Implicit Dimensional Reduction for Slender Structure Optimization
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Solution Overview
Problem
Conventional 3D finite element analysis is inefficient and inaccurate for slender structures, such as microcantilevers, due to high computational demands and automation challenges in geometric dimensional reduction, leading to poor quality finite elements and inconsistent results.
Innovation Solution
An implicit dimensional reduction method using an algebraic process that captures the geometry via a 3D finite element mesh and the physics via classic beam theory, allowing for efficient and accurate analysis and optimization within a standard 3D CAD environment, without explicit geometric reduction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional 3D finite element analysis is used for slender structures, then the analysis can be performed with standard tools, but the computational demands increase significantly and results become inaccurate
Solution Approach 1:
The patent extracts and removes the slender region from the parent body, separating it from the 3D model. This extracted slender region is then analyzed using 1D beam theory, which is computationally efficient and accurate for such geometries, while the remaining 3D region is analyzed using conventional FEA. The results are coupled to provide the complete solution.
Solution Approach 2:
The patent performs dimensional reduction by analyzing the extracted slender region using 1D beam theory instead of 3D FEA. This dimensionality change from 3D to 1D significantly reduces computational demands while maintaining accuracy for slender structures. The stiffness matrices from different dimensions are then coupled together.
2Productivity
If explicit geometric reduction is performed to replace 3D slender regions with 1D or 2D elements, then computational efficiency improves, but the process becomes complex and difficult to automate
Solution Approach 1:
The patent merges the 3D FEA analysis of the parent body with the 1D beam analysis of the slender region by coupling their stiffness matrices. The coupled system combines matrices of different dimensions (3D and 1D) into a unified system that can be solved efficiently. This merging approach maintains the advantages of both methods while automating the process.
Solution Approach 2:
The patent uses an intermediary coupling process that connects the 3D and 1D analyses. The coupling stiffness matrix acts as an intermediary that bridges the two different dimensional analyses, allowing them to work together seamlessly. This intermediary approach simplifies the automation process compared to complete explicit geometric reduction.
3Measurement precision
If the slender region is extracted and analyzed separately using 1D beam theory, then computational efficiency and accuracy improve, but the coupling of matrices from different dimensions becomes complex
Solution Approach 1:
The patent segments the structure into two distinct parts: the parent body analyzed with 3D FEA and the slender region analyzed with 1D beam theory. Each segment is analyzed using the most appropriate method for its geometry, improving accuracy. The segmentation also simplifies the overall process by allowing independent analysis of each part before coupling.
Solution Approach 2:
The patent creates a universal coupled analysis system that can handle both 3D and 1D elements together. The coupled stiffness matrix formulation is universal and can accommodate different dimensional elements, making the process automatable and applicable to various structures with slender regions, not just specific cases.
Data Source
AI summary
A method and system for simulating and analyzing the behavior of a structural component of a computerized model in response to a simulated event to determine an optimized shape for the component is disclosed. The shape is optimized using an implicit dimensional reduction rather than an explicit geometric replacement by discarding data of a 3D discretization that has little or no bearing on the performance of the component to a simulated event. The reduced dataset is then collapsed onto a lower dimension projection that is applied over a force vector that is representative of the simulated event to determine the behavior of the component to the simulated event. Optimization tools may then be used to modify the physical attributes of the component and performance of the component once again simulated until an optimized component is determined.