<div class="csl-bib-body">
<div class="csl-entry">Key, F., & Freinberger, L. (2025, September 15). <i>A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy</i> [Conference Presentation]. The Thirteenth International Conference on Isogeometric Analysis (IGA 2025), Eindhoven, Netherlands (the).</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/219600
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dc.description.abstract
From the classical theory of linear elasticity, the principle of minimum complementary energy can be used to calculate compatible stress fields for static solids or structures. However, the minimum must only be sought among statically admissible stress fields, yielding a constrained problem. Based on the complementary energy principle, numerical methods have been developed both in the fields of analytical methods and stress-based finite element analysis (FEA). While analytical methods, such as power series approaches, are limited to problems with regular geometries and boundary conditions, the development of specific elements in stress-based FEA resulted in problems with large numbers of degrees of freedom, e.g., due to more than 20 degrees of freedom per element [1]. The same holds usually true if accurate stress results have to be computed based on displacement-based FEA. In response, our approach involves a spline-based stress function that automatically ensures static admissibility and provides the solution, i.e., the stress field, by applying the principle of complementary energy. We show that the properties of splines allow for flexibility in terms of geometry and boundary conditions as well as efficiency in the number of degrees of freedom, yielding accurate approximations of the unknown stress field. We will present results for different types of 2D plane stress problems. First, we will use common benchmark problems, to which analytical methods can be applied, to validate our approach. Furthermore, we will consider composite beams with anisotropic material behavior [2] as well as non-prismatic beams [3] discussed in the literature, demonstrating the approach's applicability to problems where obtaining accurate stress results remains a challenge for existing methods. REFERENCES [1] R. H. Gallagher, Finite element structural analysis and complementary energy. Finite Elements in Analysis and Design (1993) 115-126. [2] G. Balduzzi, S. Morganti, J. Füssl, M. Aminbaghai, A. Reali, and F. Auricchio, Modeling the non-trivial behavior of anisotropic beams: a simple Timoshenko beam with enhanced stress recovery and constitutive relations. Composite Structures (2019) 111265. [3] V. Mercuri, G. Balduzzi, D. Asprone, and F. Auricchio, Structural analysis of non-prismatic beams: Critical issues, accurate stress recovery, and analytical definition of the Finite Element (FE) stiffness matrix. Engineering Structures (2020) 110252.
en
dc.language.iso
en
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dc.subject
Stress Analysis
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dc.subject
Stress Function
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dc.subject
Spline Approximation
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dc.subject
Complementary Energy
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dc.subject
Linear Elastostatics
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dc.title
A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.researchTopic.id
C4
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tuw.researchTopic.id
C3
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.name
Computational System Design
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tuw.researchTopic.value
40
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tuw.researchTopic.value
60
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tuw.publication.orgunit
E317-01-1 - Forschungsgruppe Numerische Analyse- und Designmethoden
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tuw.author.orcid
0000-0001-6622-4806
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tuw.event.name
The Thirteenth International Conference on Isogeometric Analysis (IGA 2025)
en
tuw.event.startdate
14-09-2025
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tuw.event.enddate
17-09-2025
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Eindhoven
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tuw.event.country
NL
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tuw.event.presenter
Key, Fabian
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wb.sciencebranch
Maschinenbau
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wb.sciencebranch
Sonstige Technische Wissenschaften
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
2030
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wb.sciencebranch.oefos
2119
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
40
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wb.sciencebranch.value
30
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wb.sciencebranch.value
30
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item.languageiso639-1
en
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item.grantfulltext
none
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.cerifentitytype
Publications
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item.fulltext
no Fulltext
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crisitem.author.dept
E317-01-1 - Forschungsgruppe Numerische Analyse- und Designmethoden
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crisitem.author.dept
E317-01-1 - Forschungsgruppe Numerische Analyse- und Designmethoden
