Finite element methods for coupled thermoelasticity and coupled consolidation of clay. (English) Zbl 0539.73005

Ženíšek, Alexander

RAIRO, Anal. Numér. 18, 183-205 (1984).

The author considers the following linear and coupled two-dimensional problems: (1) dynamical thermoelasticity, (2) quasistatical thermoelasticity, (3) consolidation of clay, the dependent variables being the displacements and temperature for (1) and (2), and the displacements and pore water pressure for (3). He derives a variational formulation as a basis for a finite element triangulation of the Hermitean type with respect to the spatial domain whereas the time domain is approximated by means of the Newmark method. The existence and uniqueness of the approximate solution is proved and the maximum rate of convergence is established using methods of functional analysis. Special attention is given to the quadrature formulas to be used.

Reviewer: H.Bufler

MSC:

74F05	Thermal effects in solid mechanics
74L10	Soil and rock mechanics
74S99	Numerical and other methods in solid mechanics
74G30	Uniqueness of solutions of equilibrium problems in solid mechanics
74H25	Uniqueness of solutions of dynamical problems in solid mechanics
35A15	Variational methods applied to PDEs
74S30	Other numerical methods in solid mechanics (MSC2010)

Keywords:

hyperbolic; elliptic; linear and coupled two-dimensional problems; dynamical thermoelasticity; quasistatical thermoelasticity; consolidation of clay; dependent variables being the displacements and temperature; displacements and pore water pressure; finite element triangulation of the Hermitean type; spatial domain; time domain is approximated by means of the Newmark method; existence; maximum rate of convergence