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Assessment of various isogeometric contact surface refinement strategies

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Abstract

Since its inception, isogeometric analysis (IGA) has shown significant advantages over Lagrange polynomials-based finite element analysis (FEA), especially for contact problems. IGA often uses C\(^\text {1}\)-continuous non-uniform rational B-splines (NURBS) as basis functions, providing a smooth description of kinematic variables across the contact interface. This leads to increased accuracy and stability in the numerical solutions. However, from the existing literature on isogeometric contact analysis, it is not yet clear what interpolation order and continuity of NURBS one should employ to accurately capture the distribution of contact forces across the contact interface. The present work aims to fill this gap and provides a comparative assessment of different NURBS-based standard (conventional) refinement strategies for contact problems within the IGA framework. A recently proposed refinement strategy, known as the varying-order (VO) based NURBS discretization, has demonstrated its capability to refine geometry through the implementation of order elevation in a controlled manner. However, a detailed investigation that directly compares the VO based NURBS discretization with the standard NURBS discretization has not yet been carried out. Therefore, a thorough study of the VO based discretization strategy is also conducted, evaluating its effectiveness in comparison with the standard discretization strategy for contact problems. For this, a few examples on contact problems are solved using an in-house MATLAB® code. The solution to these examples shows that quadratic order standard NURBS discretization is sufficient to achieve the desired level of solution accuracy just by increasing the mesh size. It is further demonstrated that VO based discretization can achieve much higher accuracy than standard discretization, even with a coarse mesh, by generating additional degrees of freedom in the contact boundary layer. In addition, VO based discretization makes considerable savings in analysis time to achieve the same accuracy level as standard discretization.

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Notes

  1. In the current simulation, an Intel® Xeon® CPU E5-2630 v4 operating at 2.20GHz, featuring 10 cores, 32GB 2400MHz DDR4 RAM, and 25MB cache is utilized.

  2. In the current simulation, an Intel® Xeon® CPU E5-2640 v4 operating at 2.40GHz, featuring 10 cores, 64GB 2133MHz DDR4 RAM, and 25MB cache is utilized.

  3. In the current simulation, an Intel® Xeon® CPU E5-2650 v2 operating at 2.60 GHz, featuring 8 cores, 32GB 1866 MHz DDR3 RAM, and 20 MB cache is utilized.

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Acknowledgements

The authors gratefully acknowledge the support from Science and Engineering Research Board (SERB), Department of Science and Technology (DST) under Project Nos. CRG/2022/002218 and IMP/2019/000276 and Vikram Sarabhai Space Centre (VSSC), Indian Space Research Organisation (ISRO) through MoU No. ISRO:2020:MOU:NO:480.

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  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Sumit Kumar Das & Sachin Singh Gautam

  2. Department of Engineering Mechanics, KTH Royal Institute of Technology, SE 100 44, Stockholm, Sweden

    Vishal Agrawal

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Das, S.K., Agrawal, V. & Gautam, S.S. Assessment of various isogeometric contact surface refinement strategies. J Braz. Soc. Mech. Sci. Eng. 46, 175 (2024). https://doi.org/10.1007/s40430-024-04712-5

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