Nonlinear Composite Beam Theory

From an authoritative expert whose work on modern helicopter rotor blade analysis has spanned over three decades, comes the first consistent and rigorous presentation of beam theory. Beginning with an overview of the theory developed over the last 60 years, Dr. Hodges addresses the kinematics of beam deformation, provides a simple way to characterize strain in an initially curved and twisted beam, and offers cross-sectional analysis for beams with arbitrary cross sections and composed of arbitrary materials. He goes on to present a way to accurately recover all components of cross-sectional strain and stress before providing a natural one-dimensional (1-D) theory of beams. Sample results for both cross-sectional and 1-D analysis are presented as is a parallel treatment for thin-walled beams.

Annotation This is the first monograph devoted to the foundation of the theory of composite anisotropic thin-walled beams and to its applications in various problems involving the aeronautical/aerospace, helicopter, naval and mechanical structures. Throughout the theoretical part, an effort was made to provide the treatment of the subject by using the equations of the 3-D elasticity theory. Non-classical effects such as transverse shear, warping constraint, anisotropy of constituent materials yielding the coupling of twist-bending (lateral), bending (transversal)-extension have been included and their implications have been thoroughly analyzed. Thermal effects have been included and in order to be able to circumvent their deleterious effects, functionally graded materials have been considered in their construction. Implications of the application of the tailoring technique and of the active feedback control on free vibration, dynamic response, instability and aeroelasticity of such structures have been amply investigated. Special care was exercised throughout this work to address and validate the adopted solution methodologies and the obtained results against those available in the literature and obtained via numerical or experimental means.

This book presents a comprehensive study of the nonlinear statics and dynamics of composite beams and consists of solutions with and without active elements embedded in the beams. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Two independent numerical solutions for the steady state and the transient responses are presented. The author illustrates that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. Other key areas considered include calculation of the effect of perturbing the steady state solution, coupled nonlinear flap-lag dynamics of a rotating articulated beam with hinge offset and aerodynamic damping, and static and dynamic responses of nonlinear composite beams with embedded anisotropic piezo-composite actuators. The book is intended as a thorough study of nonlinear elasticity of slender beams and is targeted to researchers, graduate students, and practicing engineers in the fields of structural dynamics, aerospace structures, and mechanical engineering.

Nonlinear Finite Element Analysis of Composite and Reinforced Concrete Beams presents advanced methods and techniques for the analysis of composite and FRP reinforced concrete beams. The title introduces detailed numerical modeling methods and the modeling of the structural behavior of composite beams, including critical interfacial bond-slip behavior. It covers a new family of composite beam elements developed by the authors. Other sections cover nonlinear finite element analysis procedures and the numerical modeling techniques used in commercial finite element software that will be of particular interest to engineers and researchers executing numerical simulations. Gives advanced methods and techniques for the analysis of composite and fiber Reinforced Plastic (FRP) and reinforced concrete beams Presents new composite beam elements developed by the authors Introduces numerical techniques for the development of effective finite element models using commercial software Discusses the critical issues encountered in structural analysis Maintains a clear focus on advanced numerical modeling

Many engineering problems can be solved using a linear approximation. In the Finite Element Analysis (FEA) the set of equations, describing the structural behaviour is then linear K d = F (1.1) In this matrix equation, K is the stiffness matrix of the structure, d is the nodal displacements vector and F is the external nodal force vector. Characteristics of linear problems is that the displacements are proportional to the loads, the stiffness of the structure is independent on the value of the load level. Though behaviour of real structures is nonlinear, e.g. displacements are not proportional to the loads; nonlinearities are usually unimportant and may be neglected in most practical problems.

* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Provides ready-to-use governing equations.

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of nonlinear dynamics in dynamical systems and deformable solids.