Integrating geometric modeling and structure analysis: towards the digital future of engineering

Abstract

Numerical method has revolutionized the engineering. With the rapid development of modern computers, the numerical method will play a more important role in the future of engineering. However, a large amount of human effort is still required in an analysis to convert a geometric model to a numerical model which can be accepted by computers. This manual process is time consuming and error prone, especially in an adaptive analysis where the mesh needs to be updated frequently. Additional challenges are imposed by new data formats used in industry, such as stereolithography (STL) models, virtual reality (VRML) models and digital image. In this thesis, a numerical framework is developed to link geometric modeling and structure analysis automatically based on the scaled boundary finite element method, which is capable of modeling polyhedrons with arbitrary number of faces and edges by discretizing their boundaries only. This framework accepts multiple data formats as input. High quality polyhedron meshes can be generated using octree algorithm with minimum human interventions. The meshes for different parts of a model can be generated independently and merged automatically by modifying the surface meshes on their interfaces only. No interface constraints or special shape functions are required in the analysis. Composite materials with inclusions such as fibers and anchors can also be modeled. Adaptive mesh refinement can be implemented based on a posterior error estimation. The meshes can be modified locally due to the advantage of the polyhedron elements. A virtual city analysis is performed using this framework, where a numerical model of a city block is constructed to simulate the ground settlement, the air flow between buildings and the effect of earthquakes. Large scale modeling and analysis are possible because of the automation and efficiency of the proposed method. The meshes generated for individual buildings, underground structures and terrain in the virtual city are reusable. The numerical framework proposed in this thesis has been successfully applied by other researchers in acoustic, contact mechanics, fluid-structure interaction and many others.