Stability of Nonlinearly Elastic Rods PDF Download
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Author: J. H. Maddocks
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
Author: J. H. Maddocks
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
Author: Teodor Atanackovic
Publisher: World Scientific
ISBN: 9814497703
Category : Technology & Engineering
Languages : en
Pages : 441
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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: N. C. Owen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Teodor M. Atanackovic
Publisher: World Scientific
ISBN: 9810230540
Category : Technology & Engineering
Languages : en
Pages : 441
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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: Charles Shirley Kenney
Publisher:
ISBN:
Category : Elastic rods and wires
Languages : en
Pages : 124
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Book Description
Author: Daniel Martinez Peters
Publisher:
ISBN:
Category :
Languages : en
Pages : 164
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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: Nicholas C. Owen
Publisher:
ISBN:
Category : Deformations (Mechanics)
Languages : en
Pages : 50
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Book Description
Author: Y. B. Fu
Publisher: Cambridge University Press
ISBN: 0521796954
Category : Mathematics
Languages : en
Pages : 541
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Book Description
Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.
Author: Clifford Truesdell
Publisher: Springer
ISBN: 3662397765
Category : Technology & Engineering
Languages : en
Pages : 755
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Book Description
Author: J. H. Maddocks
Publisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 116
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