Hello Eng-Tips team,
I am trying to solve the below problem analytically
โโฯ + ๐_๐ฅ = ๐ (๐^2 ๐ข)/(๐๐ก^2 ) --> (1) is the governing equation
[Note: In the above problem, b_x = 0 (no body forces)]
IC: u(x,0) = v(x,0) = 0
BC: u(0,t) =0; u'(x=1,t) = F(t)/(A*E2)
[Note: Since force (F(t)) is applied on bar that has modulus E2, I'm assuming the BC is F(t)/(A*E2)]].
I'm having trouble understanding how to solve the above problem.
Q1). Does interface conditions come into play in this problem? The displacements, stresses are continuous at the interface (Assuming it is perfectly bonded).
Q2). If I consider each portion of the bar individually (material1 or material2), how do the boundary conditions behave?
Any help would be much appreciated. Thank you!
I am trying to solve the below problem analytically

โโฯ + ๐_๐ฅ = ๐ (๐^2 ๐ข)/(๐๐ก^2 ) --> (1) is the governing equation
[Note: In the above problem, b_x = 0 (no body forces)]
IC: u(x,0) = v(x,0) = 0
BC: u(0,t) =0; u'(x=1,t) = F(t)/(A*E2)
[Note: Since force (F(t)) is applied on bar that has modulus E2, I'm assuming the BC is F(t)/(A*E2)]].
I'm having trouble understanding how to solve the above problem.
Q1). Does interface conditions come into play in this problem? The displacements, stresses are continuous at the interface (Assuming it is perfectly bonded).
Q2). If I consider each portion of the bar individually (material1 or material2), how do the boundary conditions behave?
Any help would be much appreciated. Thank you!