GitHub

Guide

The FinEtools package is used here to solve linear stress analysis (deformation) problems.

Modules

The package FinEtoolsDeforLinear has the following structure:

  • FinEtoolsDeforLinear is the top-level module.
  • Linear deformation: AlgoDeforLinearModule (algorithms), DeforModelRedModule (model-reduction definitions, 3D, plane strain and stress, and so on), FEMMDeforLinearBaseModule, FEMMDeforLinearModule, FEMMDeforLinearMSModule, FEMMDeforWinklerModule (FEM machines to evaluate the matrix and vector quantities), MatDeforModule, MatDeforElastIsoModule, MatDeforElastOrthoModule (elastic material models).

Linear deformation FEM machines

For the base machine for linear deformation, FEMMDeforLinearBase, assumes standard isoparametric finite elements. It evaluates the interior integrals:

  • The stiffness matrix, the mass matrix.

  • The load vector corresponding to thermal strains.

Additionally:

  • Function to inspect integration points.

The FEM machine FEMMDeforLinear simply stores the data required by the base FEMMDeforLinearBase.

The machine FEMMDeforWinkler is specialized for the boundary integrals for bodies supported on continuously distributed springs:

  • Compute the stiffness matrix corresponding to the springs.

The mean-strain FEM machine FEMMDeforLinearMS implements advanced hexahedral and tetrahedral elements based on multi-field theory and energy-sampling stabilization. It provides functions to compute:

  • The stiffness matrix, the mass matrix.

  • The load vector corresponding to thermal strains.

Additionally it defines:

  • Function to inspect integration points.

Materials for linear deformation analysis

The module MatDeforModule provides functions to convert between vector and matrix (tensor) representations of stress and strain. Further, functions to rotate stress and strain between different coordinate systems (based upon the model-reduction type, 3-D, 2-D, or 1-D) are provided.

Currently there are material types for isotropic and orthotropic linear elastic materials. The user may add additional material types by deriving from AbstractMatDefor and equipping them with three methods: (1) compute the tangent moduli, (2) update the material state, (3) compute the thermal strain.

For full generality, material types should implement these methods for fully three-dimensional, plane strain and plane stress, 2D axially symmetric, and one-dimensional deformation models.

Linear deformation algorithms

There are algorithms for

  • Linear static analysis;
  • Export of the deformed shape for visualization;
  • Export of the nodal and elementwise stress fields for visualization;
  • Modal (free-vibration) analysis;
  • Export of modal shapes for visualization;
  • Subspace-iteration method implementation.

Model data

Model data is a dictionary, with string keys, and arbitrary values. The documentation string for each method of an algorithm lists the required input. For instance, for the method linearstatics of the AlgoDeforLinearModule, the modeldata dictionary needs to provide key-value pairs for the finite element node set, and the regions, the boundary conditions, and so on.

The modeldata may be also supplemented with additional key-value pairs inside an algorithm and returned for further processing by other algorithms.