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The Fictitious Force Method-Numerical Applications and Arc-Length

Title: The Fictitious Force Method-Numerical Applications and Arc-Length

Principal investigator: Pedro Gala

Research team: Ricardo Joel Teixeira Costa

Dates start/end: 6-2018 / 12-2018


Practical Analysis and Design of Reinforced Concrete Structures nowadays still is based on simple com- prehensive global linear elastic models formed mainly with 1D elements, despite of the powerful 3D Nonlinear Finite Element Method (NLFEM) analysis packages available. The use of these complex NLFEM models, seems to be restricted to the study of local phenomena due to the large amount of time required to validate the models, perform the analysis and interpret the results. Accordingly, many times their use is replaced by Stress Field Models.

This scenario justified the development of the Fictitious Force Method (FFM), see [1], a simple but effec- tive 1D materially nonlinear analysis method of skeletal structures, emerging as a natural extension of the P-Delta geometric nonlinear analysis method [2]. In FFM the material nonlinear behavior is consid- ered in supplementary loading systems, during an iterative procedure made of simple operations where the same stiffness can be used in all iterations.

The FFM has been used in several recent studies [3][4][5] and is presently implemented in the software EvalS [6]. In the scope of these studies, it was found that in order to properly analyse the “post-peek” be- haviour of frame structures it is necessary to adapt the general FFM frame-work in order to make it suit- able to implement an arc-length procedure. Accordingly, the main objectives of this research project are:

i) To develop the desired FFM/arc-length procedure, making FFM suitable for the analysis of reinforced concrete structures exhibiting post-peak behaviour, e.g. a dedicated example previously studied by the research team and (exhibiting postpeak behaviour), see [7] and [8].

ii) To validate the FFM/arc-length procedure throughout the numerical analysis of a set of benchmark case studies.

iii) To identify the sufficient convergence conditions of FFM/arc-length procedure (therefore in cases whith post-peak behaviour).