Home / Examples / Stress Analysis [Galileo] / Example 30: Material with Temperature-Dependent Anisotropic Coefficient of Thermal Expansion

Example 30: Material with Temperature-Dependent Anisotropic Coefficient of Linear Thermal Expansion

General

The material has the temperature-dependent anisotropic coefficient of linear thermal expansion. The deformation under thermal load is analyzed.
Multi-step thermal load analysis is performed with multiple reached temperatures. The stresses for each reached temperature are solved.
Unless specified in the list below, the default conditions will be applied.

Results will vary depending on Femtet version and the PC environment.

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

Analysis Conditions

The temperature is applied evenly on the model.

Opt for the thermal load in the analysis condition, and set the reference temperature and the reached temperature.

There is no need to couple with the thermal analysis [Watt].

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Type	Static Analysis
Options	Select Thermal Load

The Step/Thermal Load tab is set as follows.

In this setting, thermal load analysis is performed with 3 reached temperatures step by step.

Tab

Setting Item

Settings

Step/Thermal Load

Step Setting

Multi-step Thermal Load Analysis

Reference temperature

25[deg]

Step/Reached Temperature Setting

Step	Substeps	Reached Temperature [deg]
1	1	50
2	1	75
3	1	100

Model

The model is a cubic solid body. The material has the temperature-dependent anisotropic coefficient of linear thermal expansion. The outer boundary condition is

set with no displacement.

Body Attributes and Materials

The temperature dependency for the coefficient of linear thermal expansion is set for the range of 25-50, 50-75, and 75-100 [deg].

For each temperature range, the anisotropy is set.

Material Name

Tab

Properties

Material_Property_001

Elasticity

Material Type: Elastic/Isotropic

Temperature Dependency: No

Young's Modulus: 1×109 [Pa]

Poisson's Ratio: 0.3

Coefficient of Linear Thermal Expansion

Temperature Dependency: Yes

Anisotropy: Anisotropic

The temperature dependency of the coefficient of linear thermal expansion is set as follows.

The direction of the body attribute is by default. Components (x, y, z) of the coefficient of linear thermal expansion correspond to the coordinates (X, Y, Z) of the modeling window.

* This is not the actual material's property.

Boundary Conditions

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Settings

Outer Boundary Condition

Mechanical

Displacement

Select all X/Y/Z components.

UX=0, UY=0, UZ=0

Results

The figure below shows the principal stress at 50 deg.

From 25 to 50 deg, it is supposed to expand in X direction. However, as the outer boundary is fully fixed, the compressive stress is exhibited instead.

The figure below shows the principal stress at 75 deg.

From 50 to 75 deg, it is supposed to expand in Y direction. Again, as the outer boundary is fully fixed, the compressive stress in Y direction is exhibited instead, and added to that of X direction.

The figure below shows the principal stress at 100 deg.

From 75 to 100 deg, it is supposed to expand in Z direction. Again, as the outer boundary is fully fixed, the compressive stress in Z direction is exhibited instead, and added to those of X and Y directions.