Topology Optimization for Developable Surface Structures

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Solution Overview

Problem

Current methods for designing developable structures are either limited to post-processing of existing geometries or require manual intervention, lacking automation and efficiency in creating designs with developable surfaces that can be easily fabricated without stretching or tearing.

Innovation Solution

The implementation of a density-based topology optimization method with a surface developability constraint, which includes defining nodal density and determining surface normal directions to create geometric domains with developable surfaces, allowing for automated design exploration and fabrication of thin-walled or solid volumetric structures.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If automatic conversion of given geometry to developable pieces is used, then manufacturing precision is improved, but device complexity increases and requires input geometries at the outset

Engineering Contradiction:

Improvedevelopable surface accuracyVSAvoidconversion process complexity

Core Design Contradiction:

Manufacturing precisionVSDevice complexity

Solution Approach 1:

Instead of converting existing geometries to developable surfaces, the invention inverts the approach by directly generating developable surfaces from design specifications and boundary conditions. The topology optimization process creates developable structures natively rather than transforming pre-existing geometries, eliminating the need for complex conversion algorithms.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The design system performs self-service by automatically generating developable surfaces through integrated topology optimization without requiring external geometry input or manual intervention. The process autonomously determines the optimal developable structure based on performance objectives and boundary conditions, making the system self-sufficient.

Inventive Principle:

Principle #25Self-service

2Productivity

If user-guided interactive design is used, then design speed is improved, but extent of automation deteriorates due to manual intervention

Engineering Contradiction:

Improvedesign speedVSAvoidautomated control

Core Design Contradiction:

ProductivityVSExtent of automation

Solution Approach 1:

The system achieves full automation by performing all design operations autonomously without user guidance or manual intervention. The topology optimization process automatically generates developable surfaces based on specified boundary conditions and performance objectives, making the design system self-sufficient and completely automated while maintaining high speed.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The automated topology optimization framework provides universal functionality by handling all aspects of developable surface design in a single integrated process. It simultaneously performs structural optimization, surface developability enforcement, and geometry generation, replacing multiple manual operations with one automated system.

Inventive Principle:

Principle #6Universality (Multi-functionality)

3Manufacturing precision

If parametric or non-parametric input geometries are required, then manufacturing precision is improved, but adaptability deteriorates for design exploration

Engineering Contradiction:

Improvegeometry accuracyVSAvoiddesign exploration capability

Core Design Contradiction:

Manufacturing precisionVSAdaptability or versatility

Solution Approach 1:

The invention reverses the traditional workflow by generating geometries directly from design specifications rather than converting input geometries. This approach enables design exploration by allowing users to specify performance objectives and boundary conditions without requiring pre-defined geometries, thereby improving adaptability while maintaining precision through the optimization process.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The system performs preliminary action by pre-defining boundary conditions, material properties, and performance objectives before the optimization process. This allows the automated generation of developable surfaces tailored to specific design requirements, enabling both design exploration and manufacturing precision without needing input geometries.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS11501032B2Surface developability constraint for density-based topology optimization

Publication Date: 2022.11.15 KK TOYOTA CHUO KENKYUSHO

AI summary

Methods are provided for designing a structure with developable surfaces using a surface developability constraint. The surface developability constraint is developed based on the discovery of a sufficient condition for surface piecewise developability, namely surface normal directions lie on a small, finite number of planes. Automated methods and algorithms may include providing a design domain and a characteristic function of a material in the design domain to be optimized. The methods include defining a nodal density of the material, and determining surface normal directions of a plurality of planes. A density gradient that describes the surface normal directions is then determined. The methods include performing a topology optimization process on the design domain using a surface developability constraint that is based, at least in part, on the characteristic function. A geometric domain is then created for the structure using results from the topology optimization.