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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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Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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Lift01:23

Lift

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Lift is a fundamental aerodynamic force that acts perpendicular to the direction of airflow. It plays a central role in achieving and sustaining flight and in stabilizing various vehicles. Lift primarily originates from pressure differences created across surfaces, such as an airfoil. A lower pressure region forms above the wing, while a higher pressure region forms below it, generating an upward force. This differential results from the shape and orientation of the airfoil, enabling the wing...
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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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Flexural Stress01:16

Flexural Stress

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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
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Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Related Experiment Video

Updated: Jan 8, 2026

Structural Design and Manufacturing of a Cruiser Class Solar Vehicle
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Geometrically nonlinear high-fidelity aerostructural optimization for highly flexible wings.

Alasdair C Gray1, Graeme J Kennedy2, Joaquim R R A Martins1

  • 1Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI USA.

Structural and Multidisciplinary Optimization : Journal of the International Society for Structural and Multidisciplinary Optimization
|December 12, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for simultaneously optimizing aircraft wing shape and structure using nonlinear models. This approach accurately accounts for extreme flexibility in high-aspect-ratio wings, crucial for efficient aircraft design.

Keywords:
AeroelasticityGeometric nonlinearityHigh aspect-ratio wing designMultidisciplinary design optimization

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Area of Science:

  • Aerospace Engineering
  • Computational Mechanics
  • Optimization Theory

Background:

  • Multidisciplinary Design Optimization (MDO) advances enable simultaneous aerodynamic and structural wing design using high-fidelity models.
  • Current MDO methods accurately trade off drag and mass but struggle with geometrically nonlinear behavior in high-aspect-ratio wings.
  • Linear structural analysis is insufficient for modeling the extreme flexibility and nonlinearities of next-generation aircraft wings.

Purpose of the Study:

  • To demonstrate the first simultaneous optimization of wing aerodynamic shape and structural sizing using high-fidelity geometrically nonlinear models.
  • To develop and implement computational tools for nonlinear structural analysis and aeroelastic coupling.
  • To investigate the impact of geometric nonlinearity on the design and performance of highly flexible aircraft wings.

Main Methods:

  • Implementation of a novel geometrically nonlinear shell element, an efficient nonlinear solver, and a constitutive model for stiffened shells.
  • Coupling nonlinear structural analysis with Computational Fluid Dynamics (CFD) via a geometrically nonlinear transfer scheme.
  • Optimization of a single-aisle commercial transport aircraft wing with 547 design variables and 1277 constraints.

Main Results:

  • Optimized designs exhibit extreme flexibility (aspect ratio > 19, deflections > 30% semispan).
  • Geometric nonlinearity had minimal impact on aerodynamic performance, planform, and overall aircraft mass.
  • The Brazier effect, a nonlinear phenomenon, introduces significant internal loads missed by linear analysis, necessitating nonlinear methods for feasible designs.

Conclusions:

  • The developed framework provides the computational foundation for designing next-generation high-aspect-ratio wings.
  • Exploiting extreme wing flexibility through geometrically nonlinear analysis is key to designing more efficient aircraft.
  • This research enables the pursuit of innovative wing designs by treating extreme flexibility as an opportunity, not a constraint.