Finite Element Solver Algorithm Selection for Structural Analysis
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Solution Overview
Problem
Existing structural analysis methods using the finite element method face challenges in efficiently solving simultaneous linear equations, leading to longer analysis times due to the properties of direct and iterative methods, where direct methods require increased memory and computations for agglomerated shapes, and iterative methods may not converge for plate-rafter-like shapes.
Innovation Solution
A structural analysis method that evaluates the degree of agglomeration of a model and selects between direct and iterative methods based on this evaluation to optimize the solution approach, using the finite element method, thereby reducing analysis time by matching the method to the model's shape properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the direct method is used to solve simultaneous linear equations, then the solution is obtained directly and accurately, but the memory requirements and computation time increase significantly for agglomerated model shapes
Solution Approach 1:
The patent applies dynamics by making the solution method adaptable and changeable based on model characteristics. The system dynamically selects between direct and iterative methods by evaluating the degree of agglomeration, allowing the solution approach to adapt to different model shapes rather than using a fixed method for all cases
Solution Approach 2:
The patent changes the parameter of solution method selection based on the evaluated degree of agglomeration. By calculating agglomeration metrics from model information and using this evaluation to determine whether to apply direct or iterative methods, the system optimizes computational efficiency while maintaining solution accuracy
2Loss of time
If the iterative method is used to solve simultaneous linear equations, then the computation time is reduced for agglomerated shapes, but the method may not converge for plate-rafter-like shapes
Solution Approach 1:
The system dynamically adjusts the solution method based on real-time evaluation of model characteristics. By calculating the degree of agglomeration from model information and using this evaluation to select the appropriate method, the system ensures both speed and reliability for different model types
Solution Approach 2:
The patent implements feedback by evaluating model characteristics (degree of agglomeration) and using this evaluation to inform the selection of the solution method. This feedback mechanism ensures that the chosen method is appropriate for the specific model shape, preventing convergence issues while maintaining computational efficiency
3Device complexity
If a fixed solution method is used for all model types, then the implementation is simple, but the analysis time increases due to inefficiency for specific model shapes
Solution Approach 1:
The patent applies preliminary action by evaluating model characteristics (degree of agglomeration) before executing the solution process. This preliminary evaluation allows the system to select the most appropriate solution method in advance, avoiding inefficiency during the actual computation phase
Solution Approach 2:
The system changes the parameter of solution method selection based on evaluated model characteristics. By calculating agglomeration metrics from model information and using this evaluation to determine whether to apply direct or iterative methods, the system optimizes computational efficiency
Data Source
AI summary
A structural analysis method executed by a computer, includes acquiring model information; evaluating based on the acquired model information, a degree of agglomeration of a model subject to analysis; and selecting for the model, a direct method or an iterative method as an algorithm to solve simultaneous linear equations of a structural analysis solver that uses a finite element method, the direct method or the iterative method being selected based on a result of evaluation of the degree of agglomeration of the model.