Gu, Randy JWang, XiyunGu, Randy JYang, LianxiangHorvath, TamasChang, Yin-Ping2024-10-112024-10-112024-01-01https://hdl.handle.net/10323/18331The ill-posed boundary value problems, such as contact problems, adhesive joint analysis, and damage identification, are of foremost importance in the design and manufacturing of machines. The analysis of these problems has attracted considerable attention from engineers and researchers in various industries. This dissertation presents a novel hybrid finite element method for solving ill-posed boundary value problems through inverse engineering, with a focus on accurately determining contact stress, identifying damage, and analyzing adhesive joints in mechanical engineering. A significant aspect of this method involves integrating empirical measurements with numerical simulations to enhance both the accuracy and reliability of finite element analyses under insufficient boundary conditions. A constrained optimization framework is also employed in this study. The method is evaluated through seven case studies, which include assessments of plate bending, rigid contact problems, Hertzian contact problems, damage identification tasks, single lap joint, and T-peel joint evaluations. A novel constraint equation based on the gradient of the loading function is introduced as well. These case studies highlight the method’s comprehensive applicability and effectiveness across a range of complex engineering challenges. The dissertation outlines future work that aims to expand the methods application to three-dimensional problems, improve the optimization algorithms, and explore further applications. This work lays a foundation for advancing more complex and reliable modeling techniques in mechanical engineering, with significant implications for both research and industrial applications.