Page 210 - Marine Structural Design

186 Part II Ultimate Strength

(9.95)

where {dh)represents the increments of nodal displacements.
Substituting Eqs. (9.94) and (9.95) into Eq. (9.92), dAiand dAjare expressed in terms of {dh}.
Substituting them into Eq. (9.954, the elasto-plastic stiffness matrix after local buckling is
derived as:

(9.96)

For the case in which local buckling is not considered, the elasto-plastic stifbess matrix is
given in a concrete form in Veda et al, 1969). When local buckling is considered, the terms
4; K, 4i and 4; K, 4j in the denominators in Ueda and Yao (1982) are replaced by
4; K, +i -'y,?y, and 4; K, q5j -'yryj, respectively.

9.4 Calculation Results
9.4.1 Simplified Elasto-Plastic Large Deflection Analysis

In order to check the validity of the proposed method of analysis, a series of calculations are
performed on test specimens, summarized in Table 9.4, in which a comparison is made
between calculated and measured results. Three types of analyses are performed a simplified
elasto-plastic large deflection analysis combined with a COS model and a DENT model,
respectively, for all specimens; and an elasto-plastic large deflection analysis without
considering local buckling by the finite element method. The calculated results applying COS
model and DENT model are plotted in the following figures, along with those analyzed using
the finite element method. The experimental results are plotted by the solid lines.
H series
This series is newly tested. The measured and calculated load -deflection curves are plotted in
Figure 9.7. First, the results from the simplified method have a very good correlation with
those obtained from the finite element method until the ultimate strength is attained. However,
they begin to show a little difference as lateral deflection increases. This may be attributed to
the overestimation of the plastic region size at this stage.
The calculated ultimate strengths are 7-10% lower than the experimental ones. This may be
due to a poor simulation of the simply supported end condition and the strain hardening effect
of the material. Contrary to this, the onset points of local buckling calculated using Eq. (9.33)
agree quite well with the measured ones. The post - local buckling behavior is also well
simulated by the COS model, but not so well simulated by the DENT model. Such difference
between the measured and the calculated behaviors applying DENT model is observed in all
analyzed test specimens except for the D series. This may be due to the underestimation of
forces and moments acting at the bottom of a dent, and fiuther consideration may be necessary
for the DENT model.