关键词: 功能梯度材料, 非均匀有理B样条, 映射函数, 泊松方程, 几何空间

Abstract: Functionally Gradient Material (FGM) components in irregular shapes and with complex material distribution were hard to find a suitable material distribution function to describe the mapping relations between volume fraction and geometry,and separation between geometric space and material space made the difficulty of components design increase,which impeded the transmission of design,analysis and manufacture of follow-up models.For these problems,the idea of functionally gradient materials component modeling by considering manufacture process was presented.The components' geometry and material information carrier was defined,and the representation of coupling between geometry and material by NURBS(Non-Uniform Rational B-Splines) was realized.The physical principles was excavated from preparation technology of functionally gradient material components for design modeling,the distribution function of material was established by using Poisson equation as mathematical model,and the design modeling was translated into problems on general partial differential equations with boundary value conditions.Isogeometric Analysis (IGA) was used to solve the model,which could realize the integrative expression of geometric space and material space.The examples proved effectiveness and feasibility of the proposed methods.

Key words: functionally gradient materials, non-uniform rational B-Splines, mapping function, poisson equation, geometric space