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2013 | Buch

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Nonlinear Structural Mechanics

Theory, Dynamical Phenomena and Modeling

verfasst von: Walter Lacarbonara

Verlag: Springer US

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a unified treatment of the foundations of nonlinear structural mechanics and dynamics, in addition to its modern computational aspects and the prominent nonlinear structural phenomena, tackling both the mathematical and applied sciences.

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling is an excellent reference for engineers of various disciplines, students, and researchers involved with nonlinear dynamics and structural mechanics.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Concepts, Methods, and Paradigms

Abstract

Introductory concepts such as those of geometric and material nonlinearities are presented through a rich collection of simple yet illuminating examples shedding light on the phenomenological, theoretical and computational aspects. Most of the basic concepts are elucidated, such as the geometric stiffness, the role of nonlinear constitutive laws, the linearization about a natural or prestressed equilibrium state, the critical conditions/limit states due to the loss of elastic stability and the postcritical behaviors beyond the limit states. A major focus is placed on path following techniques for the construction of equilibrium paths or for continuation of periodic solutions. The illustrative examples range from MEMS systems to flutter control of airfoils.

Walter Lacarbonara

Chapter 2. Stability and Bifurcation of Structures

Abstract

An overview of the modern theory of stability and bifurcation is presented in the context of mechanical and structural systems subject to conservative and nonconservative forces. The static and dynamic loss of stability is discussed in a unified framework enriched by a variety of paradigmatic examples featuring flutter of thin airfoils and bluff bodies, galloping, the Mathieu-type instability due to parametric excitations and the stability of distributed-parameter systems such as cables, beams, rings, wings, plates, and bridge structures, including the torsional-flexural instability of thin-walled beams.

Walter Lacarbonara

Chapter 3. The Elastic Cable: From Formulation to Computation

Abstract

This chapter addresses the derivation of the nonlinear problem of purely extensible elastic cables, treated as a one-dimensional continuum. The cable problem combines the striking simplicity of its nonlinear formulation with its eminently complex structural behavior. The cable problem is employed here as a powerful illustrative problem which allows the chief steps in a full nonlinear reduced formulation of the governing equations to be introduced, together with the leading computational steps in nonlinear structural analyses and further provides the motivation for studying nonlinear structural systems such as beams, arches, and rings within the more general context of three-dimensional theory. Cable applications feature the nonlinear formulation for tethered satellite systems employed in space applications and the study of the galloping instability of iced cables subject to steady winds.

Walter Lacarbonara

Chapter 4. Nonlinear Mechanics of Three-Dimensional Solids

Abstract

This chapter presents the theory of nonlinear three-dimensional solids with regard to the geometry of deformation, stress, interactions with the environment, and constitutive equations. A unique feature of this presentation is that a few key concepts such as the stretch vector or the surface stretch vector are introduced in an original fashion that paves the way for reduced structural theories of special slender (beam-like) or thin (plate-like) bodies. The presented nonlinear three-dimensional theory constitutes the theoretical framework from which reduced or constrained theories of slender or thin bodies can be deduced or within which they can be fully justified. A few examples are presented to show the richness of the implications stemming from three-dimensional theory.

Walter Lacarbonara

Chapter 5. The Nonlinear Theory of Beams

Abstract

The nonlinear theory of beams undergoing planar motions is presented in its kinematic, dynamical, and constitutive aspects. The classical form of the equations of motion and the associated weak form are derived together with ad hoc approximate theories for planar weakly nonlinear motions such as the Mettler theory. Experimental results that corroborate the analytical predictions are presented for beams restricted to planar motion. The theory is then generalized to three-dimensional finite motions in the context of exact, intrinsic, and induced theories derived from three-dimensional theory. Different constrained versions of the theory, the linearized elastodynamic problem, the axial-torsional-shearing/flexural uncoupling, and the nonlinear coupling between different load-carrying mechanisms are presented.

Walter Lacarbonara

Chapter 6. Elastic Instabilities of Slender Structures

Abstract

This chapter addresses the static and dynamic loss of stability of slender beams. The buckling problem is discussed for uniform and nonuniform straight beams with compact cross sections subject to conservative instabilizing loads. In addition, the loss of stability of the straight equilibrium configuration of slender beams with open thin-walled cross sections into twisted/bent buckled states is addressed in general theoretical and computational terms and with examples. Dynamic instabilities called parametric resonances are studied both theoretically and experimentally in slender beams subject to parametric excitations such as pulsating end thrusts causing large-amplitude oscillations. The chapter also presents a fully nonlinear model of aircraft wings subject to steady airflows causing a Hopf bifurcation called flutter together with a discussion of post-flutter behaviors.

