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An evolutionary approach is presented to solve the topology optimization of the structures with tension-only or compression-only materials. To find their optimal topologies by traditional methods is very hard for the sake of the material in the structures should be considered as nonlinear and an isotropic one in structural analysis process. To avoid such difficulties, the reference-interval with material-replacement Method is given and the major ideas are as follows. Firstly, a floating reference interval of strain energy density (SED) is adopted to control the update of the design variables. Secondly, a material-replacement scheme is used to simplify the structural analysis process, i.e., the original tension-only or compression-only material is replaced with an isotropic porous material to obtain the approximate strain and stress fields of the original structure. The effective strain energy density (ESED) field of the original structure is obtained with respect to the approximate fields, i.e., the negative principal stress makes no contribution for the ESED of a tension-only material point or vice versa. Thirdly, the update of design variables can be carried out by comparing the local ESED and the current reference interval of SED, e.g., the increment of a relative density is nonzero if the local ESED is out of the current reference interval. Finally, the reference interval changes in iterations according to the volume constraint in optimization. Numerical examples are given to show the validity and high efficiency of the present method.