## Modified Staggered Pressure Method

Most of the available nonlinear solutions assume a diagonal mass matrix for the purpose of analysis. The staggered displacement method is the most suitable coupled field problem solution procedure for the case of nonlinear analysis. In the case of the staggered pressure method some difficulties may arise due to added mass effect in equation 4.27 which changes the mass matrix from diagonal to a full matrix. For this reason the staggered pressure method was modified to apply to nonlinear analysis.

The staggered pressure method is modified by rewriting equation 4.27 in the following approximate form:

[M]{UW+[C]{U}i+i+[K]{U}i+1 = {F1}i+1+[Q] ({p}p+i At2[H]-1 ( [G]{pK+1-p[Q]T{U}i))

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

1. Solving equation 4.24 to calculate |p}*+1.

2. Substituting {p}*+1in equation 4.34 to calculate {U}i+1.

3. Substituting {U}i+1 in equation 4.26 to calculate {p}i+1 and its derivatives.

The modified staggered pressure method does not guarantee unconditional stability of the solution. In the following analysis, the modified staggered pressure method is used instead of the staggered pressure method and the results are compared with those obtained using the staggered displacement analysis procedure.

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