Material nonlinear finite element analysis and optimal design of reinforced concrete structures

Abstract

In this dissertation, effective methods for structural analysis and design are developed. For the nonlinear analysis, the effects of finite element mesh sizes on the analysis of the behavior of the structure, which is the most significant among the effects such as load step, and integration orders, etc., is investigated and a new criterion to reduce the numerical error associated with the mesh sizes is developed. This newly developed criterion is based on the fracture energy concept and can be easily implemented into a numerical analysis procedure. In particular, this approach can be used effectively with relatively large finite element mesh sizes used in most practical applications. The validity of proposed criterion is tested by comparing the analytical results from this study with those of experimental studies and other previous numerical studies. For structural optimization, a simplified, yet effective, algorithm is presented. Instead of utilizing the more sophisticated optimization model that requires many variables and complicated descriptive functions, the proposed algorithm uses an effective direct search method. After constructing the database of predetermined R/C sections which are arranged in the order of increasing resistant capacities, the relationship between the section identification numbers and the resistant capacities of sections is established by regression and used to obtain an initial solution(section) which satisfies the imposed design constraints. Assuming that there exists an optimum section near the one initially selected by continuous optimization, a direct search is conducted to find the discrete optimum solution. The optimization of the entire structure is accomplished through the individual member optimization.