[M U i [MU P At [Q pi

Substituting equation 4.11 into equation 4.8, then: ([G]+pPAt2[Q]T [M ]-1[Q]){P}i+1+[C ']{P }i+1+[K ']{p}m = {F2}j+1-p[Q]T {U }*+

In equation 4.12, the right hand side terms are known, thus, {P}i+1 can be obtained. In order to correct the approximation made in equation 4.11, {P}i+1 can be substituted in equation 4.7 to calculate {U}i+1 and its derivatives.

Therefore, the procedure of the staggered displacement method can be summarized by the following steps:

1. Solving equation 4.9 to calculate {U}*+1.

2. Substituting {U}*+1in equation 4.12 to calculate {P}i+1.

3. Substituting {P}i+1 in equation 4.7 to calculate {U}i+1 and its derivatives.

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