An existence theorem for inextensible nets with slack

Mathematics and Mechanics of Solids

Volumn 17, Issue 5, 2012, Pages 460-472

  Paroni, Roberto ^a  

^a UNIVERSITY OF SASSARI   (Italy)

Author keywords

convergence; Dimension reduction; linear elasticity; thin walled cross section beams

Indexed keywords

APPLIED LOADS; DIMENSION REDUCTION; EXISTENCE THEOREM; LINEAR ELASTICITY; THIN-WALLED CROSS-SECTION BEAMS; VARIATIONAL PROBLEMS;

MATHEMATICAL TECHNIQUES; MECHANICS;

ELASTICITY;

EID: 84863219214     PISSN: 10812865     EISSN: 17413028     Source Type: Journal    
DOI: 10.1177/1081286511423124     Document Type: Article

References (16)

1. Rivlin RS. Plane strain of a net formed by inextensible cords. J Rational Mech Anal. 1955 ; 4: 951-974
2. Rivlin RS. The deformation of a membrane formed by inextensible cords. Arch Rational Mech Anal. 1958/1959 ; 2: 447-476
3. Pipkin AC. Inextensible networks with slack. Quart Appl Math. 1982/1983 ; 40: 63-71
4. Pipkin AC. Energy minimization for nets with slack. Quart Appl Math. 1986 ; 44: 249-253
5. Williams WO Waves and Stability in Continuous Media (Sorrento, 1989). River Edge, NJ: World Scientific Publishing ; 1991: 408-418.
6. Grisvard P Elliptic problems in nonsmooth domains. Boston, MA: Pitman (Advanced Publishing Program) ; 1985 :
7. Evans LC, Gariepy RF Measure theory and fine properties of functions. (Studies in Advanced Mathematics). Boca Raton, FL: CRC Press ; 1992 :
8. Rudin W Functional analysis. 2 nd edn (International Series in Pure and Applied Mathematics). New York: McGraw-Hill, 1991. New York: McGraw-Hill ; 1991 :
9. Pipkin AC. Some developments in the theory of inextensible networks. Quart Appl Math. 1980/1981 ; 38: 343-355
10. Pipkin AC Homogenization and effective moduli of materials and media (Minneapolis, MN, 1984/1985). New York: Springer ; 1986: 182-195.
11. Ekeland I, Témam R Convex analysis and variational problems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) ; 1999 :
12. Rockafellar RT Convex analysis (Princeton Landmarks in Mathematics). Princeton, NJ: Princeton University Press ; 1997 :
13. Dunford N, Schwartz JT Linear operators. Part I (Wiley Classics Library). New York: John Wiley & Sons Inc ; 1988 :
14. Fonseca I, Leoni G Modern methods in the calculus of variations: Lp spaces (Springer Monographs in Mathematics). New York: Springer ; 2007 :
15. Šilhavý M. The divergence theorem for divergence measure vectorfields on sets with fractal boundaries. Math Mech Solids. 2009 ; 14: 445-455
16. Lucchesi M, Šilhavý M, Zani N. A new class of equilibrated stress fields for no-tension bodies. J Mech Materials Struct. 2006 ; 1: 503-539