<< Click to Display Table of Contents >> Navigation:  Flexcom > Theory > Fundamentals > Finite Element Formulation >
External Virtual Work Statement

The external virtual work statement for an accelerating pipe element is given by:

       (1)

where:

• is the increment of external virtual work

• is the distributed load vector in convected axes

• is the mass per unit length of element

• is the translational acceleration vector in convected axes,

• is the polar moment of inertia per unit length about element axis

•is the angular acceleration about convected axis

Substituting for displacements and accelerations in terms of nodal quantities and interpolation functions, in standard finite element fashion, gives the finite element form of , namely:

       (2)

where:

• is the vector of equivalent nodal loads in convected axes

• is the element mass matrix in convected axes

• is the vector of nodal accelerations in convected axes