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Related Concept Videos

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

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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.
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Fluid Pressure over Flat Plate of Variable Width01:02

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When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
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Theorems of Pappus and Guldinus: Problem Solving01:12

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Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
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Unsymmetric Loading of Thin-Walled Members01:23

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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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Bending of Curved Members - Neutral Surface01:16

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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
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Multivalued Inverse Design: Multiple Surface Geometries from One Flat Sheet.

Itay Griniasty1, Cyrus Mostajeran2, Itai Cohen1

  • 1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.

Physical Review Letters
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Summary
This summary is machine-generated.

Researchers developed a method for designing flat sheets that can transform into multiple 3D shapes. This breakthrough enables the creation of machines capable of complex tasks through shape-shifting capabilities.

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Area of Science:

  • Materials science and engineering
  • Robotics and mechanical engineering

Background:

  • Designing flat sheets to deform into specific 3D shapes is crucial for applications like micromachines, soft robotics, and medical implants.
  • Current methods typically allow sheets to achieve only a single target shape.

Purpose of the Study:

  • To demonstrate that a single flat sheet can be designed to deform into multiple distinct 3D shapes through controlled, inhomogeneous anisotropic deformation.
  • To develop an analytical method for solving the inverse problem of designing multi-shape-capable sheets.

Main Methods:

  • An analytical method was developed to solve the multivalued inverse problem for sheet deformation.
  • Inhomogeneous anisotropic deformation was applied to design the flat sheets.

Main Results:

  • A single flat sheet was successfully designed to deform into multiple surface geometries based on different actuation inputs.
  • A proof-of-concept simple swimmer capable of locomotion in fluid at low Reynolds numbers was fabricated.

Conclusions:

  • The developed method enables the design of single sheets capable of multiple shape transformations, overcoming previous limitations.
  • This approach paves the way for fabricating machines that perform complex tasks by cyclically transitioning between various shapes.