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Author: Teodor Atanackovic Publisher: World Scientific ISBN: 9814497703 Category : Technology & Engineering Languages : en Pages : 441
Book Description
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflüger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Author: Teodor Atanackovic Publisher: World Scientific ISBN: 9814497703 Category : Technology & Engineering Languages : en Pages : 441
Book Description
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflüger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Author: Teodor M. Atanackovic Publisher: World Scientific ISBN: 9810230540 Category : Technology & Engineering Languages : en Pages : 441
Book Description
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Author: M. Khalid Jawed Publisher: Springer ISBN: 3319769650 Category : Technology & Engineering Languages : en Pages : 127
Book Description
This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.
Author: Stephen P. Timoshenko Publisher: Courier Corporation ISBN: 0486134806 Category : Technology & Engineering Languages : en Pages : 562
Book Description
Written by world-renowned authorities on mechanics, this classic ranges from theoretical explanations of 2- and 3-D stress and strain to practical applications such as torsion, bending, and thermal stress. 1961 edition.
Author: N.A. Alfutov Publisher: Springer Science & Business Media ISBN: 3540490981 Category : Science Languages : en Pages : 344
Book Description
The subject discussed in this book is the stability of thin-walled elastic systems under static loads. The presentation of these problems is based on modern approaches to elastic-stability theory. Special attention is paid to the formulation of elastic-stability criteria, to the statement of column, plate and shell stability problems, to the derivation of basic relationships, and to a discussion of the boundaries of the application of analytic relationships. The author has tried to avoid arcane, nonstandard problems and elaborate and unexpected solutions, which bring real pleasure to connoisseurs, but confuse students and cause bewilderment to some practical engineers. The author has an apprehension that problems which, though interesting, are limited in application can divert the reader's attention from the more prosaic but no less sophisticated general problems of stability theory.
Author: Daniel Martinez Peters Publisher: ISBN: Category : Languages : en Pages : 164
Book Description
Branched elastic rod structures are abundant in engineering and nature, in applications ranging from MEMS devices to human spine models. While buckling is well-understood for problems of this type, stability is often difficult to assess, especially when the model is derived from a nonlinear rod theory. The purpose of this research is to establish criteria for determining nonlinear stability, based upon the minimization of an energy functional. By utilizing variational principles, and Legendre's classical work in particular, a new necessary condition for stability featuring the existence of bounded solutions to a set of Riccati differential equations is established. For a single rod, building on classical results, this condition is also shown to be sufficient for stability. The stability criteria are demonstrated on a number of examples using a simple, planar rod theory. These examples range from a classical strut under axial load to a branched tree-like structure composed of several rods. In the branched model, the stability analysis consists of finding bounded solutions to a set of Riccati equations, which are coupled at branching points. The number of Riccati equations corresponds to the number of rods in the structure. The resulting condition is only necessary for stability of a branched structure, as a sufficient condition could not be established. However, this is the first instance of a stability criterion for branched structures that is based on the second variation of the total energy. The advantage is that this method provides a systematic means of identifying unstable, and therefore physically unrealizable, configurations of a branched structure. Finally, an extension of the stability criteria to other rod theories is discussed.
Author: Teodor Atanackovic
Author: Teodor Atanackovic
Author: Teodor M. Atanackovic
Author: M. Khalid Jawed
Author: J. H. Maddocks
Author: Clifford Truesdell
Author: Stephen P. Timoshenko
Author: N.A. Alfutov
Author: Jayant S. Mandke
Author: Warner Tjardus Koiter
Author: Daniel Martinez Peters