THE EFFECTIVE PROPERTIES OF PIEZOCOMPOSITES, PART Ⅰ: SINGLE INCLUSION PROBLEM

The problem of a piezoelectric ellipsoidal inclusion in an infinite non- piezoelectric matris is very important in engineering. In this paper, it is solved via Green's function technique. The closed-form solutions of the electroelastic Eshelby's tensors for this kind of problem are obtained. The electroelastic Eshelby's tensors can be expressed by the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics, respectively, the electroelastic Eshelby's tensors can be obtained conveniently. Using these results, the closed-form solutions of the constraint elastic fields and the constraint electric fields inside the piezoelectric ellipsoidal inclusion are also obtained. These expressions can be readily utilized in solutions of numerous problems in the micromechanics of piezoelectric solids, such as the deformation and energy analysis, damage evolution and fracture of the piezoelectric materials.

Optimal Operation of Integrated Energy Systems Subject to Coupled Demand Constraints of Electricity and Natural Gas

This paper proposes a hybrid multi-objective optimization and game-theoretic approach(HMOGTA)to achieve the optimal operation of integrated energy systems(IESs)consisting of electricity and natural gas(E&G)utility networks,multiple distributed energy stations(DESs),and multiple energy users(EUs).The HMOGTA aims to solve the coordinated operation strategy of the electricity and natural gas networks considering the demand characteristics of DESs and EUs.In the HMOGTA,a hierarchical Stackelberg game model is developed for generating equilibrium strategies of DESs and EUs in each district energy network(DEN).Based on the game results,we obtain the coupling demand constraints of electricity and natural gas(CDCENs)which reflect the relationship between the amounts and prices of electricity and cooling(E&C)that DESs purchase from utility networks.Furthermore,the minimization of conflicting costs of E&G networks considering the CDCENs are solved by a multi-objective optimization method.A case study is conducted on a test IES composed of a 20-node natural gas network,a modified IEEE 30-bus system,and 3 DENs,which verifies the effectiveness of the proposed HMOGTA to realize fair treatment for all participants in the IES.