DescriptionStrain energy based topology optimization method has been used since topology optimization method was presented. Although successful examples from strain energy based topology optimization have been presented, some of the optimal configurations of these designs show stress concentrations or a localized large deformation which is highly undesirable in structure design. In this dissertation, firstly, the strain energy based topology optimization method is reviewed to discover the cause of the problems. Moreover, strain based topology optimization method is presented to avoid these drawbacks. Instead of minimizing strain energy, global effective strain function is minimized. Using this function, compliant mechanism and energy absorbing structure design problems are presented. Since these designs require flexibility and rigidity at the same time, a multi-objective optimization problem is formulated using a physical programming method. Comparisons of design examples from both the strain energy based topology optimization and the proposed method are presented and discussed. The main contributions of this dissertation are listed as follows: (1) deriving the sensitivity of the global effective strain, (2) presenting a complaint mechanism design scheme that can distribute the deformation within the entire mechanism to avoid localized deformation, (3) formulating energy absorbing function by implementing seek range class function using physical programming method.