Volume Fraction Elements in Finite Element Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional Finite Element Methods (FEMs) require increased computational resources and costs due to the need for smaller, more numerous regular elements to accurately model physical objects, as they typically ignore partially filled elements that do not fully contain the object's portion.
Innovation Solution
The method involves using partially filled regular elements with varying volume fractions for Finite Element Analysis (FEA) or Finite Element Method (FEM), allowing for larger elements and improved accuracy by considering the volume fraction of each element, which conserves processing power and time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If smaller regular elements are used to represent a physical object, then simulation accuracy is improved, but computer memory capacity and computational costs increase
Solution Approach 1:
The patent applies local quality by assigning different volume fractions to different regular elements based on their partial occupancy by the physical object. Instead of treating all elements uniformly, each element's contribution to the simulation is weighted by its actual filled portion, allowing larger elements to be used while maintaining accuracy.
Solution Approach 2:
The patent introduces volume fraction as a new parameter to characterize the occupancy of regular elements by the physical object. This parameter change allows the simulation to account for partially filled elements, enabling the use of larger elements without sacrificing accuracy, thus reducing the total number of elements required.
2Measurement precision
If smaller regular elements are used to increase simulation accuracy, then computational resources and time increase
Solution Approach 1:
By applying local quality through volume fraction weighting, the patent allows larger regular elements to be used in the mesh while still accurately representing the physical object's geometry. This reduces the total number of elements and consequently decreases computational time and resource requirements.
Solution Approach 2:
The patent implements partial action by considering only the portion of each regular element that is actually occupied by the physical object, as represented by the volume fraction. This partial consideration allows larger elements to be used without over-refining the mesh, reducing computational overhead while maintaining accuracy.
3Productivity
If partially filled regular elements are used, then processing power and time are conserved, but traditional FEM assumptions are violated
Solution Approach 1:
The patent resolves the contradiction by introducing volume fraction as an additional parameter that modifies the traditional FEM formulation. This parameter change allows partially filled elements to be incorporated into the simulation framework without requiring a complete redesign of the mesh definition process, thus improving computational efficiency while managing complexity.
Solution Approach 2:
The volume fraction acts as an intermediary parameter that bridges the gap between traditional FEM assumptions (which require fully filled elements) and the desire to use larger, partially filled elements for efficiency. This intermediary allows the simulation to accommodate partial occupancy while maintaining compatibility with standard FEM computational frameworks.
Data Source
AI summary
Examples described herein relate to apparatuses and methods for performing finite element analysis of a model of a physical object, the method comprising determining regular elements for the model, wherein each of at least some of the regular elements partially contains a portion of the model, and performing the finite element analysis based, at least in part, on the at least some of the regular elements, wherein the finite element analysis is a structural finite element analysis.