An element connects N nodes.
Nodes are handled via std::shared_ptr shared pointers: you do not have to worry about deleting them.
Add elements to a mesh using ChMesh::AddElement()
Initialize the elements by telling which node are connected with SetNodes()
Set a material property to the element by using SetMaterial()

ChElementSpring

The chrono::fea::ChElementSpring is the simplest element, and it can be used as a starting point to learn how to implement finite elements.

Moreover, it is useful for problems like trusses, suspensions, etc. this base implementation This spring assumes linear behavior, but experienced programmers can override this class and implement more advanced non-linear spring models.

2 nodes of ChNodeFEAxyz type
Large displacements allowed
Zero mass element
Parameters:
- rest length L,
- stiffness k,
- damping r
Stiffness matrix computed analytically for high performance (both material and geometric stiffness are supported).

ChElementBar

The chrono::fea::ChElementBar is quite similar to the ChElementSpring, but adds the effect of mass, and uses different parameters at construction time.

2 nodes of ChNodeFEAxyz type
Very similar to ChElementSpring, except it has a mass
No torque at the ends (like two spherical joints)
Large displacements allowed
Parameters:
- rest length L,
- Section area A,
- Young modulus E,
- damping (like in Rayleight beta parameter)
Stiffness matrix computed analytically for high performance (both material and geometric stiffness are supported).

ChElementTetra_4

The chrono::fea::ChElementTetra_4 is the simplest volume element for simulating 3D problems.

4 nodes of ChNodeFEAxyz type
Linear interpolation, constant stress
1 integration point
Corotational formulation for large displacements
Uses polar decomposition for corotated frame
Useful for solids
Fastest element for solids
Stiffness matrix computed analytically for high performance (note, geometric stiffness term not added at the moment).

ChElementTetra_10

The chrono::fea::ChElementTetra_10 is a quadratic volume element based on tetahedrons with intermediate nodes along edges, as in figure.

10 nodes of ChNodeFEAxyz type
Quadratic interpolation, linear stress
4 integration points
Corotational formulation for large displacements
Uses polar decomposition for corotated frame
Note: initial position assuming nodes n>4 exactly at mid-length of edges
Useful for solids
Stiffness matrix computed analytically for high performance (note, geometric stiffness term not added at the moment).

ChElementHexa_8

The chrono::fea::ChElementHexa_8 is a linear isoparametric element of brick type.

8 nodes of ChNodeFEAxyz type
Linear interpolation
8 integration points
Corotational formulation for large displacements
Useful for solids, with structured grids
Stiffness matrix computed analytically for high performance (note, geometric stiffness term not added at the moment).

ChElementHexa_20

The chrono::fea::ChElementHexa_20 is a quadratic isoparametric element of brick type.

20 nodes of ChNodeFEAxyz type
8 at vertexes, 12 at edges midpoints
Quadratic interpolation
27 integration points
Corotational formulation for large displacements
Useful for solids, with structured grids
Stiffness matrix computed analytically for high performance (note, geometric stiffness term not added at the moment).

ChElementBrick

The chrono::fea::ChElementBrick is a brick element implemented using the ANCF formulation.

8 nodes of ChNodeFEAxyz type
Linear interpolation
8 integration points
Use EAS Enhanced Assumed Strain
Large strains
Can use Mooney-Rivlin model for hyperelastic materials
Useful for solids, with structured grids

ChElementBrick_9

The chrono::fea::ChElementBrick_9 is a brick element implemented using the ANCF formulation.

9 nodes of ChNodeFEAxyz type (8 at the corners, 1 at the center)
Linear interpolation
8 integration points
Strain formulations for large strains:
- Green-Lagrange
- Hencky
Plasticity:
- J2 (metals)
- DruckerPrager (soil, plastics)
- DruckerPrager_Cap (soil, plastics)
Useful for solids, with structured grids

ChElementCableANCF

The chrono::fea::ChElementCableANCF is a fast element for the simulation of thin beams (cables, wires, ropes) where one is not interested in twisting, shear, etc.

2 nodes of chrono::fea::ChNodeFEAxyzD type
3 integration point (stiffness), 4 (mass)
ANCF formulation for large displacements
Thin beam (no shear)
Does not model torsional stiffness (useful for wires, cables)
Section property: A, I, E, density, damping, defined via a chrono::fea::ChBeamSectionCable object.

ChElementBeamANCF

The chrono::fea::ChElementBeamANCF is a thick beam element implemented using the ANCF formulation. As an alternative, we also provide a chrono::fea::ChElementBeamIGA with more advanced functionality in the field of Geometrically Exact Beam theory.

3 nodes of chrono::fea::ChNodeFEAxyzDD type
ANCF formulation for large displacements
Section property: rectangular width-height, E, Poisson ratio, shear correction factors, density

ChElementBeamEuler

The chrono::fea::ChElementBeamEuler is a thin beam element, using the corotated Euler-Bernoulli theory in 3D. For low/moderate bending, and if shear effects are not important (thin beam assumption), this formulation is very efficient.

