Schardt R 1994 Generalized beam theory—an adequate method for coupled stability problems. Schardt R 1966 Eine Erweiterung der technischen Biegetheorie zur berechnung prismatischer Faltwerke. Advanced beam formulations for free vibration analysis of conventional and joined wings. This formulation is extremely suitable for computer implementations and can deal with most typical engineering challenges. International Journal of Solids and Structures, 37, 535—558. Symbols and reference systems that will be used throughout the book are also introduced.
Journal of Applied Mechanics, 78. Journal of Structural Engineering, 110, 2234—2249. Chapter 1 presents the basic equations that the structural analysis is based on: equilibrium equations, strain—displacement geometrical relations, and constitutive equations. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Thin-Walled Structures, 45 2 , 185—198. The shear correction factor is mainly related to the cross-section geometry.
The tensor of inertia and, as a consequence, Equations 2. A detailed description of both formulations will be given in the following chapters of this book. One possible choice is related to the use of Taylor-like polynomials consisting of the 2D base x i z j , where i and j are positive integers. A comprehensive comparison of Euler—Bernoulli and Timoshenko theories was made by Mucichescu 1984. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. International Journal of Applied Mechanics, 2 1 , 117—143. Journal of Applied Mechanics, 68 3 , 382—391.
International Journal of Solids and Structures, 41, 2521—2537. These are known as mechanical boundary conditions. The deformed free-tip crosssections are shown in Figures 3. In: Commentarii Academiae Scientiarum Imperialis Petropolitanae, Petropoli. A large number of numerical benchmarks are given for comparison purposes. An extensive analysis of the effectiveness of higher-order theories is carried out in Chapter 12, where the so-called axiomatic—asymptotic method is presented and exploited to build reduced refined models on the basis of a given accuracy which is given as an input of the analysis. Numerical examples are given in order to highlight the differences between these two models.
It will also be of great interest to graduate and postgraduate students of mechanical, civil and aerospace engineering. Many other higher-order theories which are based on enhanced displacement fields over the beam cross-section have been introduced to include non-classical effects. The 3D elasticity equations were reduced to beam-like structures by Ladevéze and his co-workers Ladéveze and Simmonds, 1996, 1998; Ladéveze et al. Chapter 8 presents the so-called shell-like capabilities of the model. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. The cross-section is still rigid on its plane, it rotates around a neutral surface remaining plane, but it is no longer constrained to remain perpendicular to it, see Figure 2.
Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. The aforementioned literature overview clearly shows the interest in further developments of refined theories for beams. Erasmo Carrera, Gaetano Giunta and Marco Petrolo. El Fatmi R and Zenzri H 2004 A numerical method for the exact elastic beam theory: applications to homogeneous and composite beams. Review of historical contributions Beam theories are extensively used to analyze the structural behavior of slender bodies, such as columns, arches, blades, aircraft wings, and bridges. Free-vibration analyses have been carried out on hollow cylindrical and wing models Carrera et al. The calculation of such a deformed state remains the fundamental problem of 3D elasticity.
Other refined beam models can be found in the excellent review by Kapania and Raciti 1989a,b which focused on bending, vibration, wave propagations, buckling, and post-buckling. Gaetano Giunta Gaetano Giunta graduated in Aerospace Engineering at the Politecnico di Torino in 2004. Schardt R 1989 Verallgemeinerte technische biegetheorie. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. Washizu K 1968 Variational methods in elasticity and plasticity.
Strong and weak forms are provided. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. He became Associate Professor of Aerospace Structures and Computational Aeroelasticity in 2000, and Full Professor at the Politecnico di Torino in 2011. A beam model with only displacement degrees of freedom has been developed Carrera and Petrolo, 2010 and asymptotic-like results were obtained in Carrera and Petrolo 2011. In the case of a free-vibration analysis, similar considerations are still valid. Many torsion-beam theories which are effective for different types of beam sections are known. Carrera E 2003 Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking.
Wagner W and Gruttmann F 2002 A displacement method for the analysis of flexural shear stresses in thin-walled isotropic composite beams. The bending of slender beams, for instance, is well described by the Euler—Bernoulli model, which has three unknowns, whereas, torsion or thin-walled beam analysis requires more sophisticated theories with a larger number of variables. The Poisson ratio, ν, is equal to 0. In this book both symbols ε and γ are used to indicate the engineering strain components. They are the reference models to analyze slender homogeneous structures under bending loads. The first refined model of this book is given in Chapter 3, where the complete linear expansion case is presented. Journal of Aerospace Engineering, In Press.
The choice of Fτ and M is arbitrary, that is, different base functions of any order can be taken into account to model the kinematic field of a beam above the cross-section. This book details classical and modern beam theories. Carrera E, Petrolo M, and Nali P 2011 Unified formulation applied to free vibrations finite element analysis of beams with arbitrary section. This formulation is extremely suitable for computer implementations and can deal with most typical engineering challenges. Early developments, based on kinematic intuitions bending theories , by pioneers such as Leonardo da Vinci, Euler, Bernoulli, Navier, and Barre de Saint Venant, have permitted us to consider the most general three-dimensional 3D problem as a one-dimensional 1D problem in which the unknowns only depend on the beam-axis position. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc.