Geology Reference
In-Depth Information
Incremental Scheme: As shown in Figure
3a, in this method, displacement is found
by gradual loading and modification of the
stiffness matrix of the structure at the be-
ginning of each load increment. To get a
satisfactory result from this method, load-
ing increments should be quite small; oth-
erwise, it results in incorrect displacement
values.
tial stiffness method in the sense that both
methods start with the initial stiffness and
continue analysis with unbalanced loads,
however, Newton Raphson method uses
tangential stiffness of the structure at the
beginning of each analysis instead of ini-
tial stiffness. In this method too, the pro-
cess continues until the unbalanced load
becomes infinitesimally small.
Initial Stiffness method: In this method,
which is shown in Figure 3b, the structure
is analyzed with its initial stiffness. After
each analysis, internal forces of members,
which can be measured by the previously
obtained displacement, are used to find
the unbalanced forces in nodes. The un-
balanced forces are then applied again to
the structure with its initial stiffness. The
process of analysis of structure under un-
balanced forces is repeated until external
and internal forces and moments reach
equilibrium.
Combined Methods: To achieve a more
efficient method, the above techniques
can be combined. For example, Figure 3d
demonstrates the combination of the initial
stiffness method with the incremental so-
lution. Figure 3e shows Newton Raphson
method in conjunction with the incremen-
tal loading scheme. A combination of three
methods can also be seen in Figure 3f. In
this latter method, loading on structure is
divided into several segments. At the be-
ginning of every loading increment, stiff-
ness matrix of structure is established/
modified and displacement vector of struc-
Newton-Raphson method: As Figure 3c
shows, this method is similar to the ini-
Figure 3. A schematic presentation of nonlinear analysis
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