This work introduces the integration of an advanced numerical technique, the image-based Scaled Boundary Finite Element Method (SBFEM), with Bi-directional Evolutionary Structural Optimization (BESO) to solve topology optimization problems. The proposed approach enables adaptive mesh design for linear elastic materials under static loading (elastostatic), significantly reducing computational effort.
Donut-shaped structure under torsional loading.
Quadtree mesh representation.
2D rectangular beam with double circular perforations.
Our investigation has found that static response-based topology optimization can lead to impractical designs when subjected to multiple loading conditions. To address this issue, we developed a dynamic response topology optimization approach that focuses on crucial peak points to reduce computational time. Additionally, we utilized commercial software, Fusion 360, to refine the boundaries and achieve a smoother final design.
3D cantilever beam under two impulses.
3D Hammerhead structure under three dynamic loads.
The SBFE-BESO approach has been further developed for applications in manufacturing. By utilizing an iso-surface function based on the marching cubes algorithm, the obtained topological results feature smooth geometric boundaries, making them directly suitable for constructing 3D printing prototypes.
3D Tower under torsional loading.
Smoothed 3D Tower under MC algorithm.
The SBFE approach has been developed into another optimization algorithm so-called Proportional Topology Optimization and further applied the application to design the configuration of infill porous structures (named as IPTO). In this project, we are not only solved for the classical benchmark example, but we can also achieve the adaptive mesh infill layout for the complex geometry such as the femur-shaped structure, which can be pathed into the field of biomechanical engineering.
2D Infill design of the
L-bracket structure.
2D Infill design of the
femur-shaped structure.
2D Infill design of the Disk structure with uniform pressure loading.
Our proposed SBFE-BESO framework has successfully been applied to traditional single-material design and can be further extended to multi-material configuration design. By incorporating a material interpolation scheme, it enables the creation of complex geometric designs for composite structures.
Smoothed 3D Donut-shaped
for different material properties.
Smoothed 3D Donut-shaped
for 2 phase-materials.
Smoothed 3D Donut-shaped
for 3 phase-materials.
Our proposed SBFE–BESO framework can be readily extended to composite configuration design. By assigning distinct material properties to the tension and compression regions, it enables the generation of complex geometries tailored for composite structures.
Smoothed 3D Donut-shaped
for different mechanical properties.
Smoothed 3D Bridge structures
for different mechanical properties.
Building upon the recent development, the technique has been advanced into an SBFE–MMPTO framework to efficiently address multi-material design problems, ensuring clear separation of different material regions within a structure. This capability makes the proposed approach particularly promising for applications in additive manufacturing, where precise control of material distribution is essential.
3D Cantilever beam structure for
single phase-materials.
3D Cantilever beam structure for
2 phase-materials.
3D Cantilever beam structure for
3 phase-materials.