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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?

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# Finite element procedures book - Bathe

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