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Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

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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.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
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Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

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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.
The resultant force...
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Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Stresses under Combined Loadings01:23

Stresses under Combined Loadings

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When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
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Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Updated: Aug 7, 2025

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
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Multiwall Rectangular Plates under Transverse Pressure-A Non-Linear Experimental and Numerical Study.

Gilad Hakim1, Haim Abramovich1

  • 1Faculty of Aerospace Engineering, Technion-Israel Institute of Technology (I.I.T.), Haifa 32000, Israel.

Materials (Basel, Switzerland)
|March 11, 2023
PubMed
Summary
This summary is machine-generated.

This study simplifies large plate deflection analysis using a polynomial approximation. The method accurately predicts plate behavior under pressure using material properties and dimensions.

Keywords:
Föppl–von Kármán equationsmultiwall platenonlinear load–deflection curverectangular plate large deflectionvacuum chamber loading test

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Area of Science:

  • Mechanical Engineering
  • Solid Mechanics
  • Materials Science

Background:

  • Large deflection of rectangular plates under transverse pressure is complex, with Föppl-von Kármán equations offering only approximate solutions.
  • A common approximation involves separating plate behavior into small deflection and thin membrane components, often using polynomial expressions.

Purpose of the Study:

  • To derive analytical expressions for the coefficients of a third-order polynomial approximation for large plate deflections.
  • To validate the derived analytical expressions through experimental testing and finite element analysis.
  • To establish a predictive method for plate deflections based on elastic properties and dimensions.

Main Methods:

  • Derivation of analytical expressions for polynomial coefficients based on plate elastic properties and dimensions.
  • Experimental validation using a vacuum chamber loading test to measure lateral displacement of multiwall plates.
  • Numerical validation through finite element analysis (FEA) of plate behavior under pressure.

Main Results:

  • The third-order polynomial expression was found to fairly describe the non-linear relationship between pressure and lateral displacement.
  • Experimental measurements and FEA results demonstrated good agreement with the predictions from the analytical expressions.
  • The study successfully validated the polynomial approximation for predicting large plate deflections.

Conclusions:

  • The developed analytical method provides accurate expressions for predicting large plate deflections under transverse pressure.
  • This approach simplifies the analysis of plate behavior, requiring only known elastic properties and dimensions.
  • The findings offer a practical tool for engineers to estimate plate deflections efficiently.