Numerical Simulation and Customized DACM Based Design Optimization

Abstract

The diverse numerical modelling, analysis and simulation tools that have been developed and introduced to markets are intended to perform the virtual design and testing of products and systems without the construction of physical prototypes. Digital prototyping in the form of computer modelling and simulation are important means of numerical model predictions, i.e. design validation and verification. However, as the tools advance to more precise and diverse applications, the operation eventually becomes more complex, computationally expensive and error prone; this is particularly true for complex multi-disciplinary and multidimensional problems; for instance, in multi-body dynamics, Fluid-Structure Interaction (FSI) and high-dimensional numerical simulation problems. On the other hand, integrating design optimization operations into the product and system development processes, through the computer based applications, makes the process even more complex and highly expensive. This thesis analyses and discusses causes of complexity in numerical modelling, simulation and optimization operations and proposes new approaches/frameworks that would help significantly reduce the complexity and the associated computational costs. Proposed approaches mainly integrate, simplify and decompose or approximate complex numerical simulation based optimization problems into simpler, and to metamodel-based optimization problems. Despite advancing computational technologies in continuum mechanics, the design and analysis tools have developed in separate directions with regard to ‘basis functions’ of the technologies until recent developments. Basis functions are the building blocks of every continuous function. Continuous functions in every computational tool are linear combinations of specific basis functions in the function space. Since first introduced, basis functions in the design and modelling tools have developed so rapidly that various complex physical problems can today be designed and modelled to the highest precision. On the other hand, most analysis tools still utilize approximate models of the problems from the latter tools, particularly if the problem involves complex smooth geometric designs. The existing gap between the basis functions of the tools and the increasing precision of models for analysis introduce tremendous computational costs. Moreover, to transfer models from one form of basis function to another, additonal effort is required. The variation of the basis functions also demands extra effort in numerical simulation based optimization processes. This thesis discusses the recently developed integrated modelling and analysis approach that utilizes the state-of-the-art basis function (NURBS function) for both design and analysis. A numerical simulation based shape optimization framework that utilizes the state-of-the-art basis function is also presented in a study in the thesis. One of the common multidisciplinary problem that involves multiple models of domains in a single problem, fluid-structure interaction (FSI) problem, is studied in the thesis. As the name implies, the two models of domains involved in any FSI problems are fluid and structure domain models. In order to solve the FSI problems, usually three mathematical components are needed: namely, i) fluid dynamics model, ii) structural mechanics model and, iii) the FSI model. This thesis presents the challenges in FSI problems and discusses different FSI approaches in numerical analysis. A comparative analysis of computational methods, based on the coupling and temporal discretization schemes, is discussed using a benchmark problem, to give a better understanding of what a multidisciplinary problem is and the challenge for design optimizations that involve such problems. [...]