 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13554 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8194
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| In English (Mech. Solids): | | 5360 |
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| Farzana Nazir and Azher Jameel, "Total Lagrangian Based Element Free Galerkin Method for Modelling Geometric Nonlinearities in Beams," Mech. Solids. 60 (7), 6377-6401 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
7 |
Pages |
6377-6401 |
| DOI |
10.1134/S0025654425604586 |
| Title |
Total Lagrangian Based Element Free Galerkin Method for Modelling Geometric Nonlinearities in Beams |
| Author(s) |
Farzana Nazir (Department of Mechanical Engineering, National Institute of Technology Srinagar, Jammu and Kashmir, 190006 India, farzana.nazir.189@gmail.com)
Azher Jameel (Department of Mechanical Engineering, National Institute of Technology Srinagar, Jammu and Kashmir, 190006 India, jameelazher@nitsri.ac.in) |
| Abstract |
The paper investigates geometric nonlinearities produced by large deformations by using
element free Galerkin method (EFGM) based on total Lagrangian approach. EFGM is one of the
meshfree methods that has evolved as a potential numerical tool for modelling different engineering
problems. This novel technique eliminates the mesh distortion issues faced while modelling large
deformations in engineering components. Moving least square approximations have been used to
approximate the displacement fields in engineering components. Large deflections have been modelled
by the total Lagrangian approach which uses the initial undeformed configuration as the reference state
for analysis. Deformation gradient is used to map data from current deformed configuration to the initial
undeformed states. Mathematical models developed on EFGM have been coded in MATLAB to solve
different large deformation problems. The accuracy and fidelity of developed MATLAB codes have
been established by comparing the results with linear analytical solutions available in literature. The
results obtained in the current work clearly demonstrate the potential and applicability of the proposed
method and MATLAB codes for solving large deformations in engineering components. |
| Keywords |
element free Galerkin method (EFGM), MLS shape functions, geometric nonlinearity, total lagrangian approach, beams |
| Received |
24 August 2025 | Revised |
05 November 2025 | Accepted |
07 November 2025 |
| Link to Fulltext |
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