Nondimensional Shape Optimization of Nonprismatic Beams with Sinusoidal Lateral Profile
Publication: Journal of Structural Engineering
Volume 150, Issue 1
Abstract
The present paper deals with the optimal design of nonprismatic beams, i.e., beams with variable cross section. To set the optimization problem, Euler-Bernoulli unshearable beam theory is considered and the elastica equation expressing the transverse displacement as a function of the applied loads is reformulated into a system of four differential equations involving kinematic components and internal forces. The optimal solution (in terms of volume) must satisfy two constraints: the maximum Von Mises equivalent stress must not exceed an (ideal) strength, and the maximum vertical displacement is limited to a fraction of beam length. To evaluate the maximum equivalent stress in the beam, normal and shear stresses have been considered. The former was evaluated through the Navier formula, and the latter through a formula derived from Jourawsky and holding for straight and untwisted beams with bisymmetric variable cross sections. The optimal solutions as function of material unit weight, maximum strength, and applied load are presented and discussed. It is shown that the binding constraint is usually represented by the maximum stress in the beam, and that applied load and strength affect the solution more than material unit weight. To maintain the generality of the solution, the nondimensionalization according to Buckingham -theorem is implemented and a design abacus is proposed.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was supported by project MSCA-RISE-2020 Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)—ADDOPTML (ntua.gr) “Additively Manufactured Optimized Structures by Means of Machine Learning” (No. 101007595).
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Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 150 • Issue 1 • January 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Feb 17, 2023
Accepted: Aug 17, 2023
Published online: Oct 18, 2023
Published in print: Jan 1, 2024
Discussion open until: Mar 18, 2024
ASCE Technical Topics:
- Beams
- Continuum mechanics
- Cross sections
- Design (by type)
- Displacement (mechanics)
- Engineering fundamentals
- Engineering mechanics
- Load factors
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Maximum loads
- Shear stress
- Solid mechanics
- Static loads
- Statics (mechanics)
- Strength of materials
- Stress (by type)
- Structural analysis
- Structural behavior
- Structural design
- Structural engineering
- Structural mechanics
- Structural members
- Structural strength
- Structural systems
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