A non-uniform rational B-splines (NURBS) based optimization method for fiber path design Article Swipe
Xuyu Zhang
,
Yi Min Xie
,
Cong Wang
,
He Li
,
Shiwei Zhou
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2024.116963
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2024.116963
This work presents a systematic optimization method utilizing non-uniform rational B-splines (NURBS) to represent fibers in composites and design their paths. Beyond mean compliance, the objective function incorporates repulsive energy to prevent fiber knots and intersections. Utilizing NURBS control points as design variables reduces the number of design variables and expands the solution space, as they can reach any point within the design domain under the guidance of the sensitivity of the objective function in the method of moving asymptotes. Additionally, the p-norm technique for curvature constraints represents an innovative adaptation to avoid sharp turns in fibers. The work can also add fibers during optimization and enable the design of multi-layer fiber-enhanced composite structure to address various design challenges associated with optimizing fiber paths. Numerical examples show that the mean compliance decreases by 60∼70 % compared to initial configurations, and the computation time is reduced by 80 % compared to similar cases in prior work.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.cma.2024.116963
- OA Status
- hybrid
- Cited By
- 19
- References
- 97
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4394018787
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4394018787Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1016/j.cma.2024.116963Digital Object Identifier
- Title
-
A non-uniform rational B-splines (NURBS) based optimization method for fiber path designWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-04-06Full publication date if available
- Authors
-
Xuyu Zhang, Yi Min Xie, Cong Wang, He Li, Shiwei ZhouList of authors in order
- Landing page
-
https://doi.org/10.1016/j.cma.2024.116963Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.cma.2024.116963Direct OA link when available
- Concepts
-
Path (computing), Fiber, Mathematical optimization, Mathematics, Computer science, Applied mathematics, Materials science, Composite material, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
19Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 14, 2024: 5Per-year citation counts (last 5 years)
- References (count)
-
97Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4394018787 |
|---|---|
| doi | https://doi.org/10.1016/j.cma.2024.116963 |
| ids.doi | https://doi.org/10.1016/j.cma.2024.116963 |
| ids.openalex | https://openalex.org/W4394018787 |
| fwci | 9.32785362 |
| type | article |
| title | A non-uniform rational B-splines (NURBS) based optimization method for fiber path design |
| biblio.issue | |
| biblio.volume | 425 |
| biblio.last_page | 116963 |
| biblio.first_page | 116963 |
| topics[0].id | https://openalex.org/T11115 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 0.995199978351593 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2205 |
| topics[0].subfield.display_name | Civil and Structural Engineering |
| topics[0].display_name | Topology Optimization in Engineering |
| topics[1].id | https://openalex.org/T11245 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.987500011920929 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2206 |
| topics[1].subfield.display_name | Computational Mechanics |
| topics[1].display_name | Advanced Numerical Analysis Techniques |
| topics[2].id | https://openalex.org/T11583 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9864000082015991 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2210 |
| topics[2].subfield.display_name | Mechanical Engineering |
| topics[2].display_name | Advanced Measurement and Metrology Techniques |
| funders[0].id | https://openalex.org/F4320334704 |
| funders[0].ror | https://ror.org/05mmh0f86 |
| funders[0].display_name | Australian Research Council |
| is_xpac | False |
| apc_list.value | 4840 |
| apc_list.currency | USD |
| apc_list.value_usd | 4840 |
| apc_paid.value | 4840 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 4840 |
| concepts[0].id | https://openalex.org/C2777735758 |
| concepts[0].level | 2 |
| concepts[0].score | 0.5623617172241211 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q817765 |
| concepts[0].display_name | Path (computing) |
| concepts[1].id | https://openalex.org/C519885992 |
| concepts[1].level | 2 |
| concepts[1].score | 0.4922920763492584 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q161 |
