Sensitivity Calculation in Nonlinear Equilibrium Simulation
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Solution Overview
Problem
Existing methods for optimization and simulation in CAD and CAE systems are limited by computational inefficiency, particularly when dealing with non-linear behavior and small sliding contact constraints, leading to costly and resource-intensive processes.
Innovation Solution
The implementation of a computer-implemented method that iteratively optimizes models with respect to design variables by simultaneously solving for equilibrium and design response sensitivity using Linear Complementarity Problems (LCPs), enhancing computational efficiency by integrating sensitivity calculations within the LCP solver and utilizing a single global operator for displacements across multiple load cases.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing methods are used for optimization and simulation with non-linear behavior and small sliding contact constraints, then the design process can be performed, but computational resources and time are excessively consumed
Solution Approach 1:
The patent merges the sensitivity calculation process with the LCP solver by embedding the sensitivity calculation within the LCP algorithm itself. This integration allows both the equilibrium solution and sensitivity information to be obtained simultaneously in a single computational pass, eliminating the need for separate sensitivity analysis steps and significantly reducing computational time and resource consumption.
2Measurement precision
If sensitivity calculations are performed separately from equilibrium solving, then accurate sensitivity information can be obtained, but computational resources and time are significantly increased
Solution Approach 1:
The patent combines the sensitivity calculation with the LCP solver by formulating the sensitivity equations as part of the LCP system. The sensitivity information is extracted directly from the LCP solution process, ensuring accuracy while achieving computational efficiency through the unified formulation.
Solution Approach 2:
The LCP solver itself provides sensitivity information as a byproduct of solving the equilibrium problem. The algorithm automatically computes sensitivity data during the solution process without requiring external or additional computational efforts, making the system self-sufficient for both equilibrium and sensitivity analysis.
3Reliability
If multiple load cases are analyzed separately, then each case can be solved accurately, but the computational process becomes repetitive and inefficient
Solution Approach 1:
The patent formulates a unified LCP framework that can handle multiple load cases simultaneously through a single global operator for displacements. This universal formulation allows the same computational structure to serve all load cases, eliminating repetitive separate analyses while maintaining accuracy for each individual case through the consistent application of the global operator.
Data Source
AI summary
Provided are a computer-based method and system of simulating a physical real-world system. Such a method begins by defining, in memory of a processor, a model comprising a plurality of design variables where the defined model represents a real-world physical system and where behavior of the model is given by an equation stored in the memory. The method/system uses the equation to iteratively optimize the defined model with respect to a given one of the plurality of design variables by simultaneously solving for equilibrium of the model and for the design response sensitivity of the given design variable, for the equilibrium, in a given optimization iteration. According to such an embodiment, iteratively optimizing the model results in an improved simulation of the real-world physical system.