3DFEM
Python 3D finite element code
This python code allows for solving 3D structural problems using the finite element method. New features will be added over time.
This code has NOT been validated on reference cases yet.
Requirements and dependencies
-
Python 3
-
numpy, scipy
-
Paraview is suggested for visualizing exported VTK files, especially since animations are generated as a series of VTK files as handled by this software.
Current features:
Meshes
- Tetrahedral mesh generation from a set of points using scipy.spatial.Delaunay
- 4-node tetrahedral (Tet4), 6-node prism (Prism6), 8-node brick (Brick8) elements support
- Support for meshes containing different types of elements, possibly of different orders
Materials
- Linear isotropic elastic materials
Structural matrices
- Consistent mass matrix
- Linear elastic stiffness matrix
- Rayleigh damping matrix (linear combination of mass and stiffness matrices)
- Support only for zero-Dirichlet boundary conditions
- Full Gauss quadrature scheme
Reduced-Order Modeling
- Projection on linear elastic modes
Forces
- Nodal forces
- Support for modulation of the initial force vector by a given function over time steps or frequency steps in dynamical analyses
Solvers
- Modal analysis
- Linear static analysis
- Linear time-domain dynamics using the Newmark scheme and a reduced-order model based on elastic modes
Post-processing
- Export of a deformed mesh to VTK format (PolyData legacy format)
- Export of a series of deformed meshes to VTK format for animations (for visualizing elastic modes, or deformations in time-domain dynamical analyses)
Examples of solutions
Modal analysis
First linear elastic mode of a clamped-clamped beam displayed in Paraview
Time-domain dynamics
Linear elastic cantilever beam with Rayleigh damping pulled up by a constant force on its free end, then released
Linear elastic plate with Rayleigh damping excited by a nodal force, on the center of the upper face, varying with a bell curve envelope
Intended future features:
Meshes
- Support for Tet10, Prism18, Brick27 elements
Materials
- All anisotropy classes for elastic materials
- Linear viscoelastic materials using the Generalized Maxwell Model
Structural matrices
- Arbitrary Dirichlet boundary conditions
Reduced-Order Modeling
- Proper Orthogonal Decomposition (POD) for nonlinear problems
Forces
- Body forces
- Surface forces
Solvers
- Frequency-domain dynamical analysis
- Newton-Raphson method for geometrically nonlinear elastostatics and elastodynamics
- Arc-length method for geometrically nonlinear elastostatics and elastodynamics with strong nonlinearities (e.g. post-buckling analysis)
Post-processing
- Plotting of Frequency-Response Functions (FRF)
- Support for including element stress and strain components in the VTK files
Uncertainty Quantification
- Typical Maximum Entropy-probability distributions for elastic coefficients (Young's modulus, Poisson's ratio, anisotropic coefficients) for parametric uncertainties
- Typical Maximum Entropy-probability distributions for mass, linear elastic stiffness, Rayleigh damping and linear viscoelastic damping matrices for nonparametric uncertainties
- Monte Carlo method for uncertainty propagation with plotting of confidence intervals
- Gaussian Kernel Density Estimation (GKDE) for the estimation of probability density functions of observable quantities
- Causal nonparametric probabilistic models (linear viscoelasticity)