torch-fem 0.1.13

Simple finite element assemblers with torch.

torch-fem: differentiable linear elastic finite elements

Simple finite element assemblers for linear elasticity with PyTorch. The advantage of using PyTorch is the ability to efficiently compute sensitivities and use them in structural optimization.

Basic examples

The subdirectory examples->basic contains a couple of Jupyter Notebooks demonstrating the use of torch-fem for trusses, planar problems, shells and solids.

Simple cantilever beam: There are examples with linear and quadratic triangles and quads.

Optimization examples

The subdirectory examples->optimization demonstrates the use of torch-fem for optimization of structures (e.g. topology optimization, composite orientation optimization).

Simple topology optimization of a MBB beam: You can switch between analytical sensitivities and autograd sensitivities.

Simple topology optimization of a 3D beam: The model is exported to Paraview for visualization.

Simple shape optimization of a fillet: The shape is morphed with shape basis vectors and MMA + autograd is used to minimize the maximum stress.

Simple fiber orientation optimization of a plate with a hole: Compliance is minimized by optimizing the fiber orientation of an anisotropic material using automatic differentiation w.r.t. element-wise fiber angles.

Installation

Your may install torch-fem via pip with

pip install torch-fem

Minimal code

This is a minimal example of how to use torch-fem to solve a simple cantilever problem.

from torchfem import Planar
from torchfem.materials import IsotropicPlaneStress

# Define a (minimal) mesh 
nodes = torch.tensor([[0.0, 0.0], [1.0, 0.0], [2.0, 0.0], [0.0, 1.0], [1.0, 1.0], [2.0, 1.0]])
elements = torch.tensor([[0, 1, 4, 3], [1, 2, 5, 4]])

# Apply a load at the tip
tip = (nodes[:, 0] == 2.0) & (nodes[:, 1] == 1.0)
forces = torch.zeros_like(nodes)
forces[tip, 1] = -1.0

# Constrained displacement at left end
left = nodes[:, 0] == 0.0
displacements = torch.zeros_like(nodes)
constraints = torch.zeros_like(nodes, dtype=bool)
constraints[left, :] = True

# Thickness
thickness = torch.ones(len(elements))

# Material model (plane stress)
material = IsotropicPlaneStress(E=1000.0, nu=0.3)

# Create model
cantilever = Planar(nodes, elements, forces, displacements, constraints, thickness, material.C())

This creates a minimal planar FEM model:

# Solve
u, f = cantilever.solve()

# Plot
cantilever.plot(u, node_property=torch.norm(u, dim=1), node_markers=True)

This solves the model and plots the result: