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Topology optimization is the most complicated problem in structural optimization. One common approach is to utilize the concept of the design domain, such as the homogenization method and the density function approach. In this paper, a new microstructure-based design domain method is proposed. This new method gives simple closed-form expressions for effective Young's modulus and effective shear modulus in terms of phase properties and volume fractions. Using these simple relations, topology optimization problems can be formulated and solved using mathematical programming algorithms. Results of some design examples obtained from the new method are presented.