2 nodes of chrono::fea::ChNodeFEAxyzrot type
Linear interpolation
1 integration point (default)
Corotational formulation for large displacements
Thin beam (no shear), based on the Euler-Bernoulli thin beam theory
Section properties include settings for:
- A, A, Iyy, Izz, (or axial and bending rigidity),
- G, J (or torsional rigidity),
- density, damping plus optional:
- αe , ze , ye , for offset/rotated section
- zs , ys for offset shear center
The section properties are defined via chrono::fea::ChBeamSectionEuler classes, among these:
- chrono::fea::ChBeamSectionEulerSimple , for uniform elasticity, uniform density
- chrono::fea::ChBeamSectionEulerAdvanced , as above, adds offset/rotated section and shear center
- chrono::fea::ChBeamSectionEulerAdvancedGeneric , if non-uniform elasticity or non-uniform density
- chrono::fea::ChBeamSectionEulerEasyCircular , an easy-to-use shortcut
- chrono::fea::ChBeamSectionEulerEasyRectangular , an easy-to-use shortcut
both material and geometric stiffness are computed.

ChElementBeamIGA

The chrono::fea::ChElementBeamIGA is a thick beam element based on the Isogeometric Analysis (IGA) hence with a B-Spline shape, and relying on the Geometrically Exact Beam theory.

Isogeometric formulation (IGA) of a Cosserat rod, with large displacements
User-defined order n (ex: 1=linear 2=quadratic, 3=cubic).
Each element is a span of a b-spline, so each element uses n+1 control points, ie. nodes of chrono::fea::ChNodeFEAxyzrot type
Thick beam shear effects are possible, v. Timoshenko theory
Reduced integration to correct shear locking
Initial curved configuration is supported
Suggestion: use ChBuilderBeamIGA for easy creation a full B-spine, ie. given full knot sequence and points as in the second figure above.
Section defined in a modular way, via a chrono::fea::ChBeamSectionCosserat that is composed via
- Elasticity model from chrono::fea::ChElasticityCosserat, ex:
- Inertial model from chrono::fea::ChInertiaCosserat, ex:
- Damping model from chrono::fea::ChDampingCosserat (optional), ex:
  - chrono::fea::ChDampingCosseratLinear
  - chrono::fea::ChDampingCosseratRayleigh
- Plasticity model from chrono::fea::ChPlastcityCosserat (optional)
Some of the sectional properties above support the case of offsets in center of mass, center of shear, center of axial elastic forces, as well as rotation of the section axes, for defining complex beams like helicopter blades
Both material and geometric stiffness are considered.

ChElementShellReissner

The chrono::fea::ChElementShellReissner is a quadrilateral thick shell element.

4 nodes of chrono::fea::ChNodeFEAxyzrot type
Bi-linear interpolation
4 integration points (default)
Allows large displacements, exponential map used for SO3
Thick shells allowed
Based on the Reissner 6-field shell theory (w. drilling stiffness)
Can have multi-layered materials, using CLT thory
ANS, shear-lock free
Nodes need not to be aligned to shell (rotation offsets auto-computed in initialization)
Section defined in a modular way, via N layers, each with a chrono::fea::ChMaterialShellReissner composed by:
- Elasticity model from chrono::fea::ChElasticityReissner, ex:
- Damping model from chrono::fea::ChDampingReissner (optional)
  - chrono::fea::ChDampingReissnerRayleigh
  - ...
- Plasticity model from chrono::fea::ChPlasticityReissner (optional)

ChElementShellANCF

The chrono::fea::ChElementShellReissner is a quadrilateral thick shell element based on the ANCF approach.

4 nodes of chrono::fea::ChNodeFEAxyzD type
Bi-linear interpolation
4 integration points (default)
Allows large displacements, using ANCF formulation
Thick shells allowed
Can have multi-layered materials
ANS-EAS, shear-lock free
Nodes D must be aligned to shell normal at initialization

ChElementShellANCF_8

The chrono::fea::ChElementShellANCF_8 is a quadrilateral thick shell element based on the ANCF approach.

8 nodes of chrono::fea::ChNodeFEAxyzDD type
Higher order interpolation
Allows large displacements, using ANCF formulation
Thick shells allowed
Can have multi-layered materials
ANS-EAS, shear-lock free
Nodes D must be aligned to shell normal at initialization

ChElementShellBST

The chrono::fea::ChElementShellBST is a triangular thin shell element that offers very high computational efficiency.

Triangular thin-shell
6 nodes of chrono::fea::ChNodeFEAxyz type
- 1,2,3 from the triangle
- 4,5,6 from the neighbouring triangles (any can be optional if on the boundary)
Constant strain, constant curvature computed from bent triangle neighbours
Allows large deformation
Can have multi-layered materials
Based on Kirchhoff-Love theory (no shear), good for tissues, sails, etc.
Section defined in a modular way, via N layers, each with a chrono::fea::ChMaterialShellKirchhoff composed by:
- Elasticity model from chrono::fea::ChElasticityKirchhoff, ex:
- Damping model from chrono::fea::ChDampingKirchhoff (optional)
- Plasticity model from chrono::fea::ChPlasticityKirchhoff (optional)

Theory

Additional information regarding the implementation of finite elements in Chrono can be found at the
whitepapers page.

Examples

See demos and examples at the tutorials page.

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