Composite Structure Optimization via Isogeometric Analysis
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Solution Overview
Problem
Existing methods for optimizing composite structures under high-dimensional random field conditions face challenges such as geometric discrete errors in finite element analysis and low calculation efficiency due to high-dimensional randomness, especially in complex structures like cutter heads for hard rock tunnel boring machines.
Innovation Solution
A method that uses a CAD model directly for analysis, employing non-embedded stochastic analysis and a surrogate model trained through isogeometric analysis to calculate stochastic responses, eliminating geometric discrete errors and reducing computational complexity by using a stochastic polynomial expansion enhanced Dagum kernel Kriging surrogate model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional finite element analysis is used to transform CAD model to CAE model, then the analysis can be performed, but geometric discrete errors are introduced due to discretization operation of grid units
Solution Approach 1:
The patent merges the CAD modeling and CAE analysis stages by using isogeometric analysis, where NURBS basis functions are used for both geometric representation and structural analysis, eliminating the need for separate mesh discretization and reducing geometric discrete errors
Solution Approach 2:
The patent creates a precise copy of the CAD model for analysis purposes by using the same NURBS representation, avoiding the loss of geometric information that occurs during traditional mesh discretization
2Reliability
If embedded stochastic analysis is used to solve high-dimensional randomness, then the stochastic response can be obtained, but the calculation efficiency is very low due to complex explicit expressions and high-dimensional stochastic rigidity matrix
Solution Approach 1:
The patent introduces a surrogate model as an intermediary between the isogeometric analysis and optimization processes, trained on a limited number of high-fidelity samples to predict stochastic responses efficiently without requiring complex explicit expressions or high-dimensional matrix operations
Solution Approach 2:
The patent performs preliminary sampling and training of the surrogate model before the main optimization process, preparing the predictive tool in advance to avoid repeated complex calculations during optimization iterations
3Measurement precision
If experimental method is used for stochastic response analysis, then the stochastic responses can be measured, but a large number of experiments are needed and the cost is high
Solution Approach 1:
The patent creates virtual copies of the physical structure through computational modeling, using isogeometric analysis and surrogate models to simulate stochastic responses without requiring physical prototypes or extensive experimental testing
Data Source
AI summary
Provided is an optimization design method for new composite structure under a high-dimensional random field condition. The method includes the following steps: firstly, establishing a high-dimensional random field model considering spatially dependent uncertainty of material properties and loads considering the complexity of a preparation process and a service environment of a new composite structure, and then establishing an optimization design model of the new composite structure under the influence of the high-dimensional random field according to the high-rigidity and light-weight design requirement; secondly, combining a stochastic isogeometric analysis approach with a stochastic polynomial expansion enhanced Dagum kernel Kriging surrogate model, and efficiently and accurately calculating statistical characteristics of stochastic responses of the new composite structure under the influence of the high-dimensional random field; and finally, rapidly obtaining optimal design parameters of the new composite structure by utilizing a particle swarm optimization algorithm. (FIG. 1)