Bimaterial lattices with anisotropic thermal expansion

Abstract

Bimaterial lattices with anisotropic thermal expansion consist of nonidentical cells comprising a skewed triangle made of one material surrounding an unskewed triangle made of a second material. The two materials have differing individual coefficients of thermal expansion. The variation in skew angles makes the thermal expansion of the cell anisotropic. Being composed of anisotropic nonidentical cells, the assembled lattice is also anisotropic and can be designed to have different coefficients of thermal expansion on its top and bottom surfaces. Such lattices can be used as transition elements or adapters to avoid thermal-expansion mismatch between two parts of a structure made of materials with different coefficients of thermal expansion and subjected to temperature changes. In the present paper, three nonlinear algebraic equations linking skew angles with the coefficients of thermal expansion in three directions of a cell are derived, the design of several lattices is performed, the algorithm of lattice design is elaborated, and some examples are presented. © 2014 Mathematical Sciences Publishers.