×

An integral equation analysis of inelastic shells. (English) Zbl 0675.73047

Summary: This paper presents an integral equation approach for the analysis of deformation and stresses in inelastic shells of arbitrary shape subjected to arbitrary loading. The proposed mathematical model is completely consistent and is derived by transforming the three-dimensional equations from the Cartesian to the appropriate curvilinear coordinates of the shell. Appropriate kinematic assumptions for the dependence of the displacements on the thickness coordinate of the shell and assumptions regarding the loads at the ends are introduced consistently in the model to take advantage of the thinness of the shell. Numerical implementation and numerical results are presented for elastic and inelastic deformation of axisymmetric shells subjected to axisymmetric loading. These results are compared against exact elasticity, Love-Kirchhoff model analysis of inelastic cylindrical shells and finite element solutions.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74K15 Membranes
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)

Software:

MACSYMA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anand, L. (1982): Constitutive equations for the rate-dependent deformation of metals at elevated temperatures. J. Eng. Mater. Technol. 104, 12-17
[2] Banerjee, P. K.; Butterfield, R. (1981): Boundary element methods in engineering science. London: McGraw-Hill · Zbl 0499.73070
[3] Brebbia, C. A.; Telles, J. C. F.; Wrobel, L. C. (1984): Boundary element techniques: Theory and applications in engineering. Berlin, Heidelberg, New York: Springer · Zbl 0556.73086
[4] Dikmen, M. (1982): Theory of thin elastic shells. London: Pitman · Zbl 0478.73043
[5] Flügge, W. (1972): Tensor analysis and continuum mechanics. Berlin, Heidelberg, New York: Springer · Zbl 0224.73001
[6] Fung, Y. C. (1965): Foundations of solid mechanics. New York: Prentice-Hall
[7] Kollmann, F. G.; Mukherjee, S. (1984): Inelastic deformation of thin cylindrical shells under axisymmetric loading. Ing. Arch. 54, 355-367 · Zbl 0554.73064
[8] Kollmann, F. G.; Mukherjee, S. (1985): A general, geometrically linear theory of inelastic thin shells. Acta Mech. 57, 41-67 · Zbl 0575.73080
[9] Kumar, V.; Morjaria, M.; Mukherjee, S. (1980): Numerical integration of some stiff constitutive models of inelastic deformation. J. Eng. Mater. Technol. 102, 92-96
[10] Mukherjee, S.; Kumar, V.; Chang, K. J. (1977): Elevated temperature inelastic analysis of metallic media under time-varying loads using state variable theories. ERDA Report No. C00-2733-12 · Zbl 0379.73014
[11] Mukherjee, S. (1982): Boundary element methods in creep and fracture. London: Elsevier · Zbl 0534.73070
[12] Mukherjee, S.; Poddar, B. (1986): An integral equation formulation for elastic and inelastic shell analysis. In: Proc. Int. Conf. BEM in Engineering, Beijing, P. R. China. London: Pergamon Press · Zbl 0615.73096
[13] Naghdi, P. M. (1963): Foundations of elastic shell theory. In: Sneddon, I. N.; Hill, R. (eds.): Progress in solid mechanics, vol. IV. Amsterdam: North Holland · Zbl 0115.19401
[14] Naghdi, P.M. (1972): The theory of plates and shells. In: Flügge, W.; Truesdell, C. (eds.): Handbuch der Physik, vol. VIa/2. Berlin, Heidelberg, New York: Springer · Zbl 0283.73034
[15] Newton, D. A.; Tottenham, H. (1968): Boundary value problems in thin shallow shells of arbitrary plan from. J. Eng. Math. 2, 211-223 · Zbl 0179.54602
[16] Poddar, B. (1987): An integral equation analysis of inelastic shells. Ph. D. thesis, Cornell University, New York · Zbl 0675.73047
[17] Rajiyah, H.; Mukherjee, S. (1987): A comparison of boundary element and finite element methods for inelastic axisymmetric problems with large strains and rotations. In: Nakazawa, S.; Willam, K.; Rebelo, N. (eds.): Advances in inelastic analysis. AMD vol. 88, pp. 199-222 · Zbl 0627.73045
[18] Rand, R. H. (1984): Computer algebra in applied mathematics: An introduction to MACSYMA. Boston: Pitman · Zbl 0583.68012
[19] Sanders, J. L.; Simmonds, J. G. (1970): Concentrated forces on shallow cylindrical shells. J. Appl. Mech. 37, 367-373 · Zbl 0197.22004
[20] Timoshenko, S. P.; Goodier, J. N. (1970): Theory of elasticity. New York: McGraw-Hill · Zbl 0266.73008
[21] Timoshenko, S. P.; Woinowsky-Krieger, S. (1982): Theory of plates and shells. New York: McGraw-Hill · Zbl 0114.40801
[22] Tottenham, H. (1979): The boundary element method for plates and shells. In: Banerjee, P. K.; Butterfield, R. (eds): Progress in boundary element methods, vol. 2, pp. 173-205. London: Elsevier · Zbl 0451.73080
[23] Zienkiewicz, O. C. (1977): The finite element method. London: McGraw-Hill · Zbl 0435.73072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.