Civil Engineering Reference
In-Depth Information
in regions attacked by earthquakes. In this section, main dynamic analyses
supported by ABAQUS [1.29] are highlighted in order to help researchers,
designers, academics, and practitioners involved in the dynamic analyses of
steel and steel-concrete composite bridges. The dynamic analyses provided
in ABAQUS over most analyses that may be needed for the dynamic anal-
ysis of steel and steel-concrete composite bridges. The direct-integration
dynamic procedure provided in ABAQUS (Standard) offers a choice of
implicit operators for the integration of the equations of motion, while
ABAQUS (Explicit) uses the central-difference operator. In an implicit
dynamic analysis, the integration operator matrix must be inverted and a
set of nonlinear equilibrium equations must be solved at each time in-
crement. In an explicit dynamic analysis, displacements and velocities
are calculated in terms of quantities that are known at the beginning of
an increment; therefore, the global mass and stiffness matrices need not
be formed and inverted, which means that each increment is relatively
inexpensive compared to the increments in an implicit integration scheme.
The size of the time increment in an explicit dynamic analysis is limited,
however, because the central-difference operator is only conditionally
stable, whereas the implicit operator options available in ABAQUS
(Standard) are unconditionally stable and, thus, there is no such limit on
the size of the time increment that can be used for most analyses in
ABAQUS (Standard), that is, accuracy governs the time increment. The
stability limit for the central-difference method (the largest time increment
that can be taken without the method generating large, rapidly growing
errors) is closely related to the time required for a stress wave to cross
the smallest element dimension in the model; thus, the time increment
in an explicit dynamic analysis can be very short if the mesh contains
small elements or if the stress wave speed in the material is very high.
The method is, therefore, computationally attractive for problems in
which the total dynamic response time that must be modeled is only
a few orders of magnitude longer than this stability limit. Many of the
advantages of the explicit procedure also apply to slower (quasistatic)
processes for cases in which it is appropriate to use mass scaling to reduce
thewavespeed.
ABAQUS (Explicit) [1.29] offers fewer element types than ABAQUS
(Standard) [1.29]. For example, only first-order, displacement method ele-
ments (four-node quadrilaterals, eight-node bricks, etc.) and modified
second-order elements are used, and each degree of freedom in the model
must have mass or rotary inertia associated with it. However, the method
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