how to calculate structure's energy

[leiloo]

how can I calculate disipated energy by damper in structure and structure's kinetic energy and strain energy, by using Opensees and mathlab?

thanks

[Jhno]

The energy is the area inside a loop of the hysteresis. You have to record the data and then make the calculation. There is not magic command (that I am aware of) to do it.
https://www.researchgate.net/post/How_c ... ic_loading

[selimgunay]

For the strain energy, you need to record the restoring forces and displacements. For the kinetic energy, you also need accelerations. You should use the recorded data in matlab to compute the kinetic and strain energy by numerical integration. See Dynamics of Structures (Anil Chopra) Chapter 3 for relevant equations. If you don't have access to the book, please let me know

[leiloo]

By integrating motion equation in “principal of passive supplemental damping and isolation” (C.Christopoulous), these equations have been derived:
E_kinetic(t) = (1/2) * ({x ̇(t)})^T * [M] * {x ̇(t)}
E_st(t)= ∫{dx}^T * {F_(Static load)}
The question is how to calculate {x ̇(t)} and [M] in Opensees?

best regards

leiloo

[selimgunay]

You can obtain x(t) from the relevant node or element recorder.

In order to see the mass matrix, please use the printA command. Use zero damping and explicit Newmark as the integrator: "integrator NewmarkExplicit 0.5"

[leiloo]

{x ̇(t)} is the vector of global velocity, can I calculate it by " Node recorder command" for one node?

[leiloo]

thanks for your help

[selimgunay]

You can record the total velocity with the following command

recorder Node -file nodesV.out -timeSeries 1 -time -node 1 2 3 4 -dof 1 vel;

and relative velocity with

recorder Node -file nodesV.out -time -node 1 2 3 4 -dof 1 vel;

http://opensees.berkeley.edu/wiki/index ... e_Recorder

[leiloo]

1-is it correct to use command: "printA" for calculating mass matrix as below? do you have any example?
integrator LoadControl 1
system FullGeneral
analysis Static
analyze 1
printA -file Stiff.out

wipeAnalysis
system FullGeneral
integrator NewmarkExplicit 0.5
analysis Transient
analyze 1 1.
printA -file mass.out

2-for calculating kinetic energy,have I Calculate the velocity for one node or more?

thanks a lot

[selimgunay]

Yes that is correct, but you should also set the damping to zero. Please note that you should not use these commands for the analysis, they are only for printing the mass matrix. Please let me know if you experience any problems.

According to your equation, you should get the velocity from only one node.

[leiloo]

How can I set the the damping to zero?
have it special command?

thanks

[leiloo]

What force should be calculated to obtain hysteresis loop of damper ?
If possible, mention the command


thanks for your help

[selimgunay]

You can set damping to zero as follows:

set alphaM 0.0;
set betaK 0.0;
set betaKinit 0.0;
set betaKcomm 0.0;

rayleigh $alphaM $betaK $betaKinit $betaKcomm

you can use the element recorder to record the forces:

http://opensees.berkeley.edu/wiki/index ... t_Recorder

[leiloo]

when i added elements of dampers to model,the mass matrix was changed
What do you think about the reason of it?
viscoelastic damper is used


thanks for your help

[selimgunay]

Because the viscoelastic damper contributes to the damping matrix. The matrix that you get with the printA command when you use explicit Newmark is a combination of the mass and damping matrices. Therefore, to obtain the mass matrix with this command, we would like to set the damping matrix to zero. Could you remove all the damper elements to get the mass matrix?