An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and three dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases.
The solution of two parallel cracks in functionally graded materials subjected to a tensile stress loading is derived in this paper. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate parallel to the crack. The problem is formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are jumps of displace-ments across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded as a series of Jacobi polynomials to obtain the shielding effects of the two parallel cracks in functionally graded materials.
LIANG Jun Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China
