ABA-
QUS (Standard), while explicit direct integration is provided in ABAQUS
(Explicit). Modal methods are usually chosen for linear analyses because in
direct-integration dynamics, the global equations of motion of the system
must be integrated through time, which makes direct-integration methods
significantly more expensive than modal methods. Subspace-based methods
are provided in ABAQUS/Standard and offer cost-effective approaches to
the analysis of systems that are mildly nonlinear.
In ABAQUS (Standard) [1.29], dynamic studies of linear problems are
generally performed by using the eigenmodes of the system as a basis for cal-
culating the response. In such cases, the necessary modes and frequencies are
calculated first in a frequency extraction step. The mode-based procedures
are generally simple to use and the dynamic response analysis itself is usually
not expensive computationally, although the eigenmode extraction can
become computationally intensive if many modes are required for a large
model. The eigenvalues can be extracted in a prestressed system with the
“stress-stiffening” effect included (the initial stress matrix is included if
the base state step definition included nonlinear geometric effects), which
may be necessary in the dynamic study of preloaded systems. It is not possible
to prescribe nonzero displacements and rotations directly in mode-based
procedures. The method for prescribing motion in mode-based procedures
is included in transient modal dynamic analysis. Density must be defined for
all materials used in any dynamic analysis, and damping (both viscous and
structural) can be specified at the either material or step level.
5.5.2 Linear Eigenvalue Buckling Analysis
Eigenvalue buckling analysis provided by ABAQUS [1.29] is generally used
to estimate the critical buckling (bifurcation) load of structures. The analysis
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