# Finite element procedures book - Bathe

1. Dec 3, 2013

### 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

2. Dec 4, 2013

### Staff: Mentor

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?

3. Dec 4, 2013

### 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.