# Sequential

Sequential analysis is any type of structural analysis performed on a structure under prior loading (also termed preloading or prestressing).

The response of a structure is affected by its initial state, which is affected by the preloading/prestressing applied prior to the analysis of interest. Examples of sequential analysis include analysis of rotorcraft blades under centrifugal preloading, pillar-like structures under compressive preloading, preload arising from the pretensioning of bolts on a structure, and so on. Use SimSolid to account for such preloading or prestressing effects.

## Example

Structural 1 – Preload
Immovable 1
Nut tightening 1
Immovable 1
Nut tightening 1
Force 1 – 20 N
Immovable
Nut tightening
*Force 1 deleted. Editing Force 1 to be 0 N has the same affect.
When the prestressing subcase is linear static, the prestressed stiffness matrix is given by:(1)
$\overline{\text{K}}\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}\text{K}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\text{K}}_{\text{σ}}$
Where,
$\overline{\text{K}}$
Prestressed stiffness matrix
$\text{K}$
Original stiffness matrix
${\text{K}}_{\text{σ}}$
Geometric stiffness matrix that defines the prestressing. This is based on the stresses of the preloading static subcase.
Depending on preloading conditions, the resulting effect could be a weakened or stiffened structure.
• If the preloading is compressive, it typically has a weakening effect on the structure (for example, column or pillar under compressive preloading).
• If the preloading is tensile, it typically has a stiffening effect (for example, rotorcraft blade under centrifugal preloading).

When the prestressing loadcase is a non-linear static subcase, the prestressed stiffness matrix $\overline{\text{K}}$ includes the geometric stiffness matrix ${\text{K}}_{\text{σ}}$ , and also accounts for the changes of $\text{K}$ due to the converged contact status carried over from the prestressing loadcase to the prestressed loadcase.