Walter Lacarbonara

Chapter 7. The Nonlinear Theory of Curved Beams and Flexurally Stiff Cables

Abstract

This chapter discusses the nonlinear theory of curved beams and ring structures used in a wide range of engineering applications including aircraft fuselages, arch bridges, roof structures, turbomachinery blades, and water/oil/gas tanks. The theory is derived starting from planar motions proceeding toward the three-dimensional setting within which more complex motions can occur. Important aspects of the stability of arches and deeply buckled beams are discussed in the more general context of prestressed curved beams. The dynamical formulation of cables suffering axis stretching and flexural curvature is presented within the geometrically exact framework of prestressed compact curved rods. This refined theory of cables is useful to study the states of stress in boundary layers such as those arising near anchorage devices of cable stays or suspension cables with a view to the assessment of their fatigue life or damage detection techniques.

Walter Lacarbonara

Chapter 8. The Nonlinear Theory of Plates

Abstract

The formulation of geometrically exact theories for thin plates, their approximations and differences with respect to either linear or ad hoc nonlinear theories (such as the Föppl–von Karman theory) are presented. The equations of motion are modified for various situations and are compared with experimental results. Buckling and linear vibration are discussed for isotropic single-layer and multilayer composite plates. Higher order theories of thick multilayer laminated composite plates are also discussed highlighting the prominent role of normal and transverse shear deformations. These theories can be employed in a wide variety of fields (civil, aerospace, mechanical, naval, microengineering) that extensively make use of multilayer isotropic or orthotropic composite plates reinforced with conventional (e.g., carbon fibers) or nonconventional (e.g., carbon nanotubes) fibers.

Walter Lacarbonara

Chapter 9. The Nonlinear Theory of Cable-Supported Structures

Abstract

State-of-the-art nonlinear theories of formidable structures such as suspension bridges suspended in the air over thousands of meters are presented. Very long cables made of thousands of strands, beams, and tall towers are suitably coupled to maximize the static and dynamic load-bearing capacity of the bridge. The fundamental nonlinear static and dynamic behaviors are outlined by considering typical equilibrium paths that include wind-induced effects. The role of mechanical asymmetry is highlighted in the nonlinear precritical behaviors (hardening for downward vertical loads and softening for upward loads) before reaching the limit states such as the aeroelastic torsional divergence or the coupled flexural-torsional flutter condition. These nonlinear theories are particularly important for future bridge designs, especially for the limit states that result from the loss of elastic stability, flutter instability, or vortex-induced instabilities. This chapter also discusses a nonlinear modeling framework for cable-stayed bridges and for general guyed structures such as offshore platforms or masts for telecommunications.

Walter Lacarbonara

Chapter 10. The Nonlinear Theory of Arch-Supported Structures

Abstract

This chapter presents the nonlinear theory of arch-supported structures that exploit the large load-bearing capacities of arches when they are subject to compressional states of stress. These structures exhibit nonsymmetric precritical behaviors opposite to those of suspension cables (softening for downward loads and hardening for upward loads). The theory is shown in the context of a recent arch bridge design, the bridge called Ponte della Musica on the Tiber river in Rome. The elastic loss of stability due to both traffic-induced vertical loads and the flutter condition are investigated using flutter derivatives obtained in wind tunnel tests. The sensitivity of flutter with respect to important parameters such as the wind angle of attack, the level of prestress in the bridge, and structural damping is also elucidated.

Walter Lacarbonara

Chapter 11. Discretization Methods

Abstract

This chapter covers the problem of space discretization of conservative and nonconservative nonlinear distributed-parameter systems by illustrating the properties and underlying methodologies typical of prominent discretization approaches employed in mechanics and dynamics, with a specific focus on semi-analytical methods. The method of weighted residuals in the form due to Faedo and Galerkin and a powerful variational method such as the Rayleigh–Ritz method are elucidated with a wealth of details. Recent advances in nonlinear finite element formulations of dynamical problems suitable for continuation strategies are also reported.

Walter Lacarbonara

Backmatter

Titel: Nonlinear Structural Mechanics
verfasst von: Walter Lacarbonara
Verlag: Springer US
Electronic ISBN: 978-1-4419-1276-3
Print ISBN: 978-1-4419-1275-6
DOI: https://doi.org/10.1007/978-1-4419-1276-3

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