Abstract: In practice, a continuum structure is usually designed with tractions applied to a part of its boundary and prescribeddisplacements imposed on other part of the boundary. The design domains of practicalstructures are often limited and significantly affect the final optimaldesign of the structures. Structural boundaries under tractions andprescribed displacements should be treated as a subset of zero level set inthe level set methods. However, structural optimization methods based onlevel set movements do not consider these realistic requirements. Toovercome the limitations of current level set methods and the stopping issueof structural boundary movements, this paper constructs new normal speedsrequired by level set movements. And the convergence characteristics of structuraltopology optimization series solutions obtained by the proposed normalspeeds are studied. Then, we implement the algorithm of the objective functionfor a problem with the strain energy as the objective function and with material volume as a constraint by useof several robust and efficient numerical techniques of level set methods.The benefits and advantages of the proposed method are illustratedthrough two 2D examples.