{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T17:45:46Z","timestamp":1774374346821,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This study presents a comprehensive multiscale analysis of sandwich beams with a polyurethane foam (PUF) core, delivering a numerical comparison between finite element methods (FEMs) and a meshless method: the radial point interpolation method (RPIM). This work aims to combine RPIM with homogenisation techniques for multiscale analysis, being divided in two phases. In the first phase, bulk PUF material was modified by incorporating circular holes to create PUFs with varying volume fractions. Then, using a homogenisation technique coupled with FEM and four versions of RPIM, the homogenised mechanical properties of distinct PUF with different volume fractions were determined. It was observed that RPIM formulations, with higher-order integration schemes, are capable of approximating the solution and field smoothness of high-order FEM formulations. However, seeking a comparable field smoothness represents prohibitive computational costs for RPIM formulations. In a second phase, the obtained homogenised mechanical properties were applied to large-scale sandwich beam problems with homogeneous and approximately functionally graded cores, showing RPIM\u2019s capability to closely approximate FEM results. The analysis of stress distributions along the thickness of the beam highlighted RPIM\u2019s tendency to yield lower stress values near domain edges, albeit with convergence towards agreement among different formulations. It was found that RPIM formulations with lower nodal connectivity are very efficient, balancing computational cost and accuracy. Overall, this study shows RPIM\u2019s viability as an alternative to FEM for addressing practical elasticity applications.<\/jats:p>","DOI":"10.3390\/ma17184466","type":"journal-article","created":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T02:30:23Z","timestamp":1726108223000},"page":"4466","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core: A Comparative Study of Finite Element Methods and Radial Point Interpolation Method"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0539-7057","authenticated-orcid":false,"given":"Jorge","family":"Belinha","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, ISEP, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, n. 431, 4200-072 Porto, Portugal"},{"name":"Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100004","DOI":"10.1016\/j.jcomc.2020.100004","article-title":"Review of composite sandwich structure in aeronautic applications","volume":"1","author":"Castanie","year":"2020","journal-title":"Compos. 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