Jose Luis Silveira

An algorithm for shakedown analysis with nonlinear yield functions

Abstract This paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function. Firstly, variational formulations for shakedown analysis of structures under variable loads are considered. Secondly, the corresponding discrete forms are briefly recalled. Then, the algorithm is derived by combining a Newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility. The proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models. The numerical procedure is applied to a square plate with a circular hole under variable traction in two directions, and the obtained approximations are compared with available results. Finally, a rectangular plate with two small holes is considered in both plane strain and plane stress conditions. All application use the Mises condition without linearization.

Extremum principles for bounds to shakedown loads

Bounds to the safety factor for elastic shakedown of structures under variable loads are considered. These bounds represent safety factors in the separate analysis of alternating plasticity and incremental collapse. Extremum principles for these bounds are formulated and compared. The role of simple and combined mechanisms of incremental collapse is emphasized in the theoretical developments and also in two analytical applications.

Force prediction in thread milling

A mechanistic approach for modeling the thread milling process is presented. The mechanics of cutting for thread milling is analyzed as an end milling process with modified cutting edge. The geometry of threads is added to the geometry of the end milling tool to calculate the chip load area. The linear path is simulated and values of the specific energy from end milling are used to compute the cutting forces involved. A comparison between the simulation of the cutting forces for a specific tool in two different situations is made to present the force behavior acquired from the model.

Bounds to shakedown loads

The shakedown analysis of structures under variable loads is considered, and the corresponding variational principles are presented. Separate formulations for elastic (or classical) shakedown, plastic shakedown and incremental collapse are compared. Two upper bounds for classical safety factors are presented and interpreted as the result of separate analysis concerning alternating plasticity and prevention of simple mechanisms of incremental collapse. As a first application, exact solutions are obtained for a closed tube under variable pressure and temperature. This example is the Bree problem with logarithmic temperature variation across the wall. A finite element procedure for shakedown analysis of tubes is then presented. This numerical procedure is validated by comparison with the exact solutions for the closed tube. Finally, the numerical method is applied to a restrained tube under variable pressure and logarithmic temperature.

Variational Principles for Shakedown Analysis

The safety factor for elastic shakedown of structures under variable loads is considered. Variational principles for shakedown analysis are reviewed in a unified presentation, suitable to finite element discretizations, and considering nonlinear yield functions. Extremum principles for bounds to shakedown loads are also presented. A tube under thermo-mechanical loading is used to show analytical solutions, and numerical results obtained with a mixed finite element formulation.

Numerical Analysis of Metal Powders in Uniaxial Compaction

Powder consolidation constitutes an important step in the manufacture of products of high quality and precision. To obtain these components, with desired forms and final mechanical properties, it is of extreme importance to have knowledge about the processes to obtain powders, compacting and sintering. The objective of this work is to verify which model, obtained from the literature, better describes the compaction densification behavior of iron powder in closed-die. Doraivelu’s criterion was carried through the method of the finite elements with the implementation of an elastoplastic model with hardening. The influence of the yield function coefficient against the relative density was evaluated, as well as, the yield function in the hydrostatic space.