In this paper, the optimum stress distribution around a holeis investigated for LCMs materials with micropolar continuum representationto reduce the computational cost. Two classes of design variables, relativedensity and cell size distribution of the truss-like materials, are to bedetermined by optimization under the given total material volume constraint.The concurrent designs of materials and structures are obtained for threedifferent optimization formulations. In the first formulation, oneminimizes the stress around the hole; in the second formulation, oneminimizes the highest stress within the whole structure. Since the yieldstrength of truss-like materials depends on the relative materialdensity, we minimize the ratio of stress over the corresponding effectiveyield strength along the hole boundary in our third formulation, whichmaximizes the strength reserve, which seems more rational. Numerical resultsfor the three objectives validate the method proposed in this paper. Theinfluence of the ply angle (angle between the principle direction of materialand the axes of system's coordinate) on the optimum result is discussed.The dependence of the optimum design on finite element meshes is alsoinvestigated.