Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells

The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. One of the problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration. This book comprises seven chapters. Each chapter contains adequate introductory material so that an engineering graduate who is familiar with basic understanding of beams, plates and shells will be able to follow it. The advantages and disadvantages of traditional perturbation method are introduced in Chapter 1. A two-step perturbation method and its application in the nonlinear analysis of beams, plates and shells are presented in detail in each chapter. Some difficult tasks in nonlinear analysis of structures are included, for example, the nonlinear analysis of Euler-Bernoulli beams based on the exact expression of the curvature is presented in Chapter 2; the nonlinear vibration analysis of functionally graded fiber reinforced composite laminated plates in hygrothermal environments is presented in Chapter 3; the geometrically nonlinear bending analysis of shear deformable plates with four free edges resting on elastic foundations is presented in Chapter 4; the contact postbuckling analysis of composite laminated plates resting on tensionless elastic foundations subjected to thermal and mechanical loads is presented in Chapter 5; the nonlinear vibration of functionally graded fiber reinforced composite laminated cylindrical shells without or with piezoelectric fiber reinforced composite actuators is presented in Chapter 6; and the contact postbuckling analysis of anisotropic cylindrical shells surrounded by an elastic medium subjected to thermal and mechanical loads is presented in Chapter 7.