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Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁(x)=(x−L)(2x −L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x)= x(2x −L)/ Ľ². Consider E = constant, and A(x) = A (2−x/L).

Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁(x)=(x−L)(2x −L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x)= x(2x −L)/ Ľ². Consider E = constant, and A(x) = A (2−x/L).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁ (x)=(x−L)(2x−L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x) = x(2x −L) / L². Consider E= constant, and A(x) = A₁(2-x/L).
Transcribed Image Text:Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁ (x)=(x−L)(2x−L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x) = x(2x −L) / L². Consider E= constant, and A(x) = A₁(2-x/L).
X = 0 Node 1 Area = 2A₂ X = L/2 * Element Node 2 Area = A₂ Node 3 X = L
Transcribed Image Text:X = 0 Node 1 Area = 2A₂ X = L/2 * Element Node 2 Area = A₂ Node 3 X = L
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