DEVELOPMENT OF 2D NONLINEAR FINITE ELEMENT ALGORITHMS AND COMPUTATIONAL PROCEDURES FOR HISTORICAL STRUCTURES
Andres Mena Cabrera
(Thesis Supervisor: M. Yasin Fahjan)
The conservation and restoration of historical structures are great challenges for the engineering community in terms of robust analytical models. Previous researches demonstrated the importance of nonlinear effects for the analysis of historical structures. Therefore, reliable numerical models are necessary to predict the behavior of the existing historical buildings from the linear stage, through cracking and degradation until complete loss of strength. In the recent years, new numerical techniques have been developed in order to describe these structural stages. The aim of this research is to develop computational algorithms for the analysis of unreinforced masonry, which is the main composite material of historical structures. The algorithms will include computational procedures able to implement accurate and robust constitutive models complemented with advanced solution procedures of the finite element system. In this study, a series of Matlab codes is developed for both linear and nonlinear analyses of two-dimensional modeling of historical structures. TIle linear analyses include static, modal dynamic and time history procedure. The material and geometrical nonlinearities are considered for static analyses. The finite elements are quadrilateral 2D membrane elements with drilling degrees of freedom. Based on the existing theory, two different formulations of the membrane elements are presented. The first formulation (LMR4) is performed within the framework of the linear elastic static and dynamic analyses, while the second formulation (NLMR4) is oriented to nonlinear analysis. Geometrically nonlinearity is applied through the modified Newton-Raphson method with arc-length constraint and variational principles. The material nonlinearity follows modem plasticity theory, considering orthotropic plasticity via a Rankine type yield criterion for tension and a Hill type yield criterion for compression. The developed Matlab codes and procedures are validated with conventional tests and experimental results existing in the literature. The robustness and applicability of the methodologies in engineering practice are demonstrated through the analysis of two crosssections of The Fatih Mosque.