COMPUTATIONAL STRUCTURAL MECHANICS - Static and Dynamic Behaviors

Computational Structural Mechanics: Static and Dynamic Behaviors provides a cutting-edge treatment of functionally graded materials and the computational methods and solutions of FG static and vibration problems of plates. Using the Rayleigh-Ritz method, static and dynamic problems related to behavior of FG rectangular, Levy, elliptic, skew and annular plates are discussed in detail. A thorough review of the latest research results, computational methods and applications of FG technology make this an essential resource for researchers in academia and industry. Explains application-oriented treatments of the functionally graded materials used in industry Addresses relevant algorithms and key computational techniques Provides numerical solutions of static and vibration problems associated with functionally graded beams and plates of different geometries 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