| concepts[1].display_name | Fiber |
| concepts[2].id | https://openalex.org/C126255220 |
| concepts[2].level | 1 |
| concepts[2].score | 0.47166717052459717 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[2].display_name | Mathematical optimization |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.45117300748825073 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C41008148 |
| concepts[4].level | 0 |
| concepts[4].score | 0.3494533896446228 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[4].display_name | Computer science |
| concepts[5].id | https://openalex.org/C28826006 |
| concepts[5].level | 1 |
| concepts[5].score | 0.32193300127983093 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[5].display_name | Applied mathematics |
| concepts[6].id | https://openalex.org/C192562407 |
| concepts[6].level | 0 |
| concepts[6].score | 0.1575237214565277 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[6].display_name | Materials science |
| concepts[7].id | https://openalex.org/C159985019 |
| concepts[7].level | 1 |
| concepts[7].score | 0.12630566954612732 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[7].display_name | Composite material |
| concepts[8].id | https://openalex.org/C199360897 |
| concepts[8].level | 1 |
| concepts[8].score | 0.0 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q9143 |
| concepts[8].display_name | Programming language |
| keywords[0].id | https://openalex.org/keywords/path |
| keywords[0].score | 0.5623617172241211 |
| keywords[0].display_name | Path (computing) |
| keywords[1].id | https://openalex.org/keywords/fiber |
| keywords[1].score | 0.4922920763492584 |
| keywords[1].display_name | Fiber |
| keywords[2].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[2].score | 0.47166717052459717 |
| keywords[2].display_name | Mathematical optimization |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.45117300748825073 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/computer-science |
| keywords[4].score | 0.3494533896446228 |
| keywords[4].display_name | Computer science |
| keywords[5].id | https://openalex.org/keywords/applied-mathematics |
| keywords[5].score | 0.32193300127983093 |
| keywords[5].display_name | Applied mathematics |
| keywords[6].id | https://openalex.org/keywords/materials-science |
| keywords[6].score | 0.1575237214565277 |
| keywords[6].display_name | Materials science |
| keywords[7].id | https://openalex.org/keywords/composite-material |
| keywords[7].score | 0.12630566954612732 |
| keywords[7].display_name | Composite material |
| language | en |
| locations[0].id | doi:10.1016/j.cma.2024.116963 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S40006715 |
| locations[0].source.issn | 0045-7825, 1879-2138 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0045-7825 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Computer Methods in Applied Mechanics and Engineering |
| locations[0].source.host_organization | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_name | Elsevier BV |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_lineage_names | Elsevier BV |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Computer Methods in Applied Mechanics and Engineering |
| locations[0].landing_page_url | https://doi.org/10.1016/j.cma.2024.116963 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5002905406 |
| authorships[0].author.orcid | https://orcid.org/0009-0008-1554-2597 |
| authorships[0].author.display_name | Xuyu Zhang |
| authorships[0].countries | AU |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I82951845 |
| authorships[0].affiliations[0].raw_affiliation_string | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[0].institutions[0].id | https://openalex.org/I82951845 |
| authorships[0].institutions[0].ror | https://ror.org/04ttjf776 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I82951845 |
| authorships[0].institutions[0].country_code | AU |
| authorships[0].institutions[0].display_name | RMIT University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Xuyu Zhang |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[1].author.id | https://openalex.org/A5074236799 |
| authorships[1].author.orcid | https://orcid.org/0000-0001-5720-6649 |
| authorships[1].author.display_name | Yi Min Xie |
| authorships[1].countries | AU |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I82951845 |
| authorships[1].affiliations[0].raw_affiliation_string | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[1].institutions[0].id | https://openalex.org/I82951845 |
