Publications

Geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites

Hammerand, Daniel C.; Kapania, Rakesh K.

A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log timescale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson method used to find the incremental displacements in each time step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping or buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap through examples are presented here. In some cases, viscoelastic results are also obtained using the quasi-elastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.