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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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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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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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Members Made of Elastoplastic Material01:19

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
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Knowledge Based Cloud FE Simulation of Sheet Metal Forming Processes
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Nonlinear Rheological Processes Modeling in Three-Layer Plates with a Polyurethane Foam Core.

Anton Chepurnenko1

  • 1Strength of Materials Department, Faculty of Civil and Industrial Engineering, Don State Technical University, Rostov-on-Don 344000, Russia.

Polymers
|May 28, 2022
PubMed
Summary

This study introduces a new method for calculating the bending of three-layer panels, considering the nonlinear creep of polyurethane foam. Accounting for this nonlinear creep is crucial for accurate stress analysis in sandwich panels.

Keywords:
Maxwell–Gurevich equationcreepnonlinearitynumerical simulationpolyurethane foamsandwich panelsthree-layer plate

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Area of Science:

  • Materials Science
  • Structural Engineering
  • Computational Mechanics

Background:

  • Three-layer panels with polyurethane foam are common in construction.
  • Accurate structural analysis is vital for their performance and safety.

Purpose of the Study:

  • Develop a calculation method for three-layer plate bending.
  • Incorporate the nonlinear creep behavior of the polyurethane foam core.

Main Methods:

  • Utilized the non-linear Maxwell-Gurevich equation for polyurethane foam creep.
  • Employed the finite difference and Euler methods in MATLAB for numerical solutions.
  • Derived an analytical solution for hinged plates.

Main Results:

  • Verified the model against ANSYS software.
  • Revealed significant effects of nonlinear creep absent in linear analysis.
  • Observed time-varying stresses in faces and filler due to nonlinear creep.

Conclusions:

  • Nonlinear creep significantly alters stress distribution over time in sandwich panels.
  • Stresses in the faces increase initially then return to original values.
  • Stresses in the polyurethane foam filler initially decrease.
  • Accurate calculation of sandwich panels requires accounting for nonlinear creep.