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2D-axial-symmetric Elasticity - Differences between weak form and wizard solution
Posted 22 feb 2014, 12:31 GMT-5 1 Reply
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Hello,
I tried to model the deformation of a circular ring (cylindrical, axial symmetric, small deformations) by using the weak form interface. I compared my solution with a solution I generated by using the built in elasticity modul/ wizard.
I applied Dirichlet-0 boundary conditions on the inner radius, Neumann-0 conditions on the upper and lower faces and I prescribed a displacement in radial direction (Dirichilet-0 conditions in the z-direction) on the outer radius.
Unfortunately the two solutions differ.
Furthermore if I am changing the boundary conditions (Neumann-0 conditions on the inner and outer radius and Dirichlet-Conditions on the
lower and upper faces) the solver won't converge at all and no solution is obtained.
In order to narrow my mistake I modelled a 2D-cartesian plate (plane stress) - weak form and model wizard - and received two identical solutions with no problems using various boundary conditions.
So I suspect, that I made a mistake in computing the weak form in cylindrical coordinates or/ and using the weak form interface.
In basic steps my derivation of the weak form is as follows:
(T: Stress tensor, w: Vector of test-functions, u: Displacement vector, I: Identity tensor)
div(T) = 0 Equilibrium Conditions
int( w*div(T) )dV = 0 Multiplying with test functions an integrating
int( grad(w)*T )dV = int( w*T*n )dA Integrating by parts (Green's formular)
I am only interested in the left-hand-side term for Comsol implementation, so:
grad(w)*(lambda*div(u)*I + mu*sym(grad(u))) Hooke's Law
I am now expressing the differntial operators in cylindrical coordinates and keep the axial symmetry in mind.
Can you make out any mistakes in derivation? Are there any typical mistakes or important things to remember entering or using the 2D-axial-symmetric interface?
I've got to admit, that I am a bit desperate, because I've got to present my results to my professor next week.
I attached a complete derivation and my .mph file. I hope, that somebody can make out my mistake and help me.
Thank you for your support and effort.
Best regards,
Simon Baeuerle
I tried to model the deformation of a circular ring (cylindrical, axial symmetric, small deformations) by using the weak form interface. I compared my solution with a solution I generated by using the built in elasticity modul/ wizard.
I applied Dirichlet-0 boundary conditions on the inner radius, Neumann-0 conditions on the upper and lower faces and I prescribed a displacement in radial direction (Dirichilet-0 conditions in the z-direction) on the outer radius.
Unfortunately the two solutions differ.
Furthermore if I am changing the boundary conditions (Neumann-0 conditions on the inner and outer radius and Dirichlet-Conditions on the
lower and upper faces) the solver won't converge at all and no solution is obtained.
In order to narrow my mistake I modelled a 2D-cartesian plate (plane stress) - weak form and model wizard - and received two identical solutions with no problems using various boundary conditions.
So I suspect, that I made a mistake in computing the weak form in cylindrical coordinates or/ and using the weak form interface.
In basic steps my derivation of the weak form is as follows:
(T: Stress tensor, w: Vector of test-functions, u: Displacement vector, I: Identity tensor)
div(T) = 0 Equilibrium Conditions
int( w*div(T) )dV = 0 Multiplying with test functions an integrating
int( grad(w)*T )dV = int( w*T*n )dA Integrating by parts (Green's formular)
I am only interested in the left-hand-side term for Comsol implementation, so:
grad(w)*(lambda*div(u)*I + mu*sym(grad(u))) Hooke's Law
I am now expressing the differntial operators in cylindrical coordinates and keep the axial symmetry in mind.
Can you make out any mistakes in derivation? Are there any typical mistakes or important things to remember entering or using the 2D-axial-symmetric interface?
I've got to admit, that I am a bit desperate, because I've got to present my results to my professor next week.
I attached a complete derivation and my .mph file. I hope, that somebody can make out my mistake and help me.
Thank you for your support and effort.
Best regards,
Simon Baeuerle
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1 Reply Last Post 23 feb 2014, 14:30 GMT-5
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Posted:
1 decade ago
Hello,
I kind of solved my problem:
I could simulate the correct solution by using the 2D-Interface instead of the 2D-axiasymmetric-Interface.
I entered the same weak equation in cylindrical coordinates (additionally multiplied with the Jacobian) into the 2D-Interface instead of the 2D-axisymmetric.
Does somebody know in which coordinates or form I have to enter my problem into the axisymmetric-Interface to obtain a correct solution?
A fellow student simulated a heat-conduction problem by entering the weak form expressed in cylindrical coordinates (simliar to my attempt) into the axisymmetric-Interface and received a correct solution. Why does this procedure work with one independent variable and not with two variables?
Best regards,
Simon Baeuerle
I kind of solved my problem:
I could simulate the correct solution by using the 2D-Interface instead of the 2D-axiasymmetric-Interface.
I entered the same weak equation in cylindrical coordinates (additionally multiplied with the Jacobian) into the 2D-Interface instead of the 2D-axisymmetric.
Does somebody know in which coordinates or form I have to enter my problem into the axisymmetric-Interface to obtain a correct solution?
A fellow student simulated a heat-conduction problem by entering the weak form expressed in cylindrical coordinates (simliar to my attempt) into the axisymmetric-Interface and received a correct solution. Why does this procedure work with one independent variable and not with two variables?
Best regards,
Simon Baeuerle