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Topic: Reference for FEA numerical integration algorithem
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LasCondes

Posts: 1
Registered: 7/9/13
Reference for FEA numerical integration algorithem
Posted: Jul 9, 2013 5:27 AM
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Hi,

I am updating a 1 dimensional mechanical FEA algorithm that integrates forward in time. It was written in the 1980's in Fortran and is not documented.

I am looking for:
a) any guidance on a published reference on the numerical integration algorithm used.
b) comments on the selection of theta - (currently used with theta = 0.67.
c) calculation of maximum time step for stability


The algorithm is as follows:

M is the mass matrix.
K is the stiffness matrix.
C is the damping matrix = alpha*M + beta*K

delta is the timestep

u is the displacements
v is the velocity
f is the applied forces

a) Calculate the applied forces, f, for the time step.

b) solve the following matrix equation for u

[C + M/(theta*delta) + theta * delta * K] * u = [C + M/(theta*delta) - (1-theta)*delta*K]*u_old + theta*delta*f + (1-theta)*delta*f_old + M*v_old/theta

c) Calculate the new velocity

v = (u - u_old)/(theta*delta) - (1-theta)/theta*v_old

d) Update the old values

u_old = u
v_old = v
f_old = f

e) Repeat for the desired simulation time.

Any input is greatly appreciated.

Andrew



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