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Related Concept Videos

Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

Unsymmetric Loading of Thin-Walled Members: Problem Solving

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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
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Unsymmetric Loading of Thin-Walled Members01:23

Unsymmetric Loading of Thin-Walled Members

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

156
When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
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Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

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When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
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Automated shape and thickness optimization for non-matching isogeometric shells using free-form deformation.

Han Zhao1, David Kamensky1, John T Hwang1

  • 1Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, Mail Code 0411, La Jolla, CA 92093 USA.

Engineering with Computers
|December 16, 2024
PubMed
Summary

This study introduces a unified method for optimizing shell structures using isogeometric analysis (IGA) and free-form deformation (FFD). The approach ensures continuity across multiple patches, enabling efficient shape and thickness optimization for complex designs like aircraft wings.

Keywords:
Aircraft wing optimizationFEniCSFree-form deformationIsogeometric analysisKirchhoff–Love shellsLagrange extractionNon-matching coupling

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Area of Science:

  • Computational mechanics
  • Structural optimization
  • Computer-aided design (CAD)

Background:

  • Isogeometric analysis (IGA) integrates CAD and analysis using NURBS, simplifying structural optimization.
  • Optimizing real-world CAD geometries with multiple, non-matching NURBS patches presents significant challenges.
  • Existing methods struggle with maintaining continuity and efficient optimization across complex, multi-patch shell structures.

Purpose of the Study:

  • To develop a unified formulation for shape and thickness optimization of shell structures with multiple, separately parametrized patches.
  • To ensure continuity of design variables at patch intersections during the optimization process.
  • To leverage free-form deformation (FFD) for seamless integration of design and analysis models.

Main Methods:

  • Utilizing free-form deformation (FFD) to parameterize shell structures and maintain continuity.
  • Employing isogeometric Kirchhoff-Love theory for shell modeling and a penalty-based method for coupling patches.
  • Implementing Lagrange extraction to link control points and leveraging FEniCS for automated analytical derivative computation.
  • Performing isogeometric analysis (IGA) with shared extraction matrices and existing finite element assembly procedures.

Main Results:

  • A unified framework for shape and thickness optimization of multi-patch shell structures was successfully developed.
  • Continuity of design variables at patch intersections was preserved throughout the optimization process.
  • The method demonstrated efficient gradient-based optimization through automated analytical derivative computation in FEniCS.
  • Validation on benchmark problems confirmed applicability to complex shell layouts, including aircraft wings.

Conclusions:

  • The proposed unified formulation effectively addresses the challenges of optimizing complex, multi-patch shell structures.
  • The integration of FFD, IGA, and FEniCS provides an efficient and robust approach for structural optimization.
  • This methodology holds significant potential for optimizing intricate designs in aerospace and other engineering fields.