Seismic designs