Adaptive reduced integration method for nonlinear structural dynamic analysis

A reduced integration method for the coupled analysis of floating production systems

“…As described in Jacob and Ebecken (1992), the MSM presents some drawbacks. For instance, there is a deficiency in the calculation of internal forces due to the truncation of the modes of vibration with higher frequency values.…”

“…Numerical experiments (Jacob and Ebecken, 1992) have shown that the global orthogonality of the static vector is not always assured by the updating process of step B.6, which is an orthogonalization procedure against only the previous Ritz vector. Thus, the alteration consists in introducing an orthogonality test of the static vector against the previously obtained Ritz vectors; if the amplitude of any Ritz vector relative to the static vector is superior to a given threshold, step C.1 performs a global reorthogonalization.…”

“…In this work, we employ three types of termination criteria to stop the generation algorithm on step B.5 of Table 1, related respectively to measures of the adequate representation of the loading, mass, and the normalization of the Ritz vectors. Details on the derivation and implementation of these criteria may be found in Jacob and Ebecken (1992); here only the main expressions will be presented. The loading representation criterion is based on the following expression for the re-expansion of the reduced loading vector Jacob and Ebecken, 1992):…”

“…However, the benefits of applying a reduced integration method to more severe nonlinear problems may be smaller or even inexistent, mainly because the stiffness matrix (and therefore the transformation matrix) should be frequently updated along the time integration process. Jacob and Ebecken (1992) presented an adaptation of reduction techniques for nonlinear problems, including fixed offshore systems such as jackets or compliant towers. That work proposed an adaptive strategy to minimize the instances of reevaluation of the stiffness and coordinate transformation matrices, allowing the associated overheads to be compensated by the increased computational efficiency of integrating a reduced system of equations between the basis reevaluation steps.…”

“…Considering the Brazilian case, the assessment of very large deepwater oil fields in the Campos Basin around the 1980s has led to studies on compliant towers (Benjamin et al, 1988), and on semi-submersible platforms or FPSO units (de Souza et al, 1998;Jacob et al, 1999). It is well known that large displacements and severe nonlinear dynamic effects characterize the behavior of such systems; therefore, research efforts have been directed to the development of nonlinear dynamic analysis tools with improved computational efficiency (see for instance Jacob and Ebecken, 1993, 1994a, 1994b.…”