Composite material design of two‐dimensional structures using the homogenization design method

Abstract

SUMMARYComposite materials of two-dimensional structures are designed using the homogenization design method. The composite material is made of two or three di erent material phases. Designing the composite material consists of ÿnding a distribution of material phases that minimizes the mean compliance of the macrostructure subject to volume fraction constraints of the constituent phases, within a unit cell of periodic microstructures. At the start of the computational solution, the material distribution of the microstructure is represented as a pure mixture of the constituent phases. As the iteration procedure unfolds, the component phases separate themselves out to form distinctive interfaces. The e ective material properties of the artiÿcially mixed materials are deÿned by the interpolation of the constituents. The optimization problem is solved using the sequential linear programming method. Both the macrostructure and the microstructures are analysed using the ÿnite element method in each iteration step. Several examples of optimal topology design of composite material are presented to demonstrate the validity of the present numerical algorithm.

Design and application of layered composites with the prescribed magnetic permeability

“…Cases III and IV have non-zero off-diagonal terms and their layers may be inclined. Table II shows the inverse homogenization results such as the optimized shapes, the converged volume fractions, the permeability tensors obtained, the iteration numbers for the convergence and the percentage difference by (10) according to the initial material distribution of the ICDC and the ICDB. The configurations of the optimized microstructure correspond to general intuition.…”

Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures

“…The basic idea of the method was presented in the paper (Fujii et al 2001). Figure 1 illustrates a PCLD structure with the uniform cellular viscoelastic material.…”

“…In this context, it is necessary to design the microstructure of the damping material considering the macroscopic damping performances of structures, and analyze the macrostructures and microstructures simultaneously. Up till now, Fujii et al (2001) studied the compliance minimization problem of the macrostructure through topology optimization of material microstructures using the homogenization method. Rodrigues et al (2002) proposed a hierarchical optimization of material and structure method that the material properties at the macroscale are allowed to be varied from point to point.…”

Design of functionally graded composite structures in the presence of stress constraints

“…works of Sigmund and Torquato (1997), Fujii et al (2001) and Diaz and Lipton (2000). This list is by no means complete and further references to the literature can be found in the books of Bendsoe (1995), Lurie (1993), Cherkaev and Kohn (1997) and Cherkaev (2000).…”