Summary
The refined asymptotic theory developed recently is applied to three-dimensional analyses of laminated composite shallow shells with various boundary conditions. Problems of cross-ply doubly curved laminated shells subjected to transverse loads are considered. The edge conditions of the shell are such that one pair of the opposite edges is simply supported and the other may be combinations of free, clamped or simply supported edges. On the basis of the refined asymptotic formulation, a systematic and adaptive method is developed by means of separation of variables and a state-space approach, with which analytical solutions to the system of differential equations in the asymptotic theory are determined for laminated shells with various edge conditions.
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Wu, C. P., Tarn, J. Q., Chi, S. M.: A three-dimensional analysis of doubly curved laminated shells. J. Eng. Mech. Div. ASCE122, 391–401 (1996).
Wu, C. P., Tarn, J. Q., Chi, S. M.: An asymptotic theory for dynamic response of doubly curved laminated shells. Int. J. Solids Struct.33, 3813–3841 (1996).
Wu, C. P., Tarn, J. Q., Chen, P. Y.: A refined asymptotic theory of doubly curved laminated shells. J. Eng. Mech. Div. ASCE123, 1238–1246 (1997).
Librescu, L., Khdeir, A. A., Frederick, D.: A shear deformable theory of laminated composite shallow shell-type panels and their response analysis Part I: Free vibration and buckling. Acta Mech.76, 1–33 (1989).
Khdeir, A. A., Librescu, L., Frederick, D.: A shear deformable theory of laminated composite shallow shell-type panels and their response analysis Part II: Static response. Acta Mech.77, 1–12 (1989).
Khdeir, A. A.: Dynamic response of cross-ply laminated circular cylindrical shells with various boundary conditions. Acta Mech.112, 117–134 (1995).
Leissa, A. W., Qatu, M. S.: Equations of elastic deformation of laminated composite shallow shells. J. Appl. Mech.58, 181–188 (1991).
Wu, C. P., Liu, C. C.: Stress and displacement of thick doubly curved laminated shells. J. Eng. Mech. Div. ASCE120, 1403–1428 (1994).
Fan, J., Zhang, J.: Analytical solutions for thick doubly curved laminated shells. J. Eng. Mech. Div. ASCE118, 1338–1356 (1992).
Reddy, J. N.: Exact solutions of moderatively thick laminated shells. J. Eng. Mech. Div. ASCE110, 794–808 (1984).
Reddy, J. N., Liu, C. F.: A higher-order shear deformation theory of laminated elastic shells. Int. J. Eng. Sci.23, 319–330 (1985).
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Wu, C.P., Chi, Y.W. Asymptotic solutions of laminated composite shallow shells with various boundary conditions. Acta Mechanica 132, 1–18 (1999). https://doi.org/10.1007/BF01186956
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DOI: https://doi.org/10.1007/BF01186956