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Can I use COMSOL to solve this problem

Posted 04.06.2012, 18:47 GMT-4 Studies & Solvers, Structural Mechanics Version 4.2a 3 Replies

Leon Pan
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Hello everyone,
I am using COMSOL to solve a boundary value problem.
it is a long beam and fixed at one end, hinged at another end. the beam has variable stiffness and moment of inertia.
there also are several other constraints between two ends, such as hinged constraint.
I want to do a stability anlysis of steady state for this beam.
there are a variable axial force and a constant torque at top end.
the beam are bent at two direction x and y.
the motion of equation is a set of coupled 4-th order ODE.
Can anyone tell me if I can use COMSOL to solve this problem?
Thank you for any help in advance.
3 Replies Last Post 06.06.2012, 23:31 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 05.06.2012, 01:53 GMT-4
Hi

I would say yes as first guess, but you seem to have many specific conditions, forth order PDE are possible by adding intermediate 2nd order variables and a two step approach (see the KB knowledge base).

But today COMSOl is not the easiest to use if you are looking for a "rigid body" solver but OK for flexing structural design
even if the rigid body analyisi is possible, you miust "just" write out more equations (in 4.2, hopefully it will become easier in 4.3 or soon thereafter ;)

--
Good luck
Ivar
Hi I would say yes as first guess, but you seem to have many specific conditions, forth order PDE are possible by adding intermediate 2nd order variables and a two step approach (see the KB knowledge base). But today COMSOl is not the easiest to use if you are looking for a "rigid body" solver but OK for flexing structural design even if the rigid body analyisi is possible, you miust "just" write out more equations (in 4.2, hopefully it will become easier in 4.3 or soon thereafter ;) -- Good luck Ivar
Leon Pan
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Posted: 1 decade ago 05.06.2012, 11:22 GMT-4
Thank you very much, Mr. Kjelberg
I am a new user of COMSOL and can you show me how to do this stepwise.
It is a simple version of my problem here.
d4(u)/dz4 - d/dz(T(z) du/dz) - M d3(v)/dz - W u=0,
d4(v)/dz4 - d/dz(T(z) dv/dz) + M d3(u)/dz - W v=0,
and the boundary conditions is u(0) = v(0) = u(L) = v(L) = 0, d2(u)/dz2 = d2(v)/dz2 = 0 at x=0 and x=L,
another constraint is u(3L/4) = 0 and d2(u)/dz2 = 0 at x=3L/4.
Hope you can understant my equations.

And you said COMSOL isn't the easiest way for rigid body solver, can you tell me what it is?
Thanks again.
Thank you very much, Mr. Kjelberg I am a new user of COMSOL and can you show me how to do this stepwise. It is a simple version of my problem here. d4(u)/dz4 - d/dz(T(z) du/dz) - M d3(v)/dz - W u=0, d4(v)/dz4 - d/dz(T(z) dv/dz) + M d3(u)/dz - W v=0, and the boundary conditions is u(0) = v(0) = u(L) = v(L) = 0, d2(u)/dz2 = d2(v)/dz2 = 0 at x=0 and x=L, another constraint is u(3L/4) = 0 and d2(u)/dz2 = 0 at x=3L/4. Hope you can understant my equations. And you said COMSOL isn't the easiest way for rigid body solver, can you tell me what it is? Thanks again.
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago 06.06.2012, 23:31 GMT-4
The equations you posted seem to be standard Euler-Bernoulli beam equation with properties that vary along the beam length. You can solve this type of equations using beam elements in COMSOL. The elements are formulated a little differently using displacement and rotations degrees of freedom, but I believe it reduces to the same fourth order ODEs.

Nagi Elabbasi
Veryst Engineering
The equations you posted seem to be standard Euler-Bernoulli beam equation with properties that vary along the beam length. You can solve this type of equations using beam elements in COMSOL. The elements are formulated a little differently using displacement and rotations degrees of freedom, but I believe it reduces to the same fourth order ODEs. Nagi Elabbasi Veryst Engineering

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