Page 14 - Marine Structural Design

Contents xi
11.2.1 Equilibrium Equations for Cylindrical Shells .................................................................. 215
11.2.2 Axial Compression ........................................................................................................... 216
11.2.3 Bending ............................................................................................................................ 217
11.2.4 External Lateral Pressure ................................................................................................. 218
11.3 Buckling of Ring Stiffened Shells ........................................................................................... 219
1 1.3.1 Axial Compression ........................................................................................................... 219
11.3.2 Hydrostatic Pressure ......................................................................................................... 220
11.3.3 Combined Axial Compression and Pressure .................................................................... 221
11.4 Buckling of Stringer and Ring Stiffened Shells ....................................................................... 221
1 1.4.1 Axial Compression ........................................................................................................... 221
1 1.4.2 Radial Pressure ................................................................................................................. 223
11.4.3 Axial Compression and Radial Pressure .......................................................................... 223
1 1.5 References ............................................................................................................................... 224
CHAPTER 12 A THEORY OF NONLINEAR FINITE ELEMENT ANALYSIS ....................... 227
12.1 General ..................................................................................................................................... 227
12.2 Elastic Beam-Column With Large Displacements .................................................................. 228
12.3 The Plastic Node Method ........................................................................................................ 229
12.3.1 History of the Plastic Node Method ................................................................................. 229
12.3.2 Consistency Condition and Hardening Rates for Beam Cross-Sections .......................... 230
12.3.3 Plastic Displacement and Strain at Nodes ........................................................................ 233
12.3.4 Elastic-Plastic Stiffness Equation for Elements ............................................................... 235
12.4 Transformation Matrix ............................................................................................................. 236
12.5 Appendix A: Stress-Based Plasticity Constitutive Equations .................................................. 237
12.5.1 General ............................................................................................................................. 237
12.5.2 Relationship Between Stress and Strain in Elastic Region .............................................. 239
12.5.3 Yield Criterion ................................................................................................................. 240
12.5.4 Plastic Strain Increment ................................................................................................... 242
12.5.5 Stress Increment - Strain Increment Relation in Plastic Region ...................................... 246
12.6 Appendix B: Deformation Matrix ........................................................................................... 247
12.7 References ............................................................................................................................... 248
CHAPTER 13 COLLAPSE ANALYSIS OF SHIP HULLS ........................................................... 251

13.1 Introduction ............................................................................................................................. 251
13.2 Hull Structural Analysis Based on the Plastic Node Method .................................................. 252
13.2.1 Beam-Column Element .................................................................................................... 252
13.2.2 Attached Plating Element ................................................................................................. 254
13.2.3 Shear Panel Element ........................................................................................................ 257
13.2.4 Non-Linear Spring Element ............................................................................................. 257
13.2.5 Tension Tearing Rupture .................................................................................................. 257
13.2.6 Computational Procedures ............................................................................................... 259
13.3 Analytical Equations for Hull Girder Ultimate Strength ......................................................... 260
13.3.1 Ultimate Moment Capacity Based on Elastic Section Modulus ...................................... 260
13.3.2 Ultimate Moment Capacity Based on Fully Plastic Moment ........................................... 261
13.3.3 Proposed Ultimate Strength Equations ............................................................................ 263
13.4 Modified Smith Method Accounting for Corrosion and Fatigue Defects ............................... 264
13.4.1 Tensile and Comer Elements ........................................................................................... 265
13.4.2 Compressive Stiffened Panels .......................................................................................... 265
13.4.3 Crack Propagation Prediction ........................................................................................... 266
13.4.4 Corrosion Rate Model ...................................................................................................... 267
13.5 Comparisons of Hull Girder Strength Equations and Smith Method ...................................... 269
13.6 Numerical Examples Using the Proposed Plastic Node Method ............................................. 271
13.6.1 Collapse of a Stiffened Plate ............................................................................................ 271