Papers by Keyword: PCG

Abstract: To solve large symmetric indefinite linear systems in finite element discretization of 3D Biot's consolidation equations.This paper adopted diagonal preconditioned conjugate gradient method to FE program. Several numerical examples show that the diagonal PCG method are significantly more efficient than direct solution method for large-scale symmetric indefinite linear systems.

Abstract: A general model of the optimum design of structural vibration with the random parameters is introduced. Dynamic optimization design of stochastic finite element using the Preconditioned Conjugate Gradient method (PCG) is presented. The vibration equation of a system is transformed to a static problem by using the Willson method and stochastic finite element analysis of structural vibration adopts the PCG.An example is given respectively and the proposed method is robust and efficient.

Abstract: In this paper, material properties, geometry parameters and applied loads are assumed to be stochastic, sensitivity computation of structural vibration is presented. The vibration equation of a system is transformed to a static problem by using the Newmark method. In order to develop computational efficiency and allow for efficient storage, the Preconditioned Conjugate Gradient method (PCG) is also employed. The PCG is an effective method for solving a large system of linear equations and belongs to methods of iteration with rapid convergence and high precision. An example is given respectively and calculated results are compared to validate the proposed methods.

Abstract: The extrusion process provides conditions for non-uniform metal flow depending on strain, strain rate and temperature of deformation as well as deformation zone geometry. As a result of these conditions significant microstructure gradients are present within the extrudate. The extreme case of the microstructure gradient is a formation of the peripheral coarse grain structure (PCG). This phenomenon is present in many structural aluminum alloys extrudates and its presence should be eliminated or at least significantly reduced because of the mechanical properties and aesthetic points of view. A number of experiments, including physical and numerical simulations, were performed in order to understand and model the origin of the PCG in indirect extrusion of 6xxx alloys. These experiments included different alloy chemistry, various temperatures, extrusion ratios and extrusion speeds allowing analysis of their influence. Parallel to the experimental results the numerical simulation of the metal flow showing the origin of the metal in different extrudate location was performed using software package DEFORM TM. A review of performed research will be followed by the analysis of the results and discussion of future needs.