# Flexible Element

Flexible element is a two-node flexible element, that can be used for modeling of expansion bellows or flexible hoses. In the one-node expansion joints the deformation are modeled in the point (zero length expansion joint), but the two-node element is a finite length beam. The bending stiffness for two-node flexible element should be specified 4 times greater than for zero length expansion joints.

### General Properties

 Property Description Name Text field. Element can be sorted by name and selected in the  project tree Projections\sphere\cylinder1 Projections - element dimensions are input as projections on global coordinate axes DX, DY, DZ; sphere - element dimensions are input as element length L and three angles between the element axis and the global coordinate axes jX, jY, jZ; cylinder - element dimensions are input as a projection on the XY plane, projections on the Z axis and two angles between the projection on the XY plane and X and Y axes Axial Stiffness, Shear Stiffness, Torsion Stiffness, Bending Stiffness Axial Stiffness - E*A Shear Stiffness - G*Ay и G*Az Torsion Stiffness - G*It Bending Stiffness - E*Iy и E*Iz E - Elastic Modulus, G - Shear Modulus, A - cross section area, Ay, Az - Effective Shear Area, It - torsion moment of inertia, Iy, Iz - moment of inertia Shear Stiffness and Bending Stiffness automatically calculated depending on each other by equation: KL=KR*3/L^2 и KR=KL*L^2/3, where KR=EI - Bending Stiffness KL=GA - Shear Stiffness Bending stiffness KR of two-node flexible element should be specified four times greater than KR value for zero length expansion joints. Below is shown models of two types of flexible elements а - two-node flexible element (flexible beam) and b - zero length flexible element. Two node flexible element can have a deflection D, but zero length expansion joint can't deflect (D=0). The rotation angle of the model (a) will be 4 times greater than of the model (b) from the same applied moment M q2=4*q1, therefore the rotation stiffness KR will also be 4 times greater. KR of two-node flexible element = 4*KR of zero length expansion joint Therefore, the bending stiffness provided in the manufacturer catalogues should be multiplied by 4 when using in the two-node flexible element. Thrust Area Thrust area is used to model the pressure thrust forces in flexible pipe. For pressure balanced expansion joints it should be zero Total weight Total weight of the element Uniform weight Uniform weight of the flexible element