Elastic–viscoplastic, large deformation formulations of a curved quadrilateral thin shell element

An elastic–viscoplastic constitutive law is implemented in the formulations of a curved quadrilateral element based on thin shell theory. The element surface is defined using variable-order polynomials allowing representation of a wide range of shell geometries. The large displacement effects are included by using an incremental stiffness procedure together with the Lagrangian mode of description of motion. The time rate effects may be treated by using explicit, semi-explicit or implicit time marching schemes. A scheme for automatic calculation of time step is used. By allowing steady-state conditions to be reached, plasticity solutions are obtained. Both perfect plasticity and strain hardening are considered. The Von Mises yield rule and the associated flow rule are used to determine plastic deformation. The spread of plasticity in the thickness direction is allowed by using a layered model. The procedures developed are applied to solve elastic-plastic, small and large displacement problems of thin plates and shells and the results obtained are compared with existing solutions to illustrate the validity and accuracy of the present developments.

[1]  E. P. Popov,et al.  Plastic and viscoplastic analysis of axisymmetric shells , 1975 .

[2]  I. Cormeau,et al.  Numerical stability in quasi‐static elasto/visco‐plasticity , 1975 .

[3]  I. Cormeau,et al.  Elastoplastic thick shell analysis by viscoplastic solid finite elements , 1978 .

[4]  O. C. Zienkiewicz,et al.  VISCO-PLASTICITY--PLASTICITY AND CREEP IN ELASTIC SOLIDS--A UNIFIED NUMERICAL SOLUTION APPROACH , 1974 .

[5]  Implicit time integration of elasto-viscoplastic solids subject to the Mohr-Coulomb yield criterion , 1982 .

[6]  O. C. Zienkiewicz,et al.  Analysis of viscoplastic effects in pressure vessels by the finite element method , 1974 .

[7]  T. Y. Yang,et al.  A curved quadrilateral element for static analysis of shells with geometric and material nonlinearities , 1985 .

[8]  O. C. Zienkiewicz,et al.  The visco‐plastic approach to problems of plasticity and creep involving geometric non‐linear effects , 1978 .

[9]  O. C. Zienkiewicz,et al.  Plastic (or visco‐plastic) behaviour of axisymmetric bodies subjected to non‐symmetric loading—semi‐analytical finite element solution , 1979 .

[10]  H. Parisch.  Large displacements of shells including material nonlinearities , 1981 .

[11]  D. Owen,et al.  Elasto-viscoplastic and elasto-plastic large deformation analysis of thin plates and shells , 1982 .

[12]  D. Owen,et al.  Elastic-viscoplastic analysis of plates by the finite element method , 1978 .

[13]  G. Dupuis,et al.  NONLINEAR MATERIAL AND GEOMETRIC BEHAVIOR OF SHELL STRUCTURES. , 1971 .

[14]  Robert Kao.  Large deformation elastic-plastic buckling analysis of spherical caps with initial imperfections , 1980 .

[15]  Joseph Padovan,et al.  On the solution of elastic-plastic static and dynamic postbuckling collapse of general structure , 1983 .

[16]  Piotr Perzyna,et al.  The constitutive equations for rate sensitive plastic materials , 1963 .

[17]  Jan Bäcklund,et al.  Finite element analysis of elasto‐plastic shells , 1974 .

[18]  T. Y. Yang,et al.  Nonlinear dynamic analysis with a 48 d.o.f. curved thin shell element , 1985 .

[19]  J. C. Marques,et al.  Strain hardening representation for implicit quasistatic elasto-viscoplastic algorithms , 1983 .