Algorithm

Engineering

Statistics

Computer science

Mathematical optimization

Acoustics

Lattice (music)

Mechanical engineering

Design for manufacturability

Physics

Finite element method

Metamodeling

Mathematics

Kriging

Topology optimization

Combinatorics

Structural engineering

Programming language

Shape optimization

Topology (electrical circuits)

Computer Methods in Applied Mechanics and Engineering

Graded lattice sandwich structures (GLSSs) enable superior structural performances due to the continuously-varying configurations and properties of lattices in space. This paper proposes a design method for GLSSs by multiscale topology optimization. In this method, the geometrical configuration of a prototype lattice cell (PLC) is described by an explicit topology description function (TDF). Based on some sample lattice cells, a Kriging metamodel is constructed to predict the effective property of each lattice cell. Based on the Kriging metamodel, the thickness optimization of two solid face-sheets and the distribution optimization of lattice cells in core layer are respectively implemented. Driven by their equivalent densities, the configurations of lattice cells with similar topological features are generated by interpolating the shape of the PLC. Then, the graded lattice cells (GLCs) are generated. Using the proposed method, the computational burden involved in design of GLSSs can be reduced significantly. What is more, the manufacturability of GLSSs can be guaranteed by constructing a proper PLC with the help of TDF. Numerical examples in terms of compliance and natural frequency optimization of GLSSs are provided to verify the advantages of the proposed method. Also, bending tests are performed on the GLSSs fabricated by additive manufacturing (AM). The results reveal that GLSSs are stiffer and have larger natural frequencies than the uniform lattice sandwich structures.

Design of graded lattice sandwich structures by multiscale topology optimization