Numerical solution of two- and three-dimensional thermomechanical problems using the theory of a Cosserat point
The paper concerns the construction of approximate numerical nonlinear solutions such as Galerkin solutions. Here it is the notion of ``Cosserat point'' -- a model of a three-dimensional body that is essentially a point surrounded by some small volume -- which is used for that purpose in the framework of thermomechanical problems. This is presented as an alternative to other methods such as finite elements, Galerkin, etc., an approach that is peculiar to the author. Details are provided for the use of triangular elements for two-dimensional problems and tetrahedrons for three-dimensional problems, but also higher order elements with many directors and temperature fields can be developed using similar methods. Here the basic balance laws are inherently nonlinear and they are valid for arbitrary material properties. In three-dimensional problems the formulation using the theory of a Cosserat point is related to the standard Galerkin method. However, in contrast with the Galerkin method, it places fundamental restrictions on constitutive equations which ensure that the balances of angular momentum and energy are identically satisfied for all thermomechanical processes. The theory of Cosserat point can be used to complement the Galerkin method by providing a set of fundamental theoretical restrictions on the constitutive equations which can be used to evaluate different numerical integration schemes.
scientific article; zbMATH DE number 794114
scientific article