Spectral Descriptor for Structural Optimization of Deformation Modes
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Solution Overview
Problem
Current structural optimization methods for crashworthiness are limited by the need for numerous iterations and high computational costs due to their reliance on displacement measurements of individual nodes, which restricts control over deformation behavior and is inefficient for complex deformation modes.
Innovation Solution
A computer-implemented method using a spectral design representation to generate a sparse geometric descriptor for deformation modes, allowing for efficient optimization by parameterizing desired plastic deformations through spectral decomposition and selecting relevant spectral coefficients to guide the optimization process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Difficulty of detecting and measuring
If displacement measurements of individual nodes are used to evaluate deformation behavior, then the measurement process is simple, but the control over deformation behavior is limited and basic deformation modes only can be analyzed
Solution Approach 1:
The patent replaces the mechanical measurement approach (displacement of individual nodes) with a spectral field-based approach. By using spectral decomposition and field variables, the system transitions from point-based mechanical measurements to a continuous field representation that captures complex deformation modes without requiring additional physical sensors or measurement points.
Solution Approach 2:
The patent changes the parameters used to describe deformation from simple nodal displacements to spectral coefficients that represent deformation modes. This parameter transformation enables the system to capture and control complex deformation patterns by adjusting spectral coefficients, providing versatile control over deformation behavior while maintaining measurement simplicity.
2Manufacturing precision
If many iterations are performed for structural optimization, then the optimization accuracy improves, but the computational time and resources increase significantly
Solution Approach 1:
The patent transforms the optimization parameters from numerous nodal displacement variables to a reduced set of spectral coefficients representing dominant deformation modes. This parameter reduction maintains optimization accuracy by capturing essential deformation behavior while significantly reducing the dimensionality of the optimization problem, thereby decreasing computational time and iterations required.
Solution Approach 2:
The patent extracts and isolates the most significant deformation modes through spectral decomposition, separating the essential deformation characteristics from less important details. By focusing optimization on these extracted dominant modes rather than all possible nodal displacements, the system achieves accurate optimization results with reduced computational effort.
3Measurement precision
If complex deformation modes are analyzed in detail, then the deformation behavior is accurately captured, but the computational cost and processing time become prohibitively high
Solution Approach 1:
The patent changes the representation of complex deformation modes from detailed nodal displacement fields to compact spectral coefficients. This parameter transformation maintains measurement precision by preserving the essential characteristics of complex deformations while using far fewer computational resources to represent and analyze the same deformation behavior.
Solution Approach 2:
The patent segments the complex deformation field into distinct spectral components or modes through decomposition. By analyzing and controlling deformation through these segmented spectral components rather than the full complex field, the system achieves accurate deformation analysis with reduced computational cost, as only the most significant spectral components need to be resolved.
Data Source
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Figure 3A~3B
AI summary
A computer-implemented method for a structural optimization of a geometric shape of a physical object with respect to a deformation comprises a step of representing the geometric shape of the physical object in a spectral design representation in the spectral domain, and a step of determining a deformation mode and of generating a spectral descriptor of the deformation mode on the basis of the spectral design representation and spectral representation of the deformed object. The method then performs a structural optimization of a set of design variables using the generated spectral descriptor as a parameter in an objective function of the structural optimization or in at least one constraint of the structural optimization to generate an optimized set of design variables of the physical object,. The method outputs the optimized set of design variables of the physical object.