Hi every one!
I'm working on developing a shell element to be implemented in ABAQUS through UEL.
It's going through a static analysis. and as you may know for static analysis, ABAQUS just needs AMATRX and RHS to be defined via UEL. It must be mentioned that the stiffness matrix is changing at each time increment. The force that has been applied, is a concentrated force and a function of time.
I've defined the RHS as:
RHS=-[K]*{U}
where [K] is the stiffness (AMATRX) matrix and {u} is the displacement vector at each time increment.
Since I have some difficulties in getting the expected answer, I'm not sure about correctness of this RHS (I've checked B.C., stiffness matrix and etc. and all of them are correct for sure).
I would appreciate if you could help me with defining this RHS.
Best Regards,
Hello Ashkan,
The right hand side vector RHS=-[K]*{U} is particularly correct only when you have a linear elastic problem.
In fact RHS=-[K]*{U} is the simplified form of the residual vector for the linear elastic case. As your stiffness matrix changes at each increment, I think your problem is a nonlinear one.
For example, for a nonlinear plasticity problem (with small strain/deformation), RHS=-[B]T*{Stress}. For a linear elastic case {Stress}=[C]{Strain}=[C][B]{U}, one can see that RHS=-[B]T[C][B]{U}
You may want to have a look at the following books for the residual force vector:
"finite elements in plasticity theory and practice" by D. R. J. Owen, Ernest Hinton
"Computational Methods for Plasticity" by E. A. de Souza Neto, D. Peric, D. R. J. Owen
"Finite Element Procedures" by K.J. Bathe
Hope it helps,
Best regards,
Hello Ashkan,
The right hand side vector RHS=-[K]*{U} is particularly correct only when you have a linear elastic problem.
In fact RHS=-[K]*{U} is the simplified form of the residual vector for the linear elastic case. As your stiffness matrix changes at each increment, I think your problem is a nonlinear one.
For example, for a nonlinear plasticity problem (with small strain/deformation), RHS=-[B]T*{Stress}. For a linear elastic case {Stress}=[C]{Strain}=[C][B]{U}, one can see that RHS=-[B]T[C][B]{U}
You may want to have a look at the following books for the residual force vector:
"finite elements in plasticity theory and practice" by D. R. J. Owen, Ernest Hinton
"Computational Methods for Plasticity" by E. A. de Souza Neto, D. Peric, D. R. J. Owen
"Finite Element Procedures" by K.J. Bathe
Hope it helps,
Best regards,
Hi Farid,
Thanks for your valuable response.
For a nonlinear plasticity problem, as you mentioned, RHS= -[B]T*{Stress}. Is it applicable to elastic analysis as well or not?
Best Regards,
Hello Ashkan,
RHS= -[B]T*{Stress} is applicable to materially-nonlinear problem (without large deformation/ strain) where {Stress} is the vector of stress in materially-nonlinear analysis. For geometrically-nonlinear problems you may want to look at Lagrangian formulation in "Finite Element Procedures" by K.J. Bathe
Yes, RHS= -[B]T*{Stress} is applicable to linear elastic as well, if you are using classical theory (without any additional terms to include higher order displacement gradients). However, it should give you the same results as RHS=-[K]*{U}
Best wishes,
Dear Ashkan
ABAQUS manuals and tutorials have similar example tutorials, select general option to enter density and then properties under property tab. It would be useful if you could download relevant ones and reproduced the same. Select 2-3 linear examples, reproduced them and then do the same with for nonlinear analyses. You will see difference between material nonlinear problems and their solvers as well as geometrically nonlinear cases.
Regards
I recommend you become a member of the ABAQUS mailing list
https://groups.yahoo.com/group/ABAQUS
Dear Ashkan,
Have you solved the problem for coding the subroutine for nonlinear truss?
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