Author | Grioli, Giuseppe. author |
---|---|
Title | Mathematical Theory of Elastic Equilibrium [electronic resource] : Recent Results / by Giuseppe Grioli |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1962 |
Connect to | http://dx.doi.org/10.1007/978-3-642-87432-1 |
Descript | VIII, 168 p. online resource |
IโKinematic Introduction -- ยง 1. Preliminaries -- ยง 2. Fundamental quantities describing the deformation -- ยง 3. A minimum theorem in the kinematics of large deformations -- IIโBasic Equations of the Statics of Continuous Media -- ยง 1. Eulerian expressions of fundamental equations -- ยง 2. Lagrangean expressions of fundamental equations -- ยง 3. Thermodynamic potential -- IIIโIsotropic Bodies โ Thermodynamic Potential -- ยง 1. Isotropic bodies -- ยง 2. Principal properties of the thermodynamic potential -- ยง 3. A property of the thermodynamic potential -- ยง 4. Elasticity of second grade. Signoriniโs thermodynamic potential -- ยง 5. On the most general elasticity of second grade -- ยง 6. A new type of thermodynamic potential proposed by Tolotti -- ยง7. A type of thermodynamic potential proposed by Bordoni -- IVโTransformations Depending on a Parameter. Successive Equations of Elasticity -- ยง 1. Displacements depending on a parameter -- ยง 2. Successive systems. Linear elasticity -- ยง 3. Necessary conditions for the existence of solutions of the successive systems of equations -- ยง 4. On the conditions of compatibility of the successive systems of equations when constraints are present -- ยง 5. An example of a solution of order one -- ยง 6. Successive systems of equations forXrs -- ยง7. The second-order theory of Rivlin -- VโAnalytical Problems Regarding the Fundamental Equations of Isothermal Static Elasticity -- ยง 1. Preliminaries -- ยง 2. Fundamental hypotheses. Statement of the theorems of existence and uniqueness in the case of a principal orientation of infinite order -- ยง 3. Demonstration of Theorem A) -- ยง 4. On the expansion of the solution of the basic set of equations in a power series in ? when there is no axis of equilibrium -- ยง 5. On the existence of solutions and the possibility of expanding them in power series in ? when there is an axis of equilibrium -- ยง 6. Theorems of existence and uniqueness for the linear equations of isothermal static elasticity -- VIโInequalities for the Equilibrium of Slightly Deformable Elastic Bodies -- ยง 1. Preliminaries -- ยง 2. Integral properties -- ยง 3. A basic inequality -- ยง 4. A few consequences of inequality (6.16) -- ยง 5. A new general inequality -- ยง 6. Application of (6.28) to the equilibrium of cylindrical bodies -- ยง 7. On the best at in a case similar to that of uniform bending -- ยง 8. Rectangular prism. A geometrical interpretation of the results -- ยง 9. Inequalities concerning the equilibrium of an arc -- ยง 10. Inequalities regarding the deformation of slightly deformable bodies -- ยง 11. On the deformation of a homogeneous elastic shell under pressure -- ยง 12. New inequalities regarding the displacements -- ยง 13. On the variation of temperature in an adiabatic transformation -- ยง 14. Upper bounds for displacements and stresses -- ยง 15. Other upper bounds for the stresses -- VIIโIntegration of the Fundamental Problem of Static Elasticity -- ยง 1. Preliminaries -- ยง 2. Analytical preface to the integration of the static elasticity problem -- ยง 3. Polynomial approximations of stress components -- ยง 4. Integration method -- ยง 5. Validity of Menabreaโs theorem in non-isothermal cases -- ยง 6. Adaptation of the integration method of ยง 4 to non-isothermal cases -- ยง 7. On the integration of the basic problem of isothermal elastic statics in the case of finite deformation -- ยง 8. Integration method of M. Picone -- ยง 9. On integration of the static problem of the homogeneous plate of arbitrary thickness -- ยง 10. Saint-Venantโs problem -- VIIIโPlane Elasticity -- ยง 1. Preliminaries -- ยง 2. Structure of Airyโs stress function in the problem of plane deformations -- ยง 3. Meaning of the coefficients of the singular part of Airyโs function in the case of plane deformations -- ยง 4. Structure of Airyโs function in the problem of plane stress independent of y3 -- ยง 5. Structure of Airyโs function in the problem of plane stress depending on y3 -- IXโHypo-Elasticity -- ยง 1. Preliminaries -- ยง 2. Basic equations of hypo-elasticity -- ยง 3. Hypo-elastic equilibrium -- ยง 4. Lagrangean form of the equations of hypo-elasticity -- ยง 5. On the solution of the equations of hypo-elasticity in the static case for the body of grade zero -- ยง 6. Some considerations concerning the solution of the general problem of hypo-elastic statics -- XโAsymmetric Elasticity -- ยง 1. Preliminaries -- ยง 2. Basic Eulerian equations -- ยง 3. Basic Lagrangean equations -- ยง 4. Use of the thermodynamic potential -- ยง 5. Equilibrium equations in the linear theory -- ยง 6. Isothermal elastic potential for the small deformations of isotropic bodies -- ยง 7. Recapitulation of the general equations valid in the case of infinitesimal isothermal transformations -- ยง 8. Discussion of an example -- Index of Authors