What is Stress Linearization?

I. What is Stress Linearization

Stress linearization refers to a mathematical processing method that simplifies complex, non-uniformly distributed stress along a certain path into a linear distribution, so that it can be compared with stress standards in engineering specifications. This linear distribution mainly contains two components: constant stress component (also known as membrane stress component) and varying stress component (also known as bending stress component).

II. Why Perform Stress Linearization

When we use finite element software to analyze a relatively complex structural component, continuous and highly varying stress fields may appear in certain regions, which cannot be compared with our conventional specifications. The reason is that engineering design specifications are usually developed based on simple mechanical models (such as beam, plate, and shell theories), which classify stress into several categories and specify different allowable stresses for each category.

Therefore, in order to evaluate simulation results using engineering specifications, complex stress analysis results must be translated—that is, decomposed into membrane stress components and bending stress components as mentioned earlier—for comparison with engineering specifications.

In fact, the concept of stress linearization originally originated from pressure vessel design and analysis, but has now extended to various industries—it’s essentially a matter of universal applicability.

III. Core Concept: SCL

SCL, abbreviated in Chinese as stress classification line, is called Stress Classification Line in English. It can be understood as the path for stress linearization.

In finite element analysis, key points on this line are represented by nodes, and the finite element simulation outputs stress data for each node. The stress linearization tool in analysis software transforms the nodal stress data along this line into two components: membrane stress and bending stress.

IV. Stress Linearization Decomposition Process

Linearized stress is mainly classified in three ways:

1. By nature: Primary stress, secondary stress

2. By influence range: Global stress, local stress

3. By stress type: Membrane stress, bending stress, nonlinear peak stress

The third classification method is most commonly encountered because it can be directly compared with specifications.

The so-called decomposition is actually curve fitting—a mathematical method! The most common approach is curve fitting based on the least squares method. Below, we focus on the three types of stress obtained from the third classification method.

1. Membrane Stress

Definition: The average value of stress along the SCL. It is a constant value representing the uniformly distributed stress portion across the entire cross-section.

Physical meaning: Like the stress produced when stretching or compressing a uniform rod, it causes the cross-section to elongate or shorten as a whole without producing bending.

Importance: In specifications, restrictions on membrane stress are the strictest because it may lead to overall plastic collapse of the structure.

2. Bending Stress

Definition: The linearly varying stress portion. It is antisymmetrically distributed about the mid-surface of the cross-section, maximum at the outer surface and zero at the mid-surface.

Physical meaning: Like the stress produced when a beam is in pure bending, it causes the cross-section to rotate and bend.

Importance: Specifications are relatively more lenient with bending stress because structures have the ability to redistribute stress through local yielding, thereby alleviating bending effects.

3. Nonlinear Peak Stress

Definition: The remaining, highly localized nonlinear stress portion after decomposing the linear membrane and bending components.

Physical meaning: Usually caused by geometric discontinuities (such as small fillets, notches), with a very small range of action.

Importance: It may lead to fatigue cracks or brittle fracture, but will not cause significant overall deformation. In stress-based design, it is usually superimposed with membrane and bending stresses for fatigue assessment.

Actual stress = Membrane stress + Bending stress + Nonlinear peak stress.

Through the above decomposition, in actual operations, we generally compare the obtained results with specifications as follows:

1. Membrane component < Allowable membrane stress;

2. Membrane component + Bending component < N × Allowable membrane stress (specific value depends on the specification)

Through such operations, highly varying stress regions can be converted into ordinary stress comparisons. When facing irregular structures where structural design cannot be improved, stress linearization is usually a good solution.

V. Stress Linearization Operation Process in ANSYS Workbench

In ANSYS Workbench, stress linearization operation is very simple. As shown in the structural stress contour below, stress changes are quite obvious here, and it is necessary to evaluate the stress condition in the thickness direction.

Step 1: First create a new Path in the thickness direction

Step 2: Right-click on Solution, select Linearized Stress, and choose the evaluation type

Step 3: Set the selected path

Step 4: Evaluate results. As shown below, the three classifications mentioned above are clear at a glance.

VI. Notes

1. Stress linearization is a relatively traditional analysis technique;

2. Only applicable to linear elastic analysis scenarios;

3. Whether this method is applicable to your own industry needs to be considered carefully before use;

4. If the true stress distribution of components can be obtained through elastic-plastic analysis, stress linearization analysis is usually no longer necessary.

The above is the content of this issue regarding stress linearization. Everyone should now have a clear understanding of this concept, right? Welcome to repost and share!