Civil Engineering Reference
In-Depth Information
5.6 RIKS METHOD
The Riks method provided by ABAQUS [1.29] is an efficient method that is
generally used to predict unstable, geometrically nonlinear collapse of a
structure. The method can include nonlinear materials and boundary con-
ditions. The method can provide complete information about a structure's
collapse. The Riks method can be used to speed convergence of unstable
collapse of structures. Geometrically nonlinear analysis of bridges may
involve buckling or collapse behavior. Several approaches are possible for
modeling such behavior. One of the approaches is to treat the buckling
or collapse response dynamically, thus actually modeling the response with
inertia effects included as the structure snaps. This approach is easily accom-
plished by restarting the terminated static procedure and switching to a
dynamic procedure when the static solution becomes unstable. In some sim-
ple cases, displacement control can provide a solution, even when the con-
jugate load (the reaction force) is decreasing as the displacement increases.
Alternatively, static equilibrium states during the unstable phase of the
response can be found by using the
modified Riks method
supported by ABA-
QUS [1.29]. This method is used for cases where the loading is proportional,
where the load magnitudes are governed by a single scalar parameter. The
method can provide solutions even in cases of complex, unstable response of
bridges.
In complex structures involving material nonlinearity, geometric nonli-
nearity prior to buckling, or unstable postbuckling behavior, a load-
displacement (Riks) analysis must be performed to investigate the structures
accurately. The Riks method treats the load magnitude as an additional
unknown and solves loads and displacements simultaneously. Therefore,
another quantity must be used to measure the progress of the solution. ABA-
QUS [1.29] uses the arc length along the static equilibrium path in load-
displacement domain. This approach provides solutions regardless of
whether the response is stable or unstable. If the Riks step is a continuation
of a previous history, any loads that exist at the beginning of the step are
treated as dead loads with constant magnitude. A load whose magnitude
is defined in the Riks step is referred to as a reference load. All prescribed
loads are ramped from the initial (dead load) value to the reference values
specified. ABAQUS [1.29] uses Newton's method to solve the nonlinear
equilibrium equations. The Riks procedure uses very small extrapolation
of the strain increment. Modelers can provide an initial increment in arc
length along the static equilibrium path when defining the step. After that,
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