Open Access

ARTICLE

A Cell-Based Smoothed Finite Element Method for Modal Analysis of Non-Woven Fabrics

Nguyễn T. Quyền^1,*, N. Dourado², A. J. P. Gomes^3,4, F. B. N. Ferreira¹

1 2C2T—Centro de Ciência e Tecnologia Têxtil, Departamento de Engenharia Têxtil, Universidade do Minho, Campus de Azurém, Guimarães, 4804-533, Portugal
2 CMEMS-UMinho, Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, Guimarães, 4804-533, Portugal
3 Department of Computer Science, Universidade da Beira Interior, Convento de Sto. António,, Covilhã, 6201-001, Portugal
4 Instituto de Telecomunicações, R. Marquês de Ávila e Bolama, Covilhã, 6201-001, Portugal

* Corresponding Author: Nguyễn T. Quyền. Email:

Computers, Materials & Continua 2021, 67(3), 2765-2795. https://doi.org/10.32604/cmc.2021.013164

Received 30 August 2020; Accepted 30 November 2020; Issue published 01 March 2021

Abstract

The combination of a 4-node quadrilateral mixed interpolation of tensorial components element (MITC4) and the cell-based smoothed finite element method (CSFEM) was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures. This formulation was applied to numerous numerical examples of non-woven fabrics. As CSFEM schemes do not require coordinate transformation, spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two, three and four smoothing cells. An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors, which allowed to remove the integral operator in the strain smoothing operation. This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost. A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed. The developed numerical model proved to overcome the shear locking phenomenon with success, revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach. The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.

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