Plane strain and plane stress_Boye Engineering Technology

Plane strain and plane stress

7 hits 2025/8/13 10:12:29

Plane Stress vs. Plane Strain: Fundamental Concepts in Engineering Simulation

In practical engineering, computational models are typically three-dimensional (3D). However, when a model’s geometric and loading characteristics meet specific criteria, 3D problems can be simplified to two-dimensional (2D) models. This article introduces the basic concepts of plane stress and plane strain.

1. Plane Stress

Characteristics of Plane Stress Problems:

Dimensional feature: One dimension is much smaller than the other two (e.g., thin plates).
Loading feature: External forces are parallel to the plate surface and do not vary along the thickness direction.

A 3D problem that satisfies both conditions above can be simplified to a plane stress problem. For plane stress, the stress component perpendicular to the plane is zero.

Common Engineering Applications:

Typical examples include tension or compression analysis of thin plates.

2. Plane Strain

Characteristics of Plane Strain Problems:

Dimensional feature: One dimension is much larger than the other two (e.g., long structures).
Loading feature: External forces are parallel to the cross-section and do not vary along the length direction.

A 3D problem that satisfies both conditions above can be simplified to a plane strain problem. For plane strain, the strain component perpendicular to the plane is zero, but the corresponding stress component is not zero (due to constraint effects).

Common Engineering Applications:

Examples include lateral water pressure analysis of dams and uniform internal pressure analysis of pipelines.

3. Comparison of Stress and Deformation

Aspect	Plane Stress	Plane Strain
Dimensional Feature	One dimension (thickness) is much smaller.	One dimension (length) is much larger.
Perpendicular Stress	Zero (σ₃₃ = 0).	Non-zero (due to constraint from the long dimension).
Perpendicular Strain	Non-zero (ε₃₃ ≠ 0, as the thin direction can deform freely).	Zero (ε₃₃ = 0, constrained by the long dimension).

4. Setup Methods for Plane Stress and Plane Strain in ANSYS Workbench

Define the computational model as a 2D model.
Import or create the planar geometry in DesignModeler (DM).
Enter the Model module and set the problem type to either "Plane Stress" or "Plane Strain" based on the analysis requirements.

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