Topology optimization based on moving deformable components: A new computational framework

Abstract: In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexible. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach.

• The paper presents a novel framework for topology optimization with moving deformable components, reducing design variables significantly (e.g., 100 vs 3000) in example cases.
• It employs an extended finite element method to handle complex geometries and overlapping components without frequent re-meshing.
• The approach seamlessly integrates with CAD systems, offering efficient geometry control and promising applications in engineering design.

Topology Optimization Based on Moving Deformable Components: A New Computational Framework

The paper presents a novel computational framework for structural topology optimization centered around moving deformable components, diverging significantly from traditional pixel or node-point-based methodologies. This approach stands out by directly addressing several challenges associated with existing methods, such as the lack of integration with CAD systems and the high computational costs inherent in pixel-based methods.

Introduction to Topology Optimization Challenges

Traditional topology optimization has extensively used pixel or node-point-based methods, such as the SIMP method and the level-set method. These approaches typically involve discretizing the design domain into finite elements, which leads to inefficiencies. For instance, the pixel-based approaches are not directly compatible with CAD modeling systems, which prefer explicit geometric representations using splines and curves. This inconsistency poses challenges in directly applying optimization outcomes to CAD systems and downstream manufacturing processes.

Moreover, as the size and complexity of the design domain increase, the computational burdens skyrocket, requiring handling an impractically large number of design variables. The node-point-based methods face similar scalability issues due to the implicit nature of geometry representation that complicates integration with CAD systems and avoids precise control over the structural features like minimum length scale or curvature.

Framework of Moving Deformable Components

The new framework introduced in this paper adopts moving deformable components as the fundamental building blocks for topology optimization. These components represent material segments within the design domain that can be parametrically adjusted. This approach shifts the focus from pixel elimination to optimizing the layout and configuration of these deformable components. As a consequence, this method is more naturally aligned with the geometry-centric operations typical in CAD systems.

Geometry and Problem Formulation

The deformable components can undergo transformations including translation, rotation, dilation, and overlap, providing a versatile means of modifying structural topology. A significant aspect of this framework is its ability to overlap components, allowing redundant material areas to seamlessly ‘disappear’ by being absorbed by other components. The mathematical formulation involves optimizing geometry parameters such as position and orientation to achieve desired structural properties, exemplified by compliance minimization under volume constraints.

Numerical Solution and Examples

The adoption of extended finite element method (XFEM) within this framework facilitates the handling of complex geometries and overlapping components without the need for frequent re-meshing. This feature supports flexible model interactions during optimization, enabling more efficient computations.

Numerical demonstrations illustrate the framework's efficacy compared to traditional methods. For basic problems like the short-beam example, the new method required significantly fewer design variables (e.g., 100 versus over 3000 in conventional methods) while delivering comparable results. This efficiency can drastically reduce computational efforts, particularly for large-scale three-dimensional problems.

Implications and Future Directions

The moving deformable component approach offers several benefits: integration with CAD systems, reduction of computational complexity, and enhanced model flexibility. These advantages imply potential widespread applications in engineering and architecture where explicit geometry control is crucial.

Future research could expand this framework to tackle multi-physics optimization challenges, integrate global optimization techniques, and explore non-FEM based methodologies to further enhance the framework's robustness and applicability.

The development of this framework signifies a promising advancement in topology optimization, poised to bridge the gap between optimization theory and practical design needs, fostering new synergies between computational modeling and manufacturing processes. Further investigation into its capabilities and optimizations will be beneficial for broadening its applicability across various engineering fields.