Study On The Optimal Design Methods Of Discrete Variables For The Reinforced Concrete Structures

Aimed at the optimal design problems for the complex reinforced concrete (RC) structures based on finite element analysis, this thesis focuses on the elementary stiffness matrixes of plane RC material as well as the optimal methods of the discrete variables for RC structures.As to the complex RC structures, the theories of classical mechanics can hardly be used to analyze their structural responses in detail and accurately, so that optimal design should be carried out on the basis of finite element method. On the other hand, the design variables are naturally discrete due to the characteristics of structural design, where the conventional common-used optimal algorithms of the continuous variables are not able to work normally. It has a long way to go for developing the optimal method of discrete variables. In fact, the computational work of finite element analysis for the complex RC structures is expected numerous for just one time. If one must get the optimized result after calculating all of the feasible design plans, the computational work maybe unacceptable. So, it's necessary to develop and seek out the effective and reliable optimal methods and routines of the discrete variables.The main works in this thesis are as following.(1) Research and discussion on the elementary stiffness matrixes of various plane elements for RC structures' finite element analysis.With assumption of the identical displacement field, the author derives the formulae of stiffness matrix of plane RC quadrangle element with one or several tendons in combined, separate and homogeneous models respectively. The cohesive function between concrete and tendon is considered qualitatively to formulate the stiffness matrix of the plane combined RC quadrangle element with one tendon in the un-identical displacement field. Making an example of finite element analysis for a RC deep beam, the author compares and analyzes the feature, accuracy and reliability of these elements.(2) In light of the features of discrete variable, the author analyzes anddiscusses the application of 3 kinds of methods in optimal design of RC structures: direct mesh method, virtual-real mesh method and complex mesh method.Basically, these methods all belong to direct seeking method, in which the main influence factors include in initial vector, step length and seeking direction. The above-mentioned methods all attempt to find the better fittings of these factors from the discrete mesh points, in order to enhance the efficiency of optimal calculation.(3) Making use of the plane RC elements and optimal methods of discrete variables proposed in this thesis, optimal design is carried out for a RC plane frame structure, with the objective function of lowest building cost. The numerical results show that the method of this thesis is correct, effective and high efficiency.