Page 332 - Marine Structural Design

308 part II Utimate Strength

15.3.2 Nonlinear Finite Element Model
The finite element model was given in Part I1 Chapter 12.
15.3.3 Analysis Procedure
Design of offshore structure for earthquake resistance should consider operational and safety
requirements of critical piping, equipment and other important components. This dual criteria
is usually provided for by designing a structure where the deformations are within acceptable
levels and satisfy a set of yield or buckling criteria for the maximum expected level of the
earthquake ground motion. Therefore, a nonlinear dynamic analysis is necessary.
Some of the features of the present analysis procedure are:
A acceleration record, such as EL CENTRO N-S, is scaled by a scale factor to match the
probable earthquake in the areas where the structure will be installed.
A frame model is established by three-dimensional finite elements. Soil structure
interaction is taken into account by used of spring elements.
Fluid-structure interaction is induced. The contribution form the added mass in taken into
accounted by an increase of the mass of the beam-column element s. the drag forces are
treated as external loads.
A linear static analysis is performed for the structure subjected gravity loading. The results
are used as an initial condition for the subsequent dynamic analysis.
The structure mass matrix may consist of both masses applied directly at the nodes, and
element masses which are evaluated using either a lumped mass method or a consistent
mass method.
Geometrical and material nonlinearities are taken in account by use of the theory described in
the proceeding chapters.
Time history, and maximum and minimum values of displacements, and forces are presented
as calculation results. From these results, the structural integrity against the earthquake is
assessed.
The procedure has been implemented in the computer program SANDY (Bai, 1990), and used
in several analyses.

15.4 Numerical Examples
EXAMPLE 15.1: Clamped Beam Under Lateral Load
This example (see Figure 15.1) is chosen to show the efficiency of the present procedure. In
the present analysis, only one beam-column element is used to model half of the beam. The
linear and geometrical stiffness matrices as well as the deformation matrix are used. The
plastic yield condition used for rectangular cross-section is taken as
(15.6)
where the subscript “p“ indicates fully-plastic values for each stress components.
Figure 15.1 shows that the present results agree with the experimental results and the limit
load theory results (Haythomthwaite, 1957). The limit load is P, when the geometrical
nonlinearity is not taken into account.