2D FEA Stress Analysis
Interactive 2D Finite Element Analysis with multiple shapes, materials, and load types
About this Simulator
This interactive FEA simulator performs 2D stress analysis on common engineering shapes. Choose from different geometries, materials, and loading conditions. The visualization shows stress distribution using contour plots with options to view Von Mises stress, normal stresses, shear stress, or displacement magnitude.
Physics & Formulas
Von Mises Stress (Plane Stress):
$$\sigma_{vm} = \sqrt{\sigma_x^2 - \sigma_x \sigma_y + \sigma_y^2 + 3\tau_{xy}^2}$$
Constitutive Relation (Plane Stress):
$$\begin{bmatrix} \sigma_x \\ \sigma_y \\ \tau_{xy} \end{bmatrix} = \frac{E}{1-\nu^2} \begin{bmatrix} 1 & \nu & 0 \\ \nu & 1 & 0 \\ 0 & 0 & \frac{1-\nu}{2} \end{bmatrix} \begin{bmatrix} \varepsilon_x \\ \varepsilon_y \\ \gamma_{xy} \end{bmatrix}$$
How to Use
- Select a shape geometry from the dropdown (Rectangle, Plate with Hole, L-Bracket, or Cantilever)
- Choose a material to set the elastic modulus and Poisson's ratio
- Select the load type (Point, Distributed, or Moment) and adjust magnitude
- Increase mesh density for more accurate results (but slower computation)
- Switch contour types to view different stress components or displacement
- Toggle mesh visibility and deformed shape display
- Adjust deformation scale to visualize small displacements
Frequently Asked Questions
What is Finite Element Analysis?
FEA divides a structure into small elements connected at nodes. It solves equilibrium equations at each node to find displacements, then calculates stresses from the deformation. This allows analysis of complex geometries that have no analytical solution.
Why does stress concentrate around the hole?
Geometric discontinuities like holes create stress concentrations. The stress must 'flow' around the hole, causing higher values at the edges. The stress concentration factor for a circular hole in a wide plate under tension is approximately 3.
What does Von Mises stress tell us?
Von Mises stress combines all stress components into a single scalar value that can be compared to the material's yield strength. If Von Mises stress exceeds yield strength, the material will plastically deform.
Why is the deformed shape exaggerated?
Actual deformations are typically very small (micrometers). The deformation scale multiplies displacements to make them visible. Real deflections would be invisible at 1:1 scale.
