Simple Analysis

Elastic Elongation

• Total displacement = (u_i - u_j) along the element
• Axial force on node i is

• Axial force on node j is

• For the element to remain in static equilibrium, we must have U_i = -U_j

v_i = 0

v_j = 0

• Therefore, we have

• In general, the equation on the last page is written as  Ka = f

K = Element stiffness matrix

a = Element nodal displacement vector

f = Element nodal force vector

• Therefore

• K represents element properties and degrees of freedom

• f  represents the loading condition

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