# A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites

## Abstract

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 time scale, 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 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 of 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 quasielastic 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 accuracymore »

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 755581

- Report Number(s):
- SAND2000-1093J

Journal ID: ISSN 0001--1452; TRN: AH200021%%30

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article

- Journal Name:
- AIAA Journal

- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 12; Other Information: Submitted to AIAA Journal; PBD: 1 May 2000; Journal ID: ISSN 0001--1452

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; COMPOSITE MATERIALS; VISCOSITY; ELASTICITY; DEFORMATION; HYGROSCOPICITY; RHEOLOGY; THERMODYNAMIC PROPERTIES; MATHEMATICAL MODELS; NESDPS Office of Nuclear Energy Space and Defense Power Systems

### Citation Formats

```
HAMMERAND,DANIEL C., and KAPANIA,RAKESH K.
```*A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites*. United States: N. p., 2000.
Web. doi:10.2514/2.900.

```
HAMMERAND,DANIEL C., & KAPANIA,RAKESH K.
```*A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites*. United States. doi:10.2514/2.900.

```
HAMMERAND,DANIEL C., and KAPANIA,RAKESH K. Mon .
"A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites". United States. doi:10.2514/2.900. https://www.osti.gov/servlets/purl/755581.
```

```
@article{osti_755581,
```

title = {A geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites},

author = {HAMMERAND,DANIEL C. and KAPANIA,RAKESH K.},

abstractNote = {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 time scale, 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 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 of 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 quasielastic 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.},

doi = {10.2514/2.900},

journal = {AIAA Journal},

issn = {0001--1452},

number = 12,

volume = 38,

place = {United States},

year = {2000},

month = {5}

}