Large increment method for solving nonlinear structural systems
Barham, Wasim S
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In recent years, the linear analysis of structures has become no longer sufficient for many structural engineering applications. Instead, nonlinear structural analysis is often required now in engineering practice as a result of the new approaches for using all possible energy sources. Currently the displacement-based finite element method is employed for the nonlinear analysis of structures. In this method, the main unknown variables are the system displacements. Therefore, in order to represent the general force in terms of general deformation, the constitutive relations have to be linearized, and an incremental step-by-step solution approach has to be used. The displacement-based method has many shortcomings that can be summarized in three points: (1) the linearization of the constitutive model, (2) the step-by-step solution procedure, (3) and the high computational effort. The Large Increment Method (LIM) is a force-based method that has been recently developed. The main advantage of the flexibility-based large increment method over the displacement method is that it separates the linear global equilibrium and compatibility equations from the, possibly nonlinear, local constitutive relations. Consequently, LIM does not require a step-by-step approach, thus avoiding the development of cumulative errors. This work addresses the formulation and application of a finite element based large increment method for solving a range of nonlinear structural problems. The development focuses on three major topics--namely, (1) nonlinear monotonic analysis, (2) nonlinear cyclic analysis, and (3) a framework for dynamic analysis. The local stage is clearly addressed for all the nonlinear constitutive models used in this study. Because of the features of some materials models (i.e., elastic-perfectly plastic material model), the solution procedure is modified, and special treatment for flexibility calculations and return algorithm schemes are introduced. Beam and frame element libraries are established to open the door for future improvements. For all the numerical examples presented in this study, the results are compared to those obtained from the displacement-based finite element software ABAQUS. Finally, this work showed that LIM appears to be an efficient alternative method for solving nonlinear structural problems with the potential for considerable savings in computational cost and time.