Construction engineering

Electrical engineering

Physics

Basis (linear algebra)

Engineering

Mathematical analysis

Finite element method

Industrial engineering

Artificial intelligence

Topology (electrical circuits)

Topology optimization

Systems engineering

Pure mathematics

Data science

Geometry

Development (topology)

Scale (ratio)

Mathematics

Engineering design process

Computer science

Management science

Quantum mechanics

Structural engineering

Mechanical engineering

Categorization

Field (mathematics)

Structural and Multidisciplinary Optimization

Multi-scale structures, as found in nature (e.g., bone and bamboo), hold the promise of achieving superior performance while being intrinsically lightweight, robust, and multi-functional. Recent years have seen a rapid development in topology optimization approaches for designing multi-scale structures, but the field actually dates back to the seminal paper by Bendsøe and Kikuchi from 1988 (Computer Methods in Applied Mechanics and Engineering 71(2): pp. 197–224). In this review, we intend to categorize existing approaches, explain the principles of each category, analyze their strengths and applicabilities, and discuss open research questions. The review and associated analyses will hopefully form a basis for future research and development in this exciting field.

Topology optimization of multi-scale structures: a review