I have a problem while solving 1-d tapered bar(cantilever) problem

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The discussion centers on solving a 1-dimensional tapered cantilever bar problem under an axial load of 4000 N, with the cross-sectional area decreasing from 10 sq cm to 5 sq cm over 75 cm. The governing differential equation is given as -d/dx(EA du/dx) + P(x) = 0, with boundary conditions specifying that displacement u is zero at the fixed end (x=0) and the derivative of displacement du/dx is zero at the free end (x=75). Participants are seeking assistance in deriving the equations for u and du/dx based on these parameters. The problem highlights the complexities involved in analyzing tapered structures under axial loads. Effective solutions are needed to address the mathematical challenges presented.
date.chinmay
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I have a problem while solving 1-d tapered bar(cantilever) problem with one end fixed and other free with an axial load of 4000 N outwards from the free end.
Area decreases from10sqcm to 5sqcm over a length of 75 cm.

Differential equation is - d/dx(EA du/dx) + P(at x) =0

Boundary Conditions - at x=0 u=0
at x=75 du/dx=0

Please help in finding the equations for u and du/dx

Thank you.
 
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some1 please answer this question...


date.chinmay said:
I have a problem while solving 1-d tapered bar(cantilever) problem with one end fixed and other free with an axial load of 4000 N outwards from the free end.
Area decreases from10sqcm to 5sqcm over a length of 75 cm.

Differential equation is - d/dx(EA du/dx) + P(at x) =0

Boundary Conditions - at x=0 u=0
at x=75 du/dx=0

Please help in finding the equations for u and du/dx

Thank you.
 

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