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Non-linear elastic theory of rectangular reticulated shallow shell structures

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Abstract

Based on fundamental assumptions, an analysis of the constitutive relations between the internal forces and deformations of discrete rectangular reticulated structures is given. On the basis of this, an equivalent continuum model is adopted and the application of the principle of virtual work leads to non-linear governing equations and corresponding boundary conditions.

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References

  1. Ellington, J. P. and H. McCallion, Moments and deflections of a simply-supported beam grillage,Aeronaut. Q., 8 (1957), 360.

    Google Scholar 

  2. Renton, J. D., On the analysis of triangular mesh grillages,Int. J. Solids Struct., 2 (1966), 307.

    Article  Google Scholar 

  3. McDaniel, T. J. and K. J. Chang, Dynamics of rotationally periodic large space structures,J. Sound and Vib.,68, 3(1980), 351.

    Article  Google Scholar 

  4. Williams, F. W., An algorithm for exact eigenvalue calculations for rotationally periodic structures.Int. J. for Num. Meth. in Eng., 23 (1986), 609.

    Article  MATH  Google Scholar 

  5. Anderson, M. S., Buckling of periodic lattice structures,AIAA J.,19, 6(1981), 782.

    MATH  Google Scholar 

  6. Anderson, M. S., Vibration of prestressed periodic lattice structures,AIAA J., 20 (1982), 551.

    Google Scholar 

  7. Anderson, M. S. and F. W. Williams., Natural vibration and buckling of general periodic lattice structures,AIAA J.,24, 1(1986), 163.

    MATH  Google Scholar 

  8. Dean, D. L., Discrete field analysis of structural system, Course No. 203,Int. Center for Mech. Sci., Udine, Italy, Pergamon Press, 1976.

    Google Scholar 

  9. Heki, K. and T. Saka., Stress analysis of lattice plates as anisotropic continuum plates,Proc. IASS Pacific Symposium PartII on tension structures and space frames, Tokyo and Kyoto, Japan, (1973), 663.

  10. Kollár, L., Continuum equations of timber lattice shells,Acta Technica Academiae Scientiarum Hungaricae,94, 3–4(1982), 133.

    MATH  Google Scholar 

  11. Noor, A. K. et al. Continuum models for beam and platelike lattice structures,AIAA J.,16, 12(1978), 1219.

    Article  Google Scholar 

  12. Noor, A. K. and C. M. Andersen, Analysis of beamlike lattice trusses.Computer Meth. in Appl. Mech. and Eng., 20 (1979), 53.

    Article  MATH  Google Scholar 

  13. Noor, A. K. and M. P. Nemeth, Analysis of spatial beamlike lattices with rigid joints,Computer Meth. in Appl. and Eng., 24 (1980), 35.

    Article  MATH  Google Scholar 

  14. Noor, A. K. and L. S. Weisstein, Stability of beamlike lattice trusses,Computer Meth. in Appl. Meth. and Eng., 25 (1981), 179.

    Article  MATH  MathSciNet  Google Scholar 

  15. Nie Guo-hua, Non-linear theory of reticulated shallow shells, Ph.D. thesis, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University of Technology, 1990. (in Chinese)

  16. Volmir, A. S., Flexible plates and shells, Lu Wen-da et al., Trans., Science Press, Beijing, 1963. (Chinese version)

    Google Scholar 

  17. Washizu, K., Variational methods in elasticity and plasticity, Pergamon Press, 1975.

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Guo-hua, N., Ren-huai, L. Non-linear elastic theory of rectangular reticulated shallow shell structures. Appl Math Mech 15, 413–423 (1994). https://doi.org/10.1007/BF02451491

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