A study on topology optimization in linear elastic problem using artificial isotropic material is presented. An element elimination algorithm is suggested to remove a void or nearly void region in the design domain. The application of this algorithm for every iteration can reduce computation time drastically. Although new addition is not possible, the tests with several numerical examples suggest that this adding process may not be necessary in almost all cases. The influence of initial topology of a design domain is studied and shown to be significant to the final results. This can be utilized for generating design alternatives. Example cases from automobile components have shown that the element elimination procedure combined with the density redistribution algorithm is efficient and practically usable.