Finite element procedures book - Bathe

[c0der]

Hi,

I have been stuck on a problem for a while now (3.24 part c).

My attempt is as follows:

Internal virtual work = external virtual work

T/2 ∫0->L (∂u/dx)(∂v/dx)dx + ∫0->L (∂^2u/∂t^2)vdx = ∫0->L (Pv)dx

Stationarity is already invoked on this functional as it's the principle of virtual work dv/dx = δv

Using the basis functions:

u = { 3w1L/x for 0<x<L/3,
(2 - 3/L*x)w1 + (-1 +3/L*x)w2 for L/3<x<2L/3,
3w2(1 - x/L) for 2L/3<x<L }

Extracting the functions for v from the basis functions:

v = { 3L/x for 0<x<L/3,
(2 - 3/L*x) + (-1 +3/L*x) for L/3<x<2L/3,
3(1 - x/L) for 2L/3<x<L }

Integrating over each interval does not get me the answer

Help please?

 

[berkeman]

Hi,

I have been stuck on a problem for a while now (3.24 part c).

My attempt is as follows:

Internal virtual work = external virtual work

T/2 ∫0->L (∂u/dx)(∂v/dx)dx + ∫0->L (∂^2u/∂t^2)vdx = ∫0->L (Pv)dx

Stationarity is already invoked on this functional as it's the principle of virtual work dv/dx = δv

Using the basis functions:

u = { 3w1L/x for 0<x<L/3,
(2 - 3/L*x)w1 + (-1 +3/L*x)w2 for L/3<x<2L/3,
3w2(1 - x/L) for 2L/3<x<L }

Extracting the functions for v from the basis functions:

v = { 3L/x for 0<x<L/3,
(2 - 3/L*x) + (-1 +3/L*x) for L/3<x<2L/3,
3(1 - x/L) for 2L/3<x<L }

Integrating over each interval does not get me the answer

Help please?

Welcome to the PF.

What is the context for this question? Is it for schoolwork? If so, which subject? Perhaps I should move this to a different forum? Or is General Engineering the best fit?

 

[c0der]

It's self learning, postgraduate level finite element analysis. It's general engineering because you can apply it to a range of engineering problems, heat transfer, solids, fluids etc.

Thanks for your reply.