Indeterminate beam analysis with FEM
Indeterminate beam analysis with FEM
(OP)
Hi,
I want to know the analytical procedure with the use of finite element method (i.e. matrix method) to find bending moment, shear force and deflection of an indeterminate (no. of unknowns are more than no. of equations) beam. I know two of the methods viz. force method and three moment method. But these methods can't be generalized for large number of elements and/or forces. so, it will be very useful to have a FE method to solve the mentioned problem.
Thanks!
I want to know the analytical procedure with the use of finite element method (i.e. matrix method) to find bending moment, shear force and deflection of an indeterminate (no. of unknowns are more than no. of equations) beam. I know two of the methods viz. force method and three moment method. But these methods can't be generalized for large number of elements and/or forces. so, it will be very useful to have a FE method to solve the mentioned problem.
Thanks!





RE: Indeterminate beam analysis with FEM
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RE: Indeterminate beam analysis with FEM
moment distribution can solve a beam with many supports.
to use FE is simply, build a model of the beam. you can build the stiffness matrix of the beam by hand (get a structures text to figure out the stiffness matrix for a beam element, maybe NASTRAN user manual, maybe a post-grad text), and solve the FE problem as a "finite difference" problem.
another day in paradise, or is paradise one day closer ?
RE: Indeterminate beam analysis with FEM
What do you mean by "no of unknowns are more than no of equations"?
Usually I would say they are equal.
And I agree with JAE, you probably need a good textbook or some class on the subject.
Regards
Thomas
RE: Indeterminate beam analysis with FEM
another day in paradise, or is paradise one day closer ?
RE: Indeterminate beam analysis with FEM
Sorry, my mistake. I did not limit my approach to equations of equilibrium.
Regards
Thomas
RE: Indeterminate beam analysis with FEM
But I don't want complete solution to the problem. I just want how to formulate the problem. Let's for example if we have simply supported continuous beam with 3 supports. so, normally we divide the same in two parts and solve with either force or three moment equation. But if I want to use matrix method (stiffness or displacement method) by dividing the beam into say 10 elements, then how to structure a displacement and/or stiffness matrix and write the complete beam equation in the form of [k][x]=[F]?
Can anyone state the method with simple example?
As suggested by rb1957 I did refer the text books for beam stiffness problems. but normally I found determinate problems or at the most eigen value problems. I haven't found indeterminate beam problem solved using FE technique. So, if you find any particular referance for the same, it will be appriciated!
RE: Indeterminate beam analysis with FEM
You could also look on my blog where there is a series of posts on programming the stiffness method in Excel:
https://newtonexcelbach.wordpress.com/2014/01/22/f...
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Indeterminate beam analysis with FEM
I have seen your blog. It seems pretty good to have such kind of problems solved with spreadsheet. I have gone through 'Continuous Beam' module and find it good as per my requirements. I will definitly study the macros you wrote and I hope these macros will explain the assembly of stiffness matrix and finally the solution of a problem. But, if possible will you please explain the procedure to calculate stiffness matrix in brief? I think it will be quicker and helpful to those who may not aware of VBA in Excel.
Thanks once again!
RE: Indeterminate beam analysis with FEM
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Indeterminate beam analysis with FEM
Thanks for the help!
RE: Indeterminate beam analysis with FEM
Hope it helps!
Yakpol