| authorships[1].institutions[0].ror | https://ror.org/04ttjf776 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I82951845 |
| authorships[1].institutions[0].country_code | AU |
| authorships[1].institutions[0].display_name | RMIT University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Yi Min Xie |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[2].author.id | https://openalex.org/A5006203732 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-5885-6141 |
| authorships[2].author.display_name | Cong Wang |
| authorships[2].countries | AU |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I82951845 |
| authorships[2].affiliations[0].raw_affiliation_string | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[2].institutions[0].id | https://openalex.org/I82951845 |
| authorships[2].institutions[0].ror | https://ror.org/04ttjf776 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I82951845 |
| authorships[2].institutions[0].country_code | AU |
| authorships[2].institutions[0].display_name | RMIT University |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Cong Wang |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[3].author.id | https://openalex.org/A5033856059 |
| authorships[3].author.orcid | https://orcid.org/0009-0005-1232-4955 |
| authorships[3].author.display_name | He Li |
| authorships[3].countries | AU |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I82951845 |
| authorships[3].affiliations[0].raw_affiliation_string | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[3].institutions[0].id | https://openalex.org/I82951845 |
| authorships[3].institutions[0].ror | https://ror.org/04ttjf776 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I82951845 |
| authorships[3].institutions[0].country_code | AU |
| authorships[3].institutions[0].display_name | RMIT University |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | He Li |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[4].author.id | https://openalex.org/A5030412244 |
| authorships[4].author.orcid | https://orcid.org/0000-0003-2566-0948 |
| authorships[4].author.display_name | Shiwei Zhou |
| authorships[4].countries | AU |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I82951845 |
| authorships[4].affiliations[0].raw_affiliation_string | School of Engineering, RMIT University, Melbourne 3000, Australia |
| authorships[4].institutions[0].id | https://openalex.org/I82951845 |
| authorships[4].institutions[0].ror | https://ror.org/04ttjf776 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I82951845 |
| authorships[4].institutions[0].country_code | AU |
| authorships[4].institutions[0].display_name | RMIT University |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Shiwei Zhou |
| authorships[4].is_corresponding | True |
| authorships[4].raw_affiliation_strings | School of Engineering, RMIT University, Melbourne 3000, Australia |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1016/j.cma.2024.116963 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | A non-uniform rational B-splines (NURBS) based optimization method for fiber path design |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11115 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 0.995199978351593 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2205 |
| primary_topic.subfield.display_name | Civil and Structural Engineering |
| primary_topic.display_name | Topology Optimization in Engineering |
| related_works | https://openalex.org/W1979597421, https://openalex.org/W2007980826, https://openalex.org/W2061531152, https://openalex.org/W3002753104, https://openalex.org/W2077600819, https://openalex.org/W2142036596, https://openalex.org/W2072657027, https://openalex.org/W2600246793, https://openalex.org/W4238204885, https://openalex.org/W2963966623 |
| cited_by_count | 19 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 14 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 5 |
| locations_count | 1 |
| best_oa_location.id | doi:10.1016/j.cma.2024.116963 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S40006715 |
| best_oa_location.source.issn | 0045-7825, 1879-2138 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0045-7825 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Computer Methods in Applied Mechanics and Engineering |
| best_oa_location.source.host_organization | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_name | Elsevier BV |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_lineage_names | Elsevier BV |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Computer Methods in Applied Mechanics and Engineering |
