ICM Method Combined with Meshfree Approximation for Continuum Structure

The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.

STUDY ON PARAMETERS FOR TOPOLOGICAL VARIABLES FIELD INTERPOLATED BY MOVING LEAST SQUARE APPROXIMATION

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition,or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses,not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field,but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points,scaling parameter,weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.

The Galactic halo magnetic field revisited

Recently, Sun et al. published new Galactic 3D-models of magnetic fields in the disk and halo of the Milky Way and the distribution of cosmic-ray electron density by taking into account the thermal electron density model NE2001 by Cordes ＆ Lazio. The models successfully reproduce observed continuum and polarization all-sky maps and the distribution of rotation measures of extragalactic sources across the sky. However, the model parameters obtained for the Galactic halo, although reproducing the observations, seem physically unreasonable： the magnetic field needs to be significantly stronger in the Galactic halo than in the plane and the cosmic-ray distribution must be truncated at about 1 kpc to avoid excessive synchrotron emission from the halo. The reason for these unrealistic parameters was the low scale-height of the warm thermal gas of about 1 kpc adopted in the NE2001 model. However, this scale- height seemed reasonable and was well studied by numerous investigations. Recently, the scale-height of the warm gas in the Galaxy was revised by Gaensler et al. to about 1.8 kpc, by showing that the 1 kpc scale-height results from a systematic bias in the analysis of pulsar data. This implies a higher thermal electron density in the Galactic halo, which in turn reduces the halo magnetic field strength to account for the observed rotation measures of extragalactic sources. We slightly modified the NE2001 model according to the new scale-height and revised the Sun et al. model parameters accordingly： the strength of the regular halo magnetic field is now 2 μG or lower, and the physically unrealistic cutoff in z for the cosmic-ray electron density is removed. The simulations based on the revised 3D-models reproduce all-sky observations as before.