Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity

[1]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[2]  Max Beck,et al.  Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes , 1952 .

[3]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[4]  S. Antman,et al.  Travelling waves in hyperelastic rods , 1979 .

[5]  E. Boschi Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .

[6]  S. Antman,et al.  Large buckled states of rotating rods , 1980 .

[7]  R. Grammel Das kritische Drillungsmoment von Wellen , 1923 .

[8]  C. DeSilva,et al.  Thermodynamical Theory of Directed Curves , 1971 .

[9]  J. A. Haringx On highly compressible helical springs and rubber rods, and their application for vibration-free mountings , 1950 .

[10]  Topological properties of the manifolds of configurations for several simple deformable bodies , 1980 .

[11]  J. Lions Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[12]  G. Kirchhoff,et al.  Ueber das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. , 1859 .

[13]  Stuart S. Antman,et al.  Kirchhoff’s problem for nonlinearly elastic rods , 1974 .

[14]  M. Potier-Ferry On the mathematical foundations of elastic stability theory. I. , 1982 .

[15]  J. Alexander,et al.  Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems , 1981 .

[16]  J. Carr,et al.  Beck’s Problem , 1979 .

[17]  Clifford Ambrose Truesdell,et al.  Exact theory of stress and strain in rods and shells , 1957 .

[18]  H. Ziegler Principles of structural stability , 1968 .

[19]  S. Antman,et al.  Global Behavior of Buckled States of Nonlinearly Elastic Rods , 1978 .

[20]  Max Born,et al.  Untersuchungen über die Stabilität der elastischen Linie in Ebene und Raum, unter verschiedenen Grenzbedingungen , 1906 .

[21]  A. Trösch,et al.  Stabilitätsprobleme bei tordierten Stäben und Wellen , 1952 .

[22]  A. Clebsch,et al.  Theorie der Elasticität fester Körper , 1969 .

[23]  A. G. Greenhill On the Strength of Shafting When Exposed Both to Torsion and to End Thrust , 1883 .

[24]  Nonlinear analysis of a twisted axially loaded elastic rod , 1979 .

[25]  S. Antman,et al.  5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods. , 1975, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[26]  A. B. Whitman,et al.  An exact solution in a nonlinear theory of rods , 1974 .

[27]  H. Cohen A non-linear theory of elastic directed curves , 1966 .

[28]  Stuart S. Antman,et al.  Shear and necking instabilities in nonlinear elasticity , 1977 .

[29]  R. Magnus A Generalization of Multiplicity and the Problem of Bifurcation , 1976 .

[30]  Leonhard Euler,et al.  The rational mechanics of flexible or elastic bodies, 1638-1788 : introduction to Leonhardi Euleri Opera omnia, vol. X et XI seriei secundae , 2014 .

[31]  J. Keller,et al.  Strongest Columns and Isoperimetric Inequalities for Eigenvalues , 1962 .

[32]  N. Laws,et al.  A General Theory of Rods , 1966 .

[33]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

[34]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[35]  J. Keller The shape of the strongest column , 1960 .

[36]  H. Ziegler,et al.  Stabilitätsprobleme bei geraden Stäben und Wellen , 1951 .

[37]  Stuart S. Antman,et al.  Ordinary differential equations of non-linear elasticity I: Foundations of the theories of non-linearly elastic rods and shells , 1976 .

[38]  P. Goldbart,et al.  Linear differential operators , 1967 .

[39]  I. Tadjbakhsh,et al.  A nonlinear eigenvalue problem for rotating rods , 1965 .

[40]  Räumliche Verzweigungsprobleme des dünnen elastischen Stabes mit endlichen Verformungen , 1969 .

[41]  H. Weyl,et al.  Philosophy of Mathematics and Natural Science , 1950 .