Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios

A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed.A topology optimization algorithm is developed which is capable of finding microstructures with extreme properties very close to theoretical upper bounds.The effective mechanical properties of the designed composite are determined by a numerical homogenization technique.The sensitivities with respect to design variables are derived by simultaneously interpolating Young’smodulus and Poisson’s ratio using different parameters.The so-called solid isotropicmaterial with penalizationmethod is developed to establish the optimization formulation.Maximum bulk or shearmodulus is considered as the objective function,and the volume fraction of constituent phases is taken as constraints.Themethod ofmoving asymptotes is applied to update the design variables.Several 3D numerical examples are presented to demonstrate the effectiveness of the proposed structural optimization method.The effects of key parameters such as Poisson’s ratios and volume fractions of constituent phase on the final designs are investigated.A series of novel microstructures are obtained fromthe proposed approach.It is found that the optimized bulk and shearmoduli of all the studied composites are very close to the Hashin-Shtrikman-Walpole bounds.

Topology optimization of transient problem with maximum dynamic response constraint using SOAR scheme

This paper proposes a novel method for the continuum topology optimization of transient vibration problem with maximum dynamic response constraint.An aggregated index in the form of an integral function is presented to cope with the maximum response constraint in the time domain.The density filter solid isotropic material with penalization method combined with threshold projection is developed.The sensitivities of the proposed index with respect to design variables are conducted.To reduce computational cost,the second-order Amoldi reduction(SOAR)scheme is employed in transient analysis.Influences of aggregate parameter,duration of loading period,interval time,and number of basis vectors in the SOAR scheme on the final designs are discussed through typical examples while unambiguous configuration can be achieved.Through comparison with the corresponding static response from the final designs,the optimized results clearly demonstrate that the transient effects cannot be ignored in structural topology optimization.