COMPUTATIONAL STRUCTURAL MECHANICS - Static and Dynamic Behaviors

Cover......Page 1
COMPUTATIONAL
STRUCTURAL
MECHANICS:
Static and Dynamic
Behaviors
......Page 4
Copyright
......Page 5
Preface......Page 6
Acknowledgments......Page 11
1.1 Origin of FG materials......Page 12
1.2 Static bending analysis......Page 13
1.2.1 Bending of FG beams......Page 14
1.2.2 Bending of FG plates......Page 15
1.3 Dynamic (or vibration) characteristics......Page 17
1.3.1 Vibration of FG beams......Page 18
1.3.2 Vibration of FG plates......Page 19
1.4 Recent developments in numerical methods......Page 20
2.2 Recent developments......Page 22
2.3 Computational algorithms......Page 24
3.1 Background......Page 27
3.2 Recent developments......Page 28
3.3 Computational algorithms......Page 29
3.3.1 Weighting coefficients of first-order derivative......Page 30
3.3.2 Weighting coefficients of second- and higher-order derivatives......Page 31
3.3.3 Discretization of governing equation......Page 32
4.2 Recent developments......Page 35
4.3 Computational algorithms......Page 36
5.2 Numerical procedure of Laplace transform......Page 39
5.2.1 C-C FG beam......Page 40
5.2.3 C-F FG beam......Page 41
5.2.4 S-S FG beam......Page 42
5.3 Concluding remarks......Page 43
6.2 Numerical modeling......Page 44
6.3 Convergence and comparison studies......Page 49
Effect of power-law exponents......Page 52
Effect of ratio of Young's moduli of the constituents......Page 55
6.5 Concluding remarks......Page 62
7.1 Numerical modeling......Page 63
7.2 Convergence and comparison studies......Page 65
7.3 Results and discussion......Page 72
7.4 Concluding remarks......Page 91
8.1 Functionally graded triangular plate......Page 93
8.2 Numerical modeling......Page 94
8.3.1 Effect of power-law index......Page 97
8.3.2 Effect of ratio of Young's moduli......Page 99
8.4 Concluding remarks......Page 155
9.2 Convergence and validation studies......Page 156
9.3 Numerical results......Page 169
9.4 Concluding remarks......Page 182
10.1 Numerical modeling......Page 186
10.2 Convergence and comparison studies......Page 198
10.3 Results with previously proposed SDPTs......Page 199
10.4 Results with newly proposed SDPTs......Page 220
10.5 Concluding remarks......Page 241
11.2 Numerical modeling......Page 242
11.3 Convergence and validation studies......Page 245
11.4 Numerical results......Page 246
11.4.1 Effect of power-law index (k)......Page 247
11.4.4 Effect of ratio of mass densities (ρr)......Page 254
11.5 Concluding remarks......Page 268
12.1 FG annular plate......Page 271
12.2 Numerical modeling......Page 272
12.3 Numerical results......Page 274
12.4 Concluding remarks......Page 283
13.1 Functionally graded elliptic plates......Page 284
13.3.1 Effect of aspect ratio and power-law index......Page 287
13.3.2 Effect of elastic foundation moduli......Page 295
13.4 Functionally graded skew plates......Page 302
13.4.1 Numerical results......Page 304
13.5 Concluding remarks......Page 306
Bibliography......Page 309
Index......Page 321
Back Cover......Page 327