Earthquake never causes death directly, most of injuries and casualties are because of dropping things and phenomenon of ceiling collapse [1]. Thus, some efforts have been done in order to confronting damages of natural disaster such as earthquake. Using safety bed against earthquake is one of the tools for protecting people against rubble of earthquake, however, in most advanced countries, although buildings are constructed based on principles of earthquake engineering, safety beds are still used. In the first chapter of this research, a review on previous works on this area is performed and then in the second and third chapters mathematical relations and contact laws among masonry buildings in the form of discrete modeling are presented and minimization of multi objective functions using Pareto Optimality is described explicitly. Moreover, topological optimization methods (finding geometry of structure whose force lines are distinguished, in addition structure holds minimum compliance) are introduced. In the fourth chapter, it is tried to model building accompanied by its components (bricks and connections) with the aid of new software (LMGC 90) in the field of geo-technique. Then, load of rubbles on initial geometry (simple cube which its dimensions are obtained from an initial design of safety bed) is determined. The process of topological optimization utilizing element Shell 93 in several reduction volumes is done and weighted functions with several combination of weighted coefficients is minimized, afterward the optimum Pareto point is computed and final topology of structure is obtained. In fifth chapter, according to this topology, components of structure based on beam element (beam 3) are modeled. At first, the design optimization under yielding stress constraint is executed after that, this process is re-done by adding buckling constraint. The outputs of this optimization are optimal thickness, length of elements and cross sections. At the end, in sixth chapter some suggestions for final design and the obtained results from combined optimization process are presented. Key words: NSCD, load of rubbles, Safety bed, topological optimization, Pareto optimality