| best_oa_location.landing_page_url | https://doi.org/10.1016/j.cma.2024.116963 |
| primary_location.id | doi:10.1016/j.cma.2024.116963 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S40006715 |
| primary_location.source.issn | 0045-7825, 1879-2138 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0045-7825 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Computer Methods in Applied Mechanics and Engineering |
| primary_location.source.host_organization | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_name | Elsevier BV |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_lineage_names | Elsevier BV |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Computer Methods in Applied Mechanics and Engineering |
| primary_location.landing_page_url | https://doi.org/10.1016/j.cma.2024.116963 |
| publication_date | 2024-04-06 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W3008168197, https://openalex.org/W3183714763, https://openalex.org/W2622174797, https://openalex.org/W2030691777, https://openalex.org/W2030280575, https://openalex.org/W2802057894, https://openalex.org/W2124879166, https://openalex.org/W2580255818, https://openalex.org/W2553349097, https://openalex.org/W6691593245, https://openalex.org/W2001711701, https://openalex.org/W2063392684, https://openalex.org/W1990231416, https://openalex.org/W2773400987, https://openalex.org/W2057058594, https://openalex.org/W6749601254, https://openalex.org/W6800653196, https://openalex.org/W3032933050, https://openalex.org/W2033113414, https://openalex.org/W1987767871, https://openalex.org/W2077619569, https://openalex.org/W2034677912, https://openalex.org/W2991684668, https://openalex.org/W2091071314, https://openalex.org/W1967050912, https://openalex.org/W2166564986, https://openalex.org/W2149192791, https://openalex.org/W2887048650, https://openalex.org/W2896670525, https://openalex.org/W2037162522, https://openalex.org/W1829439472, https://openalex.org/W3039290975, https://openalex.org/W2132034927, https://openalex.org/W2914634383, https://openalex.org/W4284968376, https://openalex.org/W1875361751, https://openalex.org/W3107993129, https://openalex.org/W3209639787, https://openalex.org/W4382199772, https://openalex.org/W4294436696, https://openalex.org/W1995695068, https://openalex.org/W2062375387, https://openalex.org/W2083683711, https://openalex.org/W2016500323, https://openalex.org/W2931255773, https://openalex.org/W6785914576, https://openalex.org/W4206014591, https://openalex.org/W266836189, https://openalex.org/W3119201895, https://openalex.org/W4311776037, https://openalex.org/W2054869797, https://openalex.org/W2070328216, https://openalex.org/W2032844117, https://openalex.org/W2025068203, https://openalex.org/W1816001768, https://openalex.org/W2015456270, https://openalex.org/W2800848781, https://openalex.org/W2534583758, https://openalex.org/W2757627885, https://openalex.org/W1969024803, https://openalex.org/W6755146920, https://openalex.org/W4309048472, https://openalex.org/W2054029517, https://openalex.org/W4387647718, https://openalex.org/W3082360600, https://openalex.org/W1969479015, https://openalex.org/W4224939736, https://openalex.org/W2899098077, https://openalex.org/W2898445388, https://openalex.org/W6809799614, https://openalex.org/W4389321458, https://openalex.org/W4385804254, https://openalex.org/W2896431637, https://openalex.org/W2063569542, https://openalex.org/W2902048823, https://openalex.org/W2002389579, https://openalex.org/W4386922116, https://openalex.org/W2134379651, https://openalex.org/W2792470084, https://openalex.org/W4385550822, https://openalex.org/W2141377530, https://openalex.org/W6795617699, https://openalex.org/W4240834238, https://openalex.org/W2338483979, https://openalex.org/W6862251780, https://openalex.org/W2894016118, https://openalex.org/W2081856500, https://openalex.org/W2530541764, https://openalex.org/W1575923498, https://openalex.org/W2893751856, https://openalex.org/W4392521339, https://openalex.org/W4220878140, https://openalex.org/W2940361467, https://openalex.org/W3164737282, https://openalex.org/W3194046247, https://openalex.org/W2791923853, https://openalex.org/W3105070525 |
| referenced_works_count | 97 |
| abstract_inverted_index.% | 134, 147 |
| abstract_inverted_index.a | 3 |
| abstract_inverted_index.80 | 146 |
| abstract_inverted_index.an | 88 |
| abstract_inverted_index.as | 40, 54 |
| abstract_inverted_index.by | 132, 145 |
| abstract_inverted_index.in | 15, 74, 95, 152 |
| abstract_inverted_index.is | 143 |
| abstract_inverted_index.of | 46, 67, 70, 77, 109 |
| abstract_inverted_index.to | 12, 30, 91, 114, 136, 149 |
