Falko v 5.0.8
Finite Elements implemented in Falko v 5.0.8
Linear Beam element Linear beams have axial,transverseshear,bending and torsion stiffness. It is based on the smallstrain/small deflection ReisnnerTimoshenko 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).
NonLinear Beam Based on the same ReisnnerTimoshenko beam theory but in its largestrain/largedeflection form ( full nonlinear theory). This form takes in account the 2^{nd }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 GreenLagrange 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 NonLinear


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
NonLinear Rod element As linear rod elements the nonlinear rod has axial stiffness only. It is based on the smallstrain/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 NonLinear In particular: Linear and NonLinear Truss elements can have positive and negative stress/strain Linear Cable and "Gap" elements will behave like "Truss" elements NonLinear Cable elements will work only under positive stress/strain , they will go slack under compression NonLinear "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 smallstrain/smalldisplacement 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 NonLinear Membrane Same as the linear membrane elements but based on largestrain/large displacement theory (full nonlinear theory) that takes in account the 2^{nd }order strain terms and stress stiffening . The small strain tensor is replaced with the GreenLangrange strain tensor E and the Cauchy stress tensor with the PK2 stress tensor S.
Implementation: NonLinear Membrane elements are used to model tensile structure membranes when the FDM,NFDM OR DSM Methods are active. These elements are generated inside a TensoGroup >Mesh sub group, for patterning purposes in ixCube 410


Linear Shell Shell elements have membrane stiffness (in plane), bending and transverse shear stiffness (out of plane). They are based on the smallstrain/smalldeflection ReisnnerMindlin 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 inplane 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 transverseshear integration scheme to avoid the locking
NonLinear shell
Like the linear shell elements these have membrane stiffness (inplane), bending and shear stiffness (out of plane). They are also based on the same ReissnerMindlin shell theory but in its largestrain/largedeflection form (full nonlinear theory). This form takes into account the 2nd order
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 nonlinear shell elements are used for the nonlinear analysis
