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Define material property using analytical functions

Posted Feb 28, 2014, 1:31 a.m. EST Version 4.2, Version 5.2 6 Replies

You Yaohui
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Hi, everyone,
As we know, Comsol allows using analytical functions of spatial coordinates to represent variable material properties on the domain of interest. I am wondering if the material property value of each mesh element is still variable, or just some constant in the finite element formula, when running a solver?
For example, we define a Young's modulus E = a*x + b over a domain, where x is the spatial coordinate. How Comsol will tackle the Young's modulus of each element when doing calculation? Is it some constant or some interpolation functions?
Does anyone know that? thanks a lot.
6 Replies Last Post Mar 18, 2016, 9:45 a.m. EDT
Gunnar Andersson COMSOL Employee

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Posted: 1 decade ago Feb 28, 2014, 2:08 a.m. EST
The function will be evaluated for each point where its value is needed. It's not treated as constant over each element.
The function will be evaluated for each point where its value is needed. It's not treated as constant over each element.
You Yaohui
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Posted: 1 decade ago Feb 28, 2014, 2:31 a.m. EST

The function will be evaluated for each point where its value is needed. It's not treated as constant over each element.


Thank you so much your prompt reply, Mr. Andersson. By " each point where its value is needed" in your sentence, do you mean Gauss quadrature point or nodal point?
As I know, when we are calculating the element stiffness matrix with variable material properties, the material property values at Gauss quadrature points will be used. However, the material property function can be the original function, or an interpolation function derived from the nodal material property values. Am I right?
I am wondering what kind of function Comsol use to represent the variable material property within each element. Thanks a lot.
[QUOTE] The function will be evaluated for each point where its value is needed. It's not treated as constant over each element. [/QUOTE] Thank you so much your prompt reply, Mr. Andersson. By " each point where its value is needed" in your sentence, do you mean Gauss quadrature point or nodal point? As I know, when we are calculating the element stiffness matrix with variable material properties, the material property values at Gauss quadrature points will be used. However, the material property function can be the original function, or an interpolation function derived from the nodal material property values. Am I right? I am wondering what kind of function Comsol use to represent the variable material property within each element. Thanks a lot.
Gunnar Andersson COMSOL Employee

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Posted: 1 decade ago Feb 28, 2014, 2:41 a.m. EST

Thank you so much your prompt reply, Mr. Andersson. By " each point where its value is needed" in your sentence, do you mean Gauss quadrature point or nodal point?
As I know, when we are calculating the element stiffness matrix with variable material properties, the material property values at Gauss quadrature points will be used. However, the material property function can be the original function, or an interpolation function derived from the nodal material property values. Am I right?
I am wondering what kind of function Comsol use to represent the variable material property within each element. Thanks a lot.


If the value of a function is needed in a point, be it a quadrature point or nodal point, then the function is evaluated in that point.
[QUOTE] Thank you so much your prompt reply, Mr. Andersson. By " each point where its value is needed" in your sentence, do you mean Gauss quadrature point or nodal point? As I know, when we are calculating the element stiffness matrix with variable material properties, the material property values at Gauss quadrature points will be used. However, the material property function can be the original function, or an interpolation function derived from the nodal material property values. Am I right? I am wondering what kind of function Comsol use to represent the variable material property within each element. Thanks a lot. [/QUOTE] If the value of a function is needed in a point, be it a quadrature point or nodal point, then the function is evaluated in that point.
You Yaohui
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Posted: 1 decade ago Feb 28, 2014, 3:25 a.m. EST

If the value of a function is needed in a point, be it a quadrature point or nodal point, then the function is evaluated in that point.


Hi, Mr. Andersson,

Thank you so much for your answer. I totally understand what you mean. However, the function that locally represents the material property distribution within an element might be different from the function that we originally define.
For instance, as I have mentioned above, we define a Young's modulus E = a*x+b over the domain of interest, where x is the spatial coordinate. if we want to know the value of E at a quadrature point within an element, as you say, we can evaluate the function E at the quadrature point. But, in my opinion, we can also evaluate the function E at nodal points first, and then calculate the value of E at the quadrature point by interpolating from the nodal values.
I would like to know which way comsol apply. Look forward to your reply.

[QUOTE] If the value of a function is needed in a point, be it a quadrature point or nodal point, then the function is evaluated in that point. [/QUOTE] Hi, Mr. Andersson, Thank you so much for your answer. I totally understand what you mean. However, the function that locally represents the material property distribution within an element might be different from the function that we originally define. For instance, as I have mentioned above, we define a Young's modulus E = a*x+b over the domain of interest, where x is the spatial coordinate. if we want to know the value of E at a quadrature point within an element, as you say, we can evaluate the function E at the quadrature point. But, in my opinion, we can also evaluate the function E at nodal points first, and then calculate the value of E at the quadrature point by interpolating from the nodal values. I would like to know which way comsol apply. Look forward to your reply.
Dustin Gerrard
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Posted: 9 years ago Mar 18, 2016, 9:41 a.m. EDT
Gunnar, is there a way to get the element stiffness matrix? For example, can I define three points for a T6 element and use a variable elasticity E and have COMSOL return the element matrix K_i?
Gunnar, is there a way to get the element stiffness matrix? For example, can I define three points for a T6 element and use a variable elasticity E and have COMSOL return the element matrix K_i?
Gunnar Andersson COMSOL Employee

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Posted: 9 years ago Mar 18, 2016, 9:45 a.m. EDT

Gunnar, is there a way to get the element stiffness matrix? For example, can I define three points for a T6 element and use a variable elasticity E and have COMSOL return the element matrix K_i?


I'm not sure. I suggest that you search the documentation for "xmeshInfo" - this is an interface for low-level queries such as yours. Contact support if you don't find anything useful.
[QUOTE] Gunnar, is there a way to get the element stiffness matrix? For example, can I define three points for a T6 element and use a variable elasticity E and have COMSOL return the element matrix K_i? [/QUOTE] I'm not sure. I suggest that you search the documentation for "xmeshInfo" - this is an interface for low-level queries such as yours. Contact support if you don't find anything useful.

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