MeshFree|传热分析-热应力

midas NFX & MeshFree支持热传递、热对流、热辐射（空腔辐射）热应力等传热分析

Interpretation Theory

    As we discussed in Part 1, thermal stress analysis is basically aimed at examining the stability of a structure undergoing a temperature change. Therefore, the setting of the analysis process is very similar for both thermal stress and structural analysis.

    Let’s look at how to set up physical properties, and constraint and load conditions one by one on a new CAE analysis program: midas MeshFree.

   Once on MeshFree, we are able to select an Analysis Case, as shown above. In addition to Thermal Stress Analysis, MeshFree offers other analysis cases as well, and more will be added in the future.

1st Requirement for Thermal Stress Analysis: 

Material Properties

    As we said, the basic settings are the same as in structural analysis. Structural properties of the material such as modulus of elasticity, Poisson’s ratio and density are required. Physical properties such as specific heat, conductivity and exothermic coefficient, related to heat conduction, are required as well.

In addition, for thermal stress analysis, the thermal expansion coefficient is required to account for thermal expansion. For this coefficient refer to a table of standards.

    Note that the coefficient of thermal expansion is a function of temperature, increasing as temperature increases. Therefore, although it is better to find the exact coefficient of thermal expansion, it is usually chosen as a value representative to the range corresponding to a normal temperature.

* You can easily check the material properties of various materials by referring to MATWEB (www.matweb.com) *

    MeshFree has its own database of material properties, describing a variety of materials. If you specify the name of the material you are using, you can see that the thermal expansion coefficient, along with other properties, is automatically determined. If the material you are using is not in MeshFree’s database, you can always add it by entering its properties directly.

2nd Requirement for Thermal Stress Analysis: 

Constraint Conditions

   In the case of constraints, one more thing must be added besides the ones you would set to limit object deformation in structural analysis: the initial temperature. This temperature is set to 0℃ by default.

   The difference between this initial temperature and the final temperature after heat transfer is used to calculate the thermal strain and stress. For this, the initial and final temperatures at each node is necessary.

   In addition, the constraints necessary for structural analysis must be entered as well.

3rd Requirement for Thermal Stress Analysis:

Load Conditions

Confirm Thermal Stress Analysis Results

    In summary, we can do thermal stress analysis in conjunction with structural analysis by adding three parameters to the analysis: a thermal expansion coefficient, an initial temperature and a heat load.

    Let's see what the information we entered on MeshFree results. As mentioned in Thermal Stress Analysis [Part 1], this analysis ultimately aims at examining the stability of the structure.

    We need to obtain the displacement and stress undergone by the structure to understand its stability. Therefore, let’s see what results MeshFree gave us.

    When in the analysis results window, you can see the section shown in Fig. 6 situated on the upper left corner of the screen. If you click the tab of titled “Sub Case”, you will be able to choose between Steady Heat Transfer and Linear Static. If you want to see the temperature distribution, select the Steady Heat Transfer sub-case. On the other hand, select Linear Static if you want to see the displacement and stresses.

     As you might expect, and as it was mentioned in the previous part of this article, thermal stress analysis is basically a structural analysis where the temperature results from a heat transfer analysis are used as temperature loads. Therefore, to study the stability of the structure, two analyses must be performed: heat transfer analysis and linear static analysis. However, these two analyses are not conducted independently due to the sharing of several conditions. That is why both analyses are presented as sub-cases to the thermal stress analysis case.

   Since we would like to see the final result of the thermal stress analysis, we will set the sub-case to Linear Static.

   The parts with low displacement are shown in blue and those with large displacement in red, so that it is clear what areas are undergoing the most deformation. It is not shown in Fig. 7, but you can also check the maximum and minimum values and localize them by checking the “Max/Min” box.

    This time we did check the “Max/Min” box, as you can see in Fig. 8, where the location and value of the maximum and minimum stresses are shown.

    In addition to the total displacement and Von-Mises stresses shown above, you can also check out other results, such as Von-Mises strain, X/Y/Z axial displacements, 1/2/3 primary stresses.

   There are a lot of different parameters that can be modified and different results that can be studied, which can make CAE of this kind somewhat complicated. However, as you can see in this article, midas MeshFree minimizes complications in the process and allows you to focus on the actual analysis.

No geometry cleanup and simplifications

No mesh generation by user

No failed analysis

Performance and accuracy comparable to finite element method