Element Analysis Of Nonlinear Problems Research Articles

Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors

This article continues prior work of the authors on the combined a posteriori analysis for the discretization and iteration errors in the finite element approximation of linear elliptic problems to the nonlinear case. The underlying theoretical framework is again that of the Dual Weighted Residual (DWR) method for goal-oriented error control. The accuracy in the algebraic solution process can be balanced with that due to discretization using computable a posteriori error estimates in which the outer nonlinear and inner linear iteration errors are separated from the discretization error. This results in effective stopping criteria for the algebraic iteration, which are elaborated particularly for Newton-type methods. The performance of the proposed strategies is demonstrated for several nonlinear test problems.

A consistent Eulerian formulation for large deformation analysis with reference to metal-extrusion process

A critical discussion of the different formulation methods for the finite element analysis of non-linear problems is given. The discussion is concerned mainly with the differences between updated Lagrangian and Eulerian formulations, and with the specific nature and basic characteristics of each. A consistent Eulerian formulation is developed by means of the virtual work principle in an explicit form. Differences between the presented formulation and similar formulations as well as the attempted Eulerian formulations are discussed according to the classification of formulation methods. To demonstrate the applicability and the effectiveness of the Eulerian finite element analysis using a fixed mesh in space, a metal-extrusion problem has been solved. In this approach, the mesh is maintained fixed in space and the increment of stress tensors for a forward incremental step are added to a set of interpolated stress tensors. Then, these stresses are interpolated back to obtain the state of stress of the body-points momentarily occupying the fixed integration points of the mesh.

Finite element analysis of nonlinear problems in the dynamical theory of coupled thermoelasticity

This paper is concerned with the formulation of finite element models for the analysis of nonlinear problems in the dynamical theory of coupled thermoelasticity. Displacement and temperature fields are approximated over a finite element, and energy balances are formed which lead to general equations of heat conduction and motion of thermoelastic finite elements. A number of special cases are considered. Numerical results obtained from simple representative problems are also presented.