| abstract_inverted_index.The | 97 |
| abstract_inverted_index.add | 101 |
| abstract_inverted_index.and | 17, 34, 49, 105, 139 |
| abstract_inverted_index.any | 58 |
| abstract_inverted_index.can | 56, 99 |
| abstract_inverted_index.for | 84 |
| abstract_inverted_index.the | 24, 44, 51, 61, 65, 68, 71, 75, 81, 107, 128, 140 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index.also | 100 |
| abstract_inverted_index.mean | 22, 129 |
| abstract_inverted_index.show | 126 |
| abstract_inverted_index.that | 127 |
| abstract_inverted_index.they | 55 |
| abstract_inverted_index.time | 142 |
| abstract_inverted_index.with | 120 |
| abstract_inverted_index.work | 1, 98 |
| abstract_inverted_index.NURBS | 37 |
| abstract_inverted_index.avoid | 92 |
| abstract_inverted_index.cases | 151 |
| abstract_inverted_index.fiber | 32, 122 |
| abstract_inverted_index.knots | 33 |
| abstract_inverted_index.point | 59 |
| abstract_inverted_index.prior | 153 |
| abstract_inverted_index.reach | 57 |
| abstract_inverted_index.sharp | 93 |
| abstract_inverted_index.their | 19 |
| abstract_inverted_index.turns | 94 |
| abstract_inverted_index.under | 64 |
| abstract_inverted_index.work. | 154 |
| abstract_inverted_index.Beyond | 21 |
| abstract_inverted_index.design | 18, 41, 47, 62, 108, 117 |
| abstract_inverted_index.domain | 63 |
| abstract_inverted_index.during | 103 |
| abstract_inverted_index.enable | 106 |
| abstract_inverted_index.energy | 29 |
| abstract_inverted_index.fibers | 14, 102 |
| abstract_inverted_index.method | 6, 76 |
| abstract_inverted_index.moving | 78 |
| abstract_inverted_index.number | 45 |
| abstract_inverted_index.p-norm | 82 |
| abstract_inverted_index.paths. | 20, 123 |
| abstract_inverted_index.points | 39 |
| abstract_inverted_index.space, | 53 |
| abstract_inverted_index.within | 60 |
| abstract_inverted_index.(NURBS) | 11 |
| abstract_inverted_index.60∼70 | 133 |
| abstract_inverted_index.address | 115 |
| abstract_inverted_index.control | 38 |
| abstract_inverted_index.expands | 50 |
| abstract_inverted_index.fibers. | 96 |
| abstract_inverted_index.initial | 137 |
| abstract_inverted_index.prevent | 31 |
| abstract_inverted_index.reduced | 144 |
| abstract_inverted_index.reduces | 43 |
| abstract_inverted_index.similar | 150 |
| abstract_inverted_index.various | 116 |
| abstract_inverted_index.compared | 135, 148 |
| abstract_inverted_index.examples | 125 |
| abstract_inverted_index.function | 26, 73 |
| abstract_inverted_index.guidance | 66 |
| abstract_inverted_index.presents | 2 |
| abstract_inverted_index.rational | 9 |
| abstract_inverted_index.solution | 52 |
| abstract_inverted_index.B-splines | 10 |
| abstract_inverted_index.Numerical | 124 |
| abstract_inverted_index.Utilizing | 36 |
| abstract_inverted_index.composite | 112 |
| abstract_inverted_index.curvature | 85 |
| abstract_inverted_index.decreases | 131 |
| abstract_inverted_index.objective | 25, 72 |
| abstract_inverted_index.represent | 13 |
| abstract_inverted_index.repulsive | 28 |
| abstract_inverted_index.structure | 113 |
| abstract_inverted_index.technique | 83 |
| abstract_inverted_index.utilizing | 7 |
| abstract_inverted_index.variables | 42, 48 |
| abstract_inverted_index.adaptation | 90 |
| abstract_inverted_index.associated | 119 |
| abstract_inverted_index.challenges | 118 |
| abstract_inverted_index.compliance | 130 |
| abstract_inverted_index.composites | 16 |
| abstract_inverted_index.innovative | 89 |
| abstract_inverted_index.optimizing | 121 |
| abstract_inverted_index.represents | 87 |
| abstract_inverted_index.systematic | 4 |
| abstract_inverted_index.asymptotes. | 79 |
| abstract_inverted_index.compliance, | 23 |
| abstract_inverted_index.computation | 141 |
| abstract_inverted_index.constraints | 86 |
| abstract_inverted_index.multi-layer | 110 |
| abstract_inverted_index.non-uniform | 8 |
| abstract_inverted_index.sensitivity | 69 |
| abstract_inverted_index.incorporates | 27 |
| abstract_inverted_index.optimization | 5, 104 |
| abstract_inverted_index.Additionally, | 80 |
| abstract_inverted_index.fiber-enhanced | 111 |
| abstract_inverted_index.intersections. | 35 |
| abstract_inverted_index.configurations, | 138 |
| cited_by_percentile_year.max | 100 |
| cited_by_percentile_year.min | 98 |
| corresponding_author_ids | https://openalex.org/A5030412244 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I82951845 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.4099999964237213 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile.value | 0.97423635 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |