Hooke´s law in cylindical coodinates, with thermal terms

This allows for the calculation of Hooke's law in cylindrical coordinates with thermal strain terms. In summary, the conversation discusses the search for Hooke's law expressed in cylindrical coordinates with thermal strain terms and asks for links to solved elasticity problems in isotropic materials described in cylindrical coordinates.
  • #1
C4guy
2
0
Hi!


I hope this is the right subforum, if not, please inform me of the error of my ways.

It is easy to find Hooke's law for an isotropic solid in Cartesian coordinates, with thermal strain terms, by googling. It is also easy to find it in cylindrical coordinates, but without thermal strain terms.

However, I have not managed to find Hooke´s law expressed in cylindrical coordinates with thermal strain terms.

Does anyone have a link to a webpage with this expression of Hooke´s law? Does anyone have a link to solved elasticity problems in isotropic materials described in cylindical coordinates, with thermal effects?


Thanks in Advance.
c4guy
 
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  • #2
As with Cartesian coordinates, in cylindrical coordinates, you just subtract the linear thermal expansion strain from each of the three normal strains.
 

1. What is Hooke's Law in cylindrical coordinates?

Hooke's Law in cylindrical coordinates is a physical law that describes the relationship between the force applied to a cylindrical object, its deformation, and its thermal properties. It states that the force applied is directly proportional to the displacement of the object, as long as the material remains within its elastic limit.

2. What is the significance of the thermal terms in Hooke's Law?

The thermal terms in Hooke's Law take into account the effects of temperature on the material. As temperature increases, the material's stiffness may change, which affects its deformation under applied force. Including thermal terms allows for a more accurate representation of the behavior of materials under different thermal conditions.

3. How does Hooke's Law in cylindrical coordinates differ from the traditional Hooke's Law?

In traditional Hooke's Law, the force and displacement are considered in one-dimensional Cartesian coordinates. In cylindrical coordinates, the force and displacement are considered in the radial direction, tangential direction, and along the cylinder's axis. Additionally, thermal terms are included in the cylindrical version.

4. Can Hooke's Law in cylindrical coordinates be applied to all materials?

No, Hooke's Law in cylindrical coordinates is only applicable to linear elastic materials, which means that the material will return to its original shape when the force is removed. Non-linear materials, such as rubber, do not follow Hooke's Law.

5. How is Hooke's Law in cylindrical coordinates used in real-world applications?

Hooke's Law in cylindrical coordinates is used in various engineering and scientific fields to design and analyze structures, such as pipes, beams, and cylinders. It is also used in material testing to determine the material's elastic properties and behavior under different conditions.

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