Analytical shape optimization of homogeneous simply supported Euler-Bernoulli beams for mean compliance.
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| Title: | Analytical shape optimization of homogeneous simply supported Euler-Bernoulli beams for mean compliance. |
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| Authors: | Ramchandra, Rai Saurabh Kumar1 (AUTHOR) saurabkr11274-cgo@gov.in, Pratapa, Phanisri Pradeep2 (AUTHOR) ppratapa@civil.iitm.ac.in |
| Source: | Optimization & Engineering. Jun2026, Vol. 27 Issue 2, p1713-1751. 39p. |
| Subjects: | Euler-Bernoulli beam theory, Calculus of variations, Structural design, Three-dimensional printing, Structural optimization, Elastic deformation |
| Abstract: | Cross-section profile along the span of a homogeneous, simply-supported, Euler-Bernoulli beam of constant depth is obtained through shape optimization, for minimum mean compliance, under uniformly distributed load. Scope is restricted to beam designs governed by deflection or stiffness criteria rather than strength criteria that requires imposition of stress constraints. It is analytically demonstrated that a generic shape optimization setup using calculus of variations framework results in a non-prismatic beam with the commonly known I-shaped cross-section. However, it is shown that a re-formulation in terms of the geometric parameters involving the I-shape leads to characteristic special cases of non-prismatic beams that further improve the optimality of the solutions. The optimal design solutions can be described through analytical equations as demonstrated through an example. The formulations proposed consider minimum and maximum dimensional constraints that are useful for structural design applications. With advancements in manufacturing and 3D printing, this work forms an important theoretical contribution to design beams with unconventional shapes but with desired optimal behavior. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193859243 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11081-025-10068-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 39 StartPage: 1713 Subjects: – SubjectFull: Euler-Bernoulli beam theory Type: general – SubjectFull: Calculus of variations Type: general – SubjectFull: Structural design Type: general – SubjectFull: Three-dimensional printing Type: general – SubjectFull: Structural optimization Type: general – SubjectFull: Elastic deformation Type: general Titles: – TitleFull: Analytical shape optimization of homogeneous simply supported Euler-Bernoulli beams for mean compliance. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ramchandra, Rai Saurabh Kumar – PersonEntity: Name: NameFull: Pratapa, Phanisri Pradeep IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13894420 Numbering: – Type: volume Value: 27 – Type: issue Value: 2 Titles: – TitleFull: Optimization & Engineering Type: main |
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