Page 283 - Marine Structural Design

Chapter 13 Collapse Analysis of Ship Hulls 259

13.2.6 Computational Procedures

This chapter outlines the computer program SANDY and the computational procedure
implemented in the program. Further information can be found in the program manuals (Bai,
Y. 1991) and in publications (Bai & Pedersen, 1991, 1993, Bendiksen 1992).
Computer Program SANDY
The theory presented in this paper has been implemented in the general-purpose computer
program SANDY (Bai, 1991). Depending on the problem, the following solution procedures
can be applied:
Quasi-static analysis using:
Loadincrement
Displacement, or
Automatic loading, by using the current stiffness parameter method (Bergan & Smeide,
1978).
Dynamic analysis (time integration method):
1. Applying dynamic loads as time histories of nodal and element forces
2. Modeling the problem as a structure struck by a deformable mass
3. Applying dynamic loads as initial nodal velocities
4. Earthquake response analysis
Computational Procedure
The non-linear calculation procedure is as follows:
The size of the increment is determined, this is often determined in the input data
The increment of the load vector is assembled
The stiffness matrix is calculated for each element. Shear elements Gt, and stiffness matrices
are dependent on the current load. For non-linear spring elements, the stiffness factor is
calculated as a hction of the displacement and of the direction of the increment. For plate
elements, the effective width and the linear stiffness plus the eccentricity are calculated.
Subsequently, the element is treated in the same way as any other beam-column element. The
two geometric matrices are calculated and added to the linear matrix. If the element is in the
plastic range, the plastic stiffness matrix is calculated.
If a standard stiffened plate section is used, the program may first recalculate the yield surface,
by taking the new reduction factors caused by transverse and shear stress into account. If the
element is already plastic, these reduction factors are kept constant; otherwise, they would
influence the compatibility equations.
The transformation equation for each element is updated and the stifmess matrices are
transformed and added into the global matrix.
In the first step of a dynamic simulation, the global mass matrix is calculated. The system of
equations is modified according to a time-integration scheme, e.g. Newmark-P method.
Finally, the system of equations is solved. Here we use LDL decomposition and a back
substitution.