J.L. Ericksen’s Work on Cosserat Theories of Rods and Shells
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OpenAlex topics: Elasticity and Material Modeling · Structural Analysis and Optimization · Drilling and Well Engineering
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References (38)
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1. Ericksen, J.L., Truesdell, C.: Exact theory of stress and strain in rods and shells. Arch. Ration. Mech. Anal. 1, 295–323 (1958)10.1007/BF00298012 ↗
2. Euler, L.: Genuina principia doctrinae de statu equilibrii et motu corporum tam perfecte flexibilium quam elasticorum. Novi Comm. Petrop. 15, 381–413 (1770); In Op. Omnia (2) 11, 37–61
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4. Kirchhoff, G.: Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Crelle’s J. 40, 51–88 (1850); In Ges. Abh., 237–279
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10. Ericksen, J.L., Fields, T.: Handbuch der Physilk, vol. III/1, pp. 794–858. Springer, Berlin (1960)
11. Antman, S.S.: The theory of rods. In: Truesdell, C. (ed.) Handbuch der Physik, vol. VIa/2, pp. 641–703. Springer, Berlin (1972)
12. Naghdi, P.M.: The theory of shells. In: Truesdell, C. (ed.) Handbuch der Physik, vol. VIa/2, pp. 425–640. Springer, Berlin (1972)
13. Ericksen, J.L.: Simpler static problems in nonlinear theories of rods. Int. J. Solids Struct. 6, 371–377 (1970)10.1016/0020-7683(70)90045-4 ↗
14. Ericksen, J.L.: Uniformity in shells. Arch. Ration. Mech. Anal. 37, 73–84 (1970)10.1007/BF00281663 ↗
15. Ericksen, J.L.: Wave propagation in thin elastic shells. Arch. Ration. Mech. Anal. 43, 167–178 (1971)10.1007/BF00251450 ↗
16. Ericksen, J.L.: Symmetry transformations for thin elastic shells. Arch. Ration. Mech. Anal. 47, 1–14 (1972)10.1007/BF00252184 ↗
17. Ericksen, J.L.: The simplest problems for elastic Cosserat surfaces. J. Elast. 2, 101–107 (1972)10.1007/BF00046058 ↗
18. Ericksen, J.L.: Simpler problems for elastic plates. Int. J. Solids Struct. 9, 141–149 (1973)10.1016/0020-7683(73)90038-3 ↗
19. Ericksen, J.L.: Apparent symmetry of certain thin elastic shells. J. Méc. 12, 173–181 (1973)
20. Ericksen, J.L.: Apparent symmetry of plates of variable heights and thickness. Rend. Sci. Ist. Lomb. A 107, 71–82 (1973)
21. Ericksen, J.L.: Plane infinitesimal waves in homogeneous elastic plates. J. Elast. 3, 161–167 (1973)10.1007/BF00052890 ↗
22. Ericksen, J.L.: Plane waves and the stability of elastic plates. Q. Appl. Math. 32, 343–345 (1974)10.1090/qam/99677 ↗
23. Ericksen, J.L.: Equilibrium of bars. J. Elast. 5, 191–202 (1975)10.1007/BF00126984 ↗
24. Ericksen, J.L.: Simpler problems for elastic Cosserat surfaces. J. Elast. 7, 1–11 (1977)10.1007/BF00041126 ↗
25. Ericksen, J.L.: Theory of Cosserat surfaces and its applications to shells, interfaces and cell membranes. In: Glockner, G.P., Epstein, M., Malcolm, D.J. (eds.) Proc. Intl. Symp. on Recent Developments in Theory and Application of Generalized and Oriented Media, pp. 27–39 (1979). Amer. Acad. Mec.
26. Podio-Guidugli, P.: An exact derivation of the thin plate equation. J. Elast. 22, 121–133 (1989)10.1007/BF00041107 ↗
27. Antman, S.S., Marlow, R.S.: Material constraints, Lagrange multipliers, and compatibility. Arch. Ration. Mech. Anal. 116, 257–299 (1991)10.1007/BF00375123 ↗
28. Rubin, M.B.: Cosserat Theories. Kluwer, Dordrecht (2000)
29. Antman, S.S.: Nonuniqueness of equilibrium states for bars in tension. J. Math. Anal. Appl. 44, 333–349 (1973)10.1016/0022-247X(73)90063-2 ↗
30. Antman, S.S., Osborn, J.E.: The principle of virtual work and integral laws of motion. Arch. Ration. Mech. Anal. 69, 231–262 (1979)10.1007/BF00248135 ↗
31. Antman, S.S.: Convergence properties of hierarchies of dynamical theories of rods and shells. Z. Angew. Math. Phys. 48, 874–884 (1997)10.1007/s000330050070 ↗
32. Antman, S.S.: Ordinary differential equations of one-dimensional nonlinear elasticity I: foundations of the theories of nonlinearly elastic rods and shells. Arch. Ration. Mech. Anal. 61, 307–351 (1976)10.1007/BF00250722 ↗
33. Antman, S.S.: Nonlinear Problems of Elasticity, 3rd edn. Springer, Berlin (2023)
34. Dal Maso, G.: An Introduction to ${\varGamma }$-Convergence. Birkhäuser, Basel (1993)10.1007/978-1-4612-0327-8 ↗
35. von Kármán, T.: Festigkeitsprobleme in Maschinenbau. In: Enc. Math. Wiss., vol. IV/4 C, pp. 311–385 (1910)
36. Ball, J.M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63, 337–403 (1977)10.1007/BF00279992 ↗
37. Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics, 4th edn. Springer, Berlin (2016)10.1007/978-3-662-49451-6 ↗
38. James, R.D.: The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy. J. Elast. 11, 239–269 (1981)10.1007/BF00041939 ↗