메뉴 건너뛰기




Volumn 61, Issue 4, 2008, Pages 497-522

Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; BOUNDARY VALUE PROBLEMS; FREQUENCY DIVISION MULTIPLEXING; LOADING; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING; PHASE TRANSITIONS; TOPOLOGY;

EID: 54949112898     PISSN: 00335614     EISSN: 14643855     Source Type: Journal    
DOI: 10.1093/qjmam/hbn014     Document Type: Article
Times cited : (32)

References (21)
  • 1
    • 0016569455 scopus 로고
    • Equilibrium of bars
    • J. L. Ericksen, Equilibrium of bars, J. Elast. 5 (1975) 191-201.
    • (1975) J. Elast , vol.5 , pp. 191-201
    • Ericksen, J.L.1
  • 2
    • 0030215097 scopus 로고    scopus 로고
    • Ericksen's bar revisited: Energy wiggles
    • L. Truskinovsky and G. Zanzotto, Ericksen's bar revisited: Energy wiggles, J. Mech. Phys. Solids 44 (1996) 1371-1408.
    • (1996) J. Mech. Phys. Solids , vol.44 , pp. 1371-1408
    • Truskinovsky, L.1    Zanzotto, G.2
  • 3
    • 0018711591 scopus 로고
    • Co-existent phases in the one-dimensional static theory of elastic bars
    • R. D. James, Co-existent phases in the one-dimensional static theory of elastic bars, Arch. Ration. Mech. Anal. 72 (1979) 99-140.
    • (1979) Arch. Ration. Mech. Anal , vol.72 , pp. 99-140
    • James, R.D.1
  • 4
    • 0033284514 scopus 로고    scopus 로고
    • Dynamics of phase transitions and hysteresis in a viscoelastic Ericksen's bar on an elastic foundation
    • A. Vainchtein, Dynamics of phase transitions and hysteresis in a viscoelastic Ericksen's bar on an elastic foundation, J. Elast. 57 (1999) 243-280.
    • (1999) J. Elast , vol.57 , pp. 243-280
    • Vainchtein, A.1
  • 5
    • 49049120109 scopus 로고    scopus 로고
    • Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem
    • D. Y. Gao and R. W. Ogden, Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem, Z. Angew. Math. Phys. 59 (2008) 498-517.
    • (2008) Z. Angew. Math. Phys , vol.59 , pp. 498-517
    • Gao, D.Y.1    Ogden, R.W.2
  • 7
    • 0032324860 scopus 로고    scopus 로고
    • Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications
    • D. Y. Gao, Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications, IMA J. Appl. Math. 61 (1998) 199-235.
    • (1998) IMA J. Appl. Math , vol.61 , pp. 199-235
    • Gao, D.Y.1
  • 9
    • 0031164989 scopus 로고    scopus 로고
    • Discretization and hysteresis
    • R. Rogers and L. Truskinovsky, Discretization and hysteresis, Physica B 233 (1997) 370-375.
    • (1997) Physica B , vol.233 , pp. 370-375
    • Rogers, R.1    Truskinovsky, L.2
  • 10
    • 33751535189 scopus 로고    scopus 로고
    • Analysis of microstructures and phase transition phenomena in one-dimensional, non-linear elasticity by convex optimization
    • R. Meziat and J. Villalobos, Analysis of microstructures and phase transition phenomena in one-dimensional, non-linear elasticity by convex optimization, Struct. Multidisciplinary Optim. 32 (2006) 507-519.
    • (2006) Struct. Multidisciplinary Optim , vol.32 , pp. 507-519
    • Meziat, R.1    Villalobos, J.2
  • 11
    • 24144435933 scopus 로고    scopus 로고
    • On the use of nonstandard finite difference methods
    • K. C. Patidar, On the use of nonstandard finite difference methods, J. Differ. Equ. Appl. 11 (2005) 735-758.
    • (2005) J. Differ. Equ. Appl , vol.11 , pp. 735-758
    • Patidar, K.C.1
  • 12
    • 0032070043 scopus 로고    scopus 로고
    • Equilibrium conditions for Young measures
    • P. Pedregal, Equilibrium conditions for Young measures, SIAM J. Control Optim. 36 (1998) 797-813.
    • (1998) SIAM J. Control Optim , vol.36 , pp. 797-813
    • Pedregal, P.1
  • 13
    • 33746230423 scopus 로고    scopus 로고
    • Nonconvex semi-linear problems and canonical duality solutions
    • ed. D. Y. Gao & R. W. Ogden; Kluwer, Dordrecht
    • D. Y. Gao, Nonconvex semi-linear problems and canonical duality solutions, Advances in Mechanics and Mathematics, Vol. II (ed. D. Y. Gao & R. W. Ogden; Kluwer, Dordrecht 2003) 261-312.
    • (2003) Advances in Mechanics and Mathematics , vol.2 , pp. 261-312
    • Gao, D.Y.1
  • 14
    • 0343826885 scopus 로고    scopus 로고
    • Analytic solutions and triality theory for non-convex and nonsmooth variational problems with applications
    • D. Y. Gao, Analytic solutions and triality theory for non-convex and nonsmooth variational problems with applications, Nonlinear Anal. 42 (2000) 1161-1193.
    • (2000) Nonlinear Anal , vol.42 , pp. 1161-1193
    • Gao, D.Y.1
  • 16
    • 0001168373 scopus 로고
    • Geometric nonlinearity: Potential energy, complementary energy, and the gap function
    • D. Y Gao and G. Strang, Geometric nonlinearity: Potential energy, complementary energy, and the gap function, Q. Appl. Math. 47 (1989) 487-504.
    • (1989) Q. Appl. Math , vol.47 , pp. 487-504
    • Gao, D.Y.1    Strang, G.2
  • 17
    • 0033357977 scopus 로고    scopus 로고
    • General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics
    • D. Y. Gao, General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics, Meccanica 34 (1999) 169-198.
    • (1999) Meccanica , vol.34 , pp. 169-198
    • Gao, D.Y.1
  • 20
    • 4344679146 scopus 로고    scopus 로고
    • Complementary variational principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation
    • D. Y. Gao, Complementary variational principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation, Math. Mech. Solids 9 (2004) 285-305.
    • (2004) Math. Mech. Solids , vol.9 , pp. 285-305
    • Gao, D.Y.1
  • 21
    • 42649131756 scopus 로고    scopus 로고
    • Multi-scale modeling and canonical dual finite element method in phase transitions of solids
    • D. Y. Gao and H. F. Yu, Multi-scale modeling and canonical dual finite element method in phase transitions of solids, Int. J. Solids Struct. 45 (2008) 3660-3673.
    • (2008) Int. J. Solids Struct , vol.45 , pp. 3660-3673
    • Gao, D.Y.1    Yu, H.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.