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Lifetime-Oriented Structural Design Concepts- P16

Lifetime-Oriented Structural Design Concepts- P16: At the beginning of 1996, the Cooperative Research Center SFB 398 financially supported by the German Science Foundation (DFG) was started at Ruhr-University Bochum (RUB). A scientists group representing the fields of structural engineering, structural mechanics, soil mechanics, material science, and numerical mathematics introduced a research program on “lifetimeoriented design concepts on the basis of damage and deterioration aspects”. | 408 4 Methodological Implementation 4.83 4.84 4.85 is obtained. Since the linear system of equations 4.81 is non-symmetric and looses furthermore the band structure of the generalized tangent matrix it is solved by applying the partitioning technique 91 . Therefore the partial incremental solutions Aur and AuA are calculated in advance. K 1 un 1 Aur n 1r - M iX K 1 i AuA r Afterwards the increments Au Aur AuAAX and AX -f un i x . u- iX j Aur f u un i x i aua A un i x . are computed. Since this procedure is restricted to the corrector iteration a specialized predictor step adopting an user defined step length s is implemented. As shown in Figure 4.20 the load factor is increased by one and the resulting displacement increment AuA and step length s0 are calculated. Aua K _i u r s0 Aua Aua 1 4.86 Afterwards the increments of the displacement vector and the load factor are scaled such that the user defined step length s is obtained. AX -Q 1 Au AuA 4.87 Selected constraints within the framework of the present generalized arc-length method are summarized in Table 4.5. It is worth to mention that the standard control algorithms used in the present book namely the displacement and load controlled analyses are also included in Table 4.5 and the load controlled Newton-Raphson scheme has already been discussed in Section 4.2.5.2. As a particular example of the generalized path following method the algorithmic set-up of the arc-length controlled Newton-Raphson scheme is given in Figure 4.21. 4.2.6 Temporal Discretization Methods Authored by Detlef Kuhl and Sandra Krimpmann The present section is concerned with the numerical methods for the time integration of non-linear multiphysics problems by means of Newmark-a methods as well as discontinuous and continuous Galerkin schemes. Newmark-o time integration methods are using the semidiscrete balance equation evaluated at one selected time instant within a time step and finite 4.2 Numerical Methods 409 Table 4.5. Constraints and .