Study On Weighted Residual Method And Boundary Element Method For Effective Thermal Conductivity Of Particulate Compostes

It has been very important research subject in modern meso-mechanics research to investigate and analyze the effective properties of composite materials,to reveal the relation between its meso-structure and effective properties by using meso-mechanics theory and method,and thus to provide theoretical foundation and systemic analysis method for optimum design and property evaluation of composites.In the filed of thermal conduction,traditional meso-mechanics model are mainly based on particle of typical geometry such as sphere or ellipsoid,and a generally adopted premise is the assumption of perfect contact conditions at constituent interfaces.The literature on composite materials lacks today a proper theoretical framework permitting a thorough study of the conduction problem for composites with particles of irregular geometry such as polygon or arbitrary shape in the presence of a thermal contact resistance.The primary motivation of this thesis is therefore to develop proper procedures and numerical computational techniques such as the weighted residual method(WRM) and the boundary element method(BEM) in combination with meso-mechanics model for the investigation of the influence of particle geometry,volume fractions and interfacial conditions on effective thermal conductivity of composites.This research work has been done in two aspects.On the one hand,numerical approximation has been conducted for the solution of 2D steady-state heat conduction of different composites models by using WRM and BEM numerical methods.First, the linear combinations of basic set of solutions to Laplace equation under polar coordinate system are chosen as the approximations for the solution of temperature fields,boundary residual collocation method are applied to calculate the distribution of the temperature fields for single-particle model.Accurate results are obtained for the case of circle and ellipse,but for the case of polygon,the computational precision of the method is low,sometimes even not acceptable.Then,the bicubic B-spline functions are selected as the approximation to simulate the distribution of temperature fields of composites with rectangular particle by using spline subdomain collocation method.Computational results show good agreement with those from FEM.Due to the restriction of computational complication and precision,WRM boundary collocation method can only be used to simulate temperature fields of single-particle model,as for the case of some more complicated particle geometry shape it is very hard to obtain sufficient approximation solutions.Thus,BEM is adopted to analyze the thermal conduction problem of composites with particle of arbitrary geometry. Computational algorithms of BEM for both multi connected domain and composites with particle of arbitrary geometry are derived.These BEM algorithms are used to calculate the temperature distributions for composites with both single-particle model and multi-particles models.Numerical results show that,considering different interfacial conditions,BEM can well simulate the temperature distributions of composites with particle of arbitrary geometry with high computational precision.On the other hand,the computational formula for the prediction of the effective thermal conductivity of particulate composites is established.The integral formulations of temperature along interface between constituents are derived for single-particle models.Self-consistent iteration method is applied to determine the effective thermal conductivity of composite with particle of different geometry. Computational formula for the prediction of effective conductivity for multi-particle model is also established.Both prediction formulae are used to investigate the influence of particle geometry shapes,volume fractions and interfacial conditions on the effective thermal conductivity,computational results are compared with those of Hasselman.Results show that for particle with low conductivity,effective conductivities obtained from multi-particle model are higher than those from self-consistent method but very close to the results of Hasselman's dilute approximation.For composites with particle of different aspect ratios,the value of effective conductivity along the major axis is higher than that along minor axis.For different particle geometry with identical size,the particle geometry has certain effect on the effective conductivity,the prediction value for the case of circle is higher than the case of square,and ellipse is higher than rectangle.