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A general-purpose meshfree Kirchhoff–Love shell formulation

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Abstract

A thin shell formulation is developed for the approximation by a meshfree Reproducing Kernel Particle Method (RKPM). The formulation is derived from a degenerated shell approach where the structure is treated as a 3D solid subjected to kinematic constraints of the Kirchhoff–Love (KL) shell theory. To address the challenge of surface geometry representation in a meshfree method, a local parameterization using principal component analysis (PCA) is employed. Taylor-series expansion adapted to the shell formulation is developed to address the accuracy and stability issues of nodal quadrature. Several approaches that address membrane locking are also considered. The effectiveness of the proposed RKPM KL shell formulation is demonstrated using an extensive set of linear-elastic and finite-deformation inelastic test cases.

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Acknowledgements

This work was supported through the ONR Grant No. N00014-21-1-2670. J. Wang was also supported by the Hibbitt Postdoctoral Fellowship in the School of Engineering at Brown University.

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  1. School of Engineering, Brown University, 184 Hope St., Providence RI, 02912, USA

    Jiarui Wang & Yuri Bazilevs

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Wang, J., Bazilevs, Y. A general-purpose meshfree Kirchhoff–Love shell formulation. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01989-x

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