Simulation Program Dynamic Stiffness Matrix Generation
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Solution Overview
Problem
In structure analysis simulations, the accuracy of calculating physical quantities deteriorates over time steps when using a neural network to generate stiffness matrices, leading to accumulated errors that affect the convergence of nonlinear algorithms, especially in comparison to the finite element method (FEM).
Innovation Solution
A simulation program iterates between two methods for generating stiffness matrices: an initial method with lower accuracy but faster processing, such as a neural network, and a second method with higher accuracy like the FEM, dynamically switching based on error indices to maintain calculation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a neural network is used to generate stiffness matrices, then processing speed is improved, but calculation accuracy deteriorates over time steps due to accumulated errors
Solution Approach 1:
The system dynamically switches between the neural network generation method and the FEM generation method based on the time step and error accumulation. The switching mechanism adjusts the generation approach from static to dynamic, maintaining high speed when accuracy is sufficient and transitioning to high accuracy when errors accumulate, thereby resolving the contradiction between processing speed and calculation accuracy over time steps
Solution Approach 2:
The system changes the generation method parameter based on the time step index and error evaluation results. By monitoring the time step progression and switching between different generation methods (neural network vs. FEM), the system adapts the generation approach to maintain accuracy while preserving speed benefits, resolving the contradiction between processing speed and calculation accuracy
2Measurement precision
If the finite element method is used to generate stiffness matrices, then calculation accuracy is improved, but processing speed decreases
Solution Approach 1:
Instead of applying the computationally intensive FEM to all time steps, the system applies it partially only when necessary (when error accumulation is detected or at specific intervals). This partial application of the high-accuracy method maintains calculation accuracy where needed while preserving processing speed in other time steps, resolving the contradiction between calculation accuracy and processing speed
3Device complexity
If a single generation method is used throughout the simulation, then device complexity is reduced, but calculation accuracy deteriorates due to error accumulation over time steps
Solution Approach 1:
The simulation process is segmented into different phases based on time steps and error evaluation results. The system divides the generation process into multiple segments, switching between neural network generation and FEM generation at appropriate intervals. This segmentation allows the system to maintain low complexity during stable phases while improving accuracy when errors accumulate, resolving the contradiction between system complexity and calculation accuracy
Data Source
AI summary
A recording medium stores a simulation program for causing a computer to execute a process. The process includes: iterating first analysis processing based on a first generation method for generating a stiffness matrix of an analysis target; calculating an index related to an error of the stiffness matrix after the first analysis processing is iterated; changing the first generation method to a second generation method having higher accuracy based on the index related to the error; and iterating second analysis processing based on the second generation method, wherein the first analysis processing includes generating the stiffness matrix by the first generation method, and calculating a physical quantity related to the target, and the second analysis processing includes generating the stiffness matrix by the second generation method, and calculating the physical quantity related to the target.