Abstract
The advancement of computers has led to collection and handling of huge data from various resources. The inherent properties of computational mechanics application can be extracted from the appropriate data using different techniques of machine learning (ML). The present work enlights a method to employ machine learning in the field of finite element method (FEM) where evaluation of sufficient number of integrals has to be carried out. This calculation of integral by the standard Gauss–Legendre quadrature rule requires specific number of Gauss quadrature points for getting the desired accuracy which minimizes the computational cost. Whereas the element stiffness matrix is calculated numerically with required number of Gauss quadrature points for different element with respect to the material properties. Most of the auto-mesh software consider constant number of Gauss quadrature points for all the elements irrespective of their distortion and material behaviour. The main motivation of this work is to build an accurate and computationally efficient quadrature scheme with the help of standard Gauss–Legendre quadrature rule for computing elemental stiffness matrix. An efficient method is developed using a deep neural network to predict respective number of Gauss quadrature points for given element coordinates and the material properties.
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Acknowledgements
The authors gratefully acknowledge the support from SERB, DST under project IMP/2019/000276 and VSSC, ISRO through MoU No.: ISRO:2020:MOU:NO: 480.
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Chinchkar, R., Nath, D., Gautam, S.S. (2023). Design of Efficient Quadrature Scheme in Finite Element Using Deep Learning. In: Sharma, R., Kannojiya, R., Garg, N., Gautam, S.S. (eds) Advances in Engineering Design. FLAME 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-3033-3_3
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DOI: https://doi.org/10.1007/978-981-99-3033-3_3
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