Biot consolidation analysis with automatic time stepping and error control Part 1: theory and implementation

✍ Scribed by Sloan, Scott W.; Abbo, Andrew J.

• Book ID: 101220474
• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 191 KB
• Volume: 23
• Category: Article
• ISSN: 0363-9061
• DOI: 10.1002/(sici)1096-9853(199905)23:6<467::aid-nag949>3.0.co;2-r

✦ Synopsis

A new "nite element algorithm for solving elastic and elastoplastic coupled consolidation problems is described. The procedure treats the governing consolidation relations as a system of "rst-order di!erential equations and is based on the backward Euler and Thomas and Gladwell schemes with automatic subincrementation of a prescribed series of time increments. The prescribed time increments, which are called coarse time steps, serve to start the procedure and are chosen by the user. The automatic consolidation algorithm attempts to select the time subincrements such that, for a given mesh, the time-stepping (or temporal discretisation) error in the displacements lies close to a speci"ed tolerance.

Unlike existing solution techniques, the new algorithm computes not only the displacements and pore pressures, but also their derivatives with respect to time. These extra variables permit a family of unconditionally stable integration algorithms to be constructed which automatically provide an estimate of the local truncation error for each time step. This error estimate is inexpensive to compute and may be used to develop a simple and e$cient automatic time stepping mechanism. For the elastic case, the displacements and pore pressures at the end of each subincrement may be solved directly without the need for iteration. For elastoplastic behaviour, however, the governing relationships are non-linear and a system of non-linear equations must be solved to compute the updates.