Tension/Compression-Only Optimal Stiffness Design with Displacement Constraint

Tension-only or compression-only optimal stiffness design with displacement constraint is studied by a material-replacement method. In the method, the original tension-only or compression-only material is replaced with porous material which solid phase is isotropic and the modulus is equal to the tension modulus or compression one. When the material is replaced with isotropic, only approximate displacement field can be obtained. To decrease the error between the actual SED field of the structure with original material and the current SED field of the structure with isotropic material, the local effective SED of a material point is defined and can be obtained by the approximate strain and stress fields, i.e., the negative principal stress makes no contribution for the ESED of a tension-only material point or vice versa. Meanwhile, a floating reference interval of strain energy density (SED) is adopted to control the update of the design variables, i.e., the relative densities of material points in a design domain. In detail, the increment of the relative density of a material point is non-zero if the local effective SED does not located in the current reference interval. Finally, the reference interval changes in iterations with respective to the displacement constraint in optimization. Numerical examples are given to exam the validity of the method presented.