Question 3 The pressure distribution on a rectangular steel plate supporting a load is modelled by the function: where x and y are in meters. (a) Calculate the gradient of the pressure function. Hence, determine the rate of change of pressure at the point (0, 1) in the direction of ui - 2j. (b) P(x, y) = = 70-(x - 1)²-(y-2)² (MPa) (c) If the dimensions of the plate is not known, determine the location on the plate where the pressure is maximum and calculate this pressure. Show that this pressure is both a local and global maximum. If the plate is 1 m long by 2 m wide, such that 0 ≤ x ≤ 1,0 ≤ y ≤ 2, determine the minimum pressure on the plate. State any theorems used, if any.
Question 3 The pressure distribution on a rectangular steel plate supporting a load is modelled by the function: where x and y are in meters. (a) Calculate the gradient of the pressure function. Hence, determine the rate of change of pressure at the point (0, 1) in the direction of ui - 2j. (b) P(x, y) = = 70-(x - 1)²-(y-2)² (MPa) (c) If the dimensions of the plate is not known, determine the location on the plate where the pressure is maximum and calculate this pressure. Show that this pressure is both a local and global maximum. If the plate is 1 m long by 2 m wide, such that 0 ≤ x ≤ 1,0 ≤ y ≤ 2, determine the minimum pressure on the plate. State any theorems used, if any.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 3
The pressure distribution on a rectangular steel plate supporting a load is modelled by the
function:
(b)
P(x, y)
where x and y are in meters.
(a)
Calculate the gradient of the pressure function. Hence, determine the rate of change of
pressure at the point (0, 1) in the direction of u = i - 2j.
(c)
= 70-(x - 1)²-(y - 2)²2 (MPa)
If the dimensions of the plate is not known, determine the location on the plate where
the pressure is maximum and calculate this pressure. Show that this pressure is both a
local and global maximum.
If the plate is 1 m long by 2 m wide, such that 0≤x≤ 1,0 ≤ y ≤ 2, determine the
minimum pressure on the plate. State any theorems used, if any.
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