Object-Oriented Stochastic Finite Element And Reliability-Based Shape Optimization Design With Contact Problems

There are many contact problems, such as the gear meshes, the joints between shafts and disks, the tenon/mortise in aero-engines, which exist extensively in engineering structures and machinery systems. The reliability-based shape optimization by the object-oriented stochastic finite element method (SFEM) is a new field in the contact problems. It can be used to not only optimize the stress distributions and improve the ability of structures under loads, but also simplify the programming of these problems. Consequently, it is very important to research the object-oriented stochastic finite element method and use it to the reliability-based optimization in contact problems. The following problems are studied and analyzed in this dissertation.Theory and method of stochastic finite element methodAccording to the present SFEM theory, SFEM equations for concrete stochastic variables are conducted for 2-D and 3-D non-contact problems, and the methods and numerical algorithms of SFEM for contact problems are presented and researched by the substructure agglomeration method. The SFEM equations with concrete stochastic variables are be conducted and given for 2-D and 3-D contact problems as well.Theory and method of reliability-based shape optimizationThe method for reliability-based shape optimization of 3-D non-contact structures and 2-D as well as 3-D contact structures based on stochastic finite element methods are proposed and researched. The corresponding reliability-based shape optimization models and numerical algorithms are built up, and the corresponding equations are conducted. The selection of design variables, target functions, restrain conditions and shape description and numerical modeling for structures are studied and analyzed. Several examples are given to show the presented method is effectively. Finally, the method is employed to solve the reliability-based shape optimization of the tenon/mortise structure in an aero-engine so as to improve greatly the stress distributions and the safe probability of the structure.Theory, method and realization of object-oriented SFEMThis dissertation presents and researches, systematically and comprehensively at the first time, the object-oriented programming method of stochastic finite element andreliability-based shape optimization. The designs and programming of the object-oriented software, user's interface, memory management and graphic interface are performed by Visual C++6. 0 and Visual Basic 6.0, so that it is successful to obtain a comprehensive object-oriented software system based on the developed stochastic finite element method and reliability-based shape optimization.