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ixCube  Fea v 4.0.1 

 Finite Elements implemented in ixCube Fea v 4.0.1

 

Linear Beam element

Linear beams have axial,transverse-shear,bending and torsion stiffness. It is based on the small-strain/small deflection Reisnner-Timoshenko  beam theory (linear theory) : material section surfaces remain plane and unstrained, only rotated, and two transverse shear strains are allowed.This model does not take in account the warping of the section surface.  These elements have 6 degrees of freedom at each node (3 translations and 3 rotations).

Loads

Loads can be punctual (Force and Momentum), uniform (Force only)  and trapeze( Force Only).

The equivalent nodal loads are internally computed so that the final element solution is exact. The thermal loads are uniform on each element and linear in both section directions (to give two thermal bending moments). 

 

Non-Linear Beam

Based on the same  Reisnner-Timoshenko  beam theory but in its large-strain/large-deflection form ( full non-linear theory). This form takes in account the 2nd order strain terms, stress stiffening, large displacements and large rotations. In particular derivatives of the rotations are fully exact. The small strain tensor of the linear beam is replaced by the Green-Lagrange strain tensor E, and the Cauchy  stress tensor ơ by the PK2 stress tensor S.

Loads

Same as the linear beam element.

 

Implementation:

The Beam element is implemented trough  the  Beam type flag  of  linear elements.

The Behaviour field will set  the type to Linear or Non-Linear 

 

Rod  Element

The linear Rod element has axial stiffness only. There are 3 degrees of freedom at each node (Ux,Uy,Uz). The stress/strain tensors are considered purely axial and uniform trough the cross section and along each element. 

A rod element has no mass, no damping

 

Non-Linear Rod element

As linear rod elements  the non-linear rod has axial stiffness only. It is based on the small-strain/large deflection theory. The axial force is always on the current displaced line.

 

 

Implementation:

Rod elements are implemented trough the "Truss" type element, the "Cable" type element and the "Gap" type element 

The Behaviour field will set  the type to Linear or Non-Linear 

In  particular:

Linear and Non-Linear Truss elements can have positive and negative stress/strain 

Linear Cable and "Gap" elements will behave like  "Truss" elements 

Non-Linear Cable elements will work only under positive stress/strain , they will go slack under compression

Non-Linear "Gap" elements  will work only under negative stress/strain, they will elongate with zero stiffness under tension.

 

Linear Membrane 

This model has only membrane stiffness (in plane) but no bending or transverse shear stiffness (out of plane).

It is based on the small-strain/small-displacement theory. These elements have 3 degrees of freedom at each node (Ux,Uy,Uz). The strain/stress tensors are uniform trough the thickness.

 

Loads 

Loads can be (Force only)  punctual, uniform or trapeze. 

 

Remarks:

A membrane element has no mass, no damping

 

Non-Linear Membrane 

Same as the linear membrane elements but based on large-strain/large displacement theory (full non-linear theory) that takes in account the 2nd order strain terms and stress stiffening . The small strain tensor is replaced with the Green-Langrange strain tensor E and the Cauchy stress tensor with the PK2 stress tensor S. 

 

Implementation:

Non-Linear Membrane elements are used to model tensile structure membranes when the FDM,NFDM OR DSM Methods are active. 

These elements are generated inside a Tenso-Group -->Mesh sub group, for patterning purposes in ixCube 4-10  

 

Linear Shell 

Shell elements have membrane stiffness (in plane), bending and transverse shear stiffness (out of plane). They are based on the small-strain/small-deflection Reisnner-Mindlin shell theory (linear theory). The normal pinching stress (szz) is considered null.

These elements have 6 degrees of freedom x node (Ux,Uy,Uz,Rx,Ry,Rz). The in-plane terms are considered to vary linearly trough  the thickness, whereas transverse shear terms are considered uniform. 

 

Loads

Force and Momentum loads can be punctual, uniform,trapeze and pressure. 

 

Remarks

The FACEQ4 shell element has a special transverse-shear integration scheme to avoid the locking
phenomenon. 

 

Non-Linear shell 

 

Like the linear shell elements these have membrane stiffness (in-plane), bending and shear stiffness (out of plane).

They are also based on the same Reissner-Mindlin shell theory

but in its large-strain/large-deflection form (full non-linear theory). This form takes into account the 2nd order
strain terms, stress stiffening, large displacements and large rotations.
The constitutive law must be elastic (isotropic St-Venant type or orthotropic in the initial tangent plane).
The law relates the Piola-Kirchhoff-2 stress tensor S to the Green-Lagrange strain tensor E. It is used in its
plane-stress form.
No more approximation than those of the linear models is made. In particular, derivatives of the rotations
are fully exact.

 

Implementation

 

Shell  elements can be Tri or Quad  and are implemented trough the Shell group.

Linear shell elements are used in a linear analysis while non-linear shell elements are used for the non-linear analysis

 

 

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