A METHOD FOR COMPUTING THE EFFECTIVE IN-PLAN THERMOELASTIC PROPERTIES OF PERIODIC COMPOSITES BASED ON THE RADIAL INTEGRATION BOUNDARY ELEMENT METHOD

One can program not only the elastic modulus and Poisson’s ratio but also the thermal expansion coefficients of the composites which consist of artificial microstructures and multiple materials. The macro effective thermoelastic properties of the composites are determined by their microstructures. In this paper, the authors proposed a novel method to evaluate the homogenized in-plan thermoelastic properties of the composites made of the periodic microstructures, which is based on the radial integration boundary element method. The proposed method employs the representative volume elements homogenized approach to calculate the effective properties based on the displacements and stresses of the micro unit cells, while utilizing the radial integral boundary element method for solving the displacements and stresses. The proposed method does not require internal grid and domain integration, and it only relies on the displacements and surface tractions on the boundary to obtain the effective thermoelastic parameters of materials, such as elastic modulus and thermal expansion coefficients. This method has advantages such as easy implementation of parameterized modeling, which leads to priorities in structure optimization. Besides, using the boundary element method makes it easy to analyze accurately the cells with tiny structural features. What’s more, the discontinuous elements are employed at the conners of structures in this paper to simplify the implementation of the periodic boundary conditions of the representative volume elements. The authors simulated the banding problem of a composite beam using both the homogenized thermoelastic properties and the direct finite element simulation. The results of the homogenized model coincide the direct simulation well, which indicates the effectiveness of the proposed method. Using the proposed method, the authors also conducted the parametric analysis of the coefficients of thermal expansion of a cellular microstructure. The results show that one can achieve the negative thermal expansion by changing the sizes of the cellular structure’s components.