Fast parametric analysis of trimmed multi-patch isogeometric Kirchhoff-Love shells using a local reduced basis...

Area of Science:

• Computational mechanics
• Numerical analysis
• Geometric modeling

Background:

• Performing multiple simulations for design and shape optimization is computationally intensive.
• Isogeometric Kirchhoff-Love shells with trimmed, multi-patch domains present challenges due to geometry-dependent, non-affine operators.
• Parameter variations can lead to highly divergent solutions in trimmed domains.

Purpose of the Study:

• To develop an efficient model order reduction (MOR) framework for real-time solutions of trimmed, multi-patch isogeometric Kirchhoff-Love shells.
• To address the computational expense of numerous simulations in parametric studies and shape optimization.
• To enable accurate and fast analysis of complex geometries under varying parameters.

Main Methods:

• Employing a local reduced basis method combined with clustering techniques.
• Utilizing the Discrete Empirical Interpolation Method (DEIM) for affine approximation.
• Applying the reduction strategy to parametric shape optimization problems.
• Testing the framework on trimmed, multi-patch meshes, including complex geometries.

Main Results:

• The proposed framework achieves significant reduction in online computational cost compared to standard reduced basis methods.
• The approach demonstrates accuracy in solving parameterized Kirchhoff-Love shells.
• Efficient handling of geometry-dependent operators and non-affine parameter dependencies is achieved.

Conclusions:

• The developed MOR framework offers an accurate and computationally efficient solution for real-time analysis of trimmed, multi-patch isogeometric Kirchhoff-Love shells.
• This method is particularly beneficial for parametric shape optimization, enabling faster design iterations.
• The framework effectively manages complex geometries and parameter variations, outperforming traditional methods.