Meshless implementation of the geometrically exact Kirchhoff-Love shell theory

• Published in: International journal for numerical methods in engineering Vol. 100; no. 1; pp. 1 - 39
• Main Authors: Ivannikov, V., Tiago, C., Pimenta, P.M.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 05.10.2014; Wiley Subscription Services, Inc
• Subjects: Boundaries; Corners; Derivatives; geometrically exact; Mathematical analysis; Mathematical models; Meshless methods; Nonlinearity; Shell theory; thin shells
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4687

SUMMARYIn the present paper, a meshless generalized multiple fixed least squares implementation of the geometrically exact Kirchhoff–Love shell theory is described. The material time derivative of the deformation gradient and the first Piola–Kirchhoff stress tensor are considered as basic conjugate quantities to evaluate the internal power. The shell's initial geometry is reproduced exactly by the predefined mapping from a reference plane configuration. As a constitutive model, a neo‐Hookean material, whose functional is altered in compliance with the plane stress condition, is chosen.The augmented weak form, suitable for both interpolative and non‐interpolative approximations thanks to the imposition of the essential boundary conditions through Lagrange multipliers, is consistently linearized, and the resultant bilinear form proved to be symmetric. The appearance of the corner reactions, related to the jumps of the pseudo‐torsion boundary moment, requires the inclusion of additional pointwise displacement constraints at the essential boundary corners. The importance of these quantities is demonstrated in the numerical tests, revealing its positive influence on the displacements and, particularly, their derivatives (up to 3rd order) in both linear and nonlinear problems.The possibility of incorporation of drilling boundary moment for nonlinear problems was successfully assessed. Copyright © 2014 John Wiley & Sons, Ltd.