Some Remarks on the Morphology of Non-Unique Solutions in Nonlinear Elastostatics

1987 ◽  
pp. 177-184
Author(s):  
Franz Karl Labisch
Keyword(s):  
Nonlinear Elastostatics

Strict convexity, strong ellipticity, and regularity in the calculus of variations

1980 ◽  
Vol 87 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Nonlinear Systems ◽  
Calculus Of Variations ◽  
Weak Solutions ◽  
Convex Functions ◽  
Strict Convexity ◽  
Mathematical Tool ◽  
Strong Ellipticity ◽  
Regularity Of Weak Solutions ◽  
Nonlinear Elastostatics

In this paper we investigate the connection between strong ellipticity and the regularity of weak solutions to the equations of nonlinear elastostatics and other nonlinear systems arising from the calculus of variations. The main mathematical tool is a new characterization of continuously differentiable strictly convex functions. We first describe this characterization, and then explain how it can be applied to the calculus of variations and to elastostatics.

The Signorini perturbation scheme in an abstract setting

1991 ◽  
Vol 119 (3-4) ◽  
pp. 373-395 ◽  
Author(s):  
D. R. J. Chillingworth
Keyword(s):  
Logical Structure ◽  
Perturbation Scheme ◽  
Additional Symmetry ◽  
Symmetry Constraints ◽  
Bifurcation Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Abstract Algorithm ◽  
Nonlinear Elastostatics ◽  
Abstract Formulation

SynopsisThe Signorini perturbation scheme is a series expansion algorithm that locates solution branches for a class of symmetry-breaking bifurcation problems in nonlinear elastostatics. The relationship of the formal steps in the algorithm to geometric aspects of the problem is brought out in work of J. E. Marsden and Y.-H. Wan, where an abstract formulation is also considered. In this paper, the abstract algorithm and its geometry are explored further: the logical structure is clarified, and it is shown how the scheme adapts to the presence of additional symmetry constraints.

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