Approximation Of Stress Field Research Articles

A new decoupled finite element algorithm for viscoelastic flow. Part 1: Numerical algorithm and sample results

AbstractThis paper presents an algorithm for two‐dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non‐consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.

Formulations in rates and increments for elastic‐plastic analysis

AbstractMinimum principles in velocities, stress rates and plastic strain rates are extended in order to derive formulations for finite increments of displacement, stress and plastic strain fields defining complete numerical methods. Kinematical, statical and mixed principles are developed from a new variational formulation of the elastic‐plastic work‐hardening constitutive relation.The consequences of this time discretization are discussed independently of any discretization of the continuum. In particular, the incremental formulations derived from extended rate principles account for local elastic unloading and produce stress field approximations complying with equilibrium and plastic admissibility without any additional procedure, at least for piecewise linear yield functions. These properties are not fulfilled when the incremental analysis is based on direct discrete versions of classical rate principles.Finally, FEM approximations are formally introduced and the solution of the resulting finite dimensional quadratic optimization problem is considered.