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The SIMP approach is one of the most frequently used methods for topology optimization of structures. In this method, the relative density is expressed as a function of coordinates and varies from 0 to 1 within the design domain. Relative densities of 0 and 1 are associated to the existence and non-existence of the material, respectively. The finite element approach is usually utilized to analyze the problem while considering a constant relative density within each element. As a result, relative densities of the elements are assumed as the design variables. A common deficiency of such an approach is the introduction of the so-called checkerboard pattern, which is an indication of numerical instability. In this paper, a new algorithm is proposed to overcome this source of instability which is based on the concept of stress and strain smoothing. Benchmarks and practical problems are simulated and discussed in order to verify the proposed approach and to assess its performance.