A Finite Element to Perform 3D Shakedown Analysis for Limited Kinematic Hardening Materials

The use of the Design by Analysis (DBA) route is a modern trend in pressure vessel and piping international codes in mechanical engineering. However, to apply the DBA to structures under variable mechanical and thermal loads, it is necessary to assure that the plastic collapse modes, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. The tool available to achieve this target is the shakedown theory. Unfortunately, the practical numerical applications of the shakedown theory result in very large nonlinear optimization problems with nonlinear constraints. Precise, robust and efficient algorithms and finite elements to solve this problem in finite dimension has been a more recent achievements. However, to solve real problems in an industrial level, it is necessary also to consider more realistic material properties as well as to accomplish 3D analysis. Limited kinematic hardening, is a typical property of the usual steels and it should be considered in realistic applications. In this paper, a new finite element with internal thermodynamical variables to model kinematic hardening materials is developed and tested. This element is a mixed ten nodes tetrahedron and through an appropriate change of variables is possible to embed it in a shakedown analysis software developed by Zouain and co-workers for elastic ideally-plastic materials, and then use it to perform 3D shakedown analysis in cases with limited kinematic hardening materials

Particle Trajectory Tracing and Computational Electromagnetics for Accelerator and Related Technologies

The main objective of this R&D work is to simulate particle beam optics in CV-28 Cyclotron of Instituto de Engenharia Nuclear – IEN/CNEN, as a support for improvements or optimization of this particle accelerator. Besides 2D magnetostatic field computation results, the authors present an alternative method for charged particle trajectories computation in electrostatic or magnetostatic fields. This task is approached by analytical computation of trajectories, by parts, considering constant fields within each finite element. This method has some advantages over numerical integration ones: numerical miscomputation of trajectories is avoided; stability problem is also avoided, for the magnetostatic field case. Some examples are presented, including positive ion extraction from cyclotrons with strip-foil. This latter technique is an interesting alternative for upgrading positive ion cyclotrons, such as CV-28 Cyclotron. The particle trajectory computation method presented in this work is of interest not only for cyclotrons, but for accelerator and related technology, in general.

Core Reactor Calculation Using the Adaptive Remeshing with a Current Error Estimator

With the objective to improve the reactor physics calculation on a 2D and 3D nuclear reactor via the Diffusion Equation, an adaptive automatic finite element remeshing method, based on the elementary area (2D) or volume (3D) constraints, has been developed. The adaptive remeshing technique, guided by a posteriori error estimator, makes use of two external mesh generator programs: Triangle and TetGen. The use of these free external finite element mesh generators and an adaptive remeshing technique based on the current field continuity show that they are powerful tools to improve the neutron flux distribution calculation and by consequence the power solution of the reactor core even though they have a minor influence on the critical coefficient of the calculated reactor core examples. Two numerical examples are presented: the 2D IAEA reactor core numerical benchmark and the 3D model of the Argonauta research reactor, built in Brasil.

Particle Trajectory Computation for Accelerators and Related Technologies

This work reports an alternative method for single non-relativistic charged particle trajectory computation in 2D electrostatic or magnetostatic fields. This task is approached by analytical computation of particle trajectory, by parts, considering the constant fields within each finite element. This method has some advantages over numerical integration ones: numerical miscomputation of trajectories, and stability problems can be avoided. Among the examples presented in this paper, an interesting alternative approach for positive ion extraction from cyclotrons is shown, using strip-foils. Other particle optics devices can benefit of a method such the one proposed in this paper, as beam bending devices, spectrometers, among others. This method can be extended for particle trajectory computation in 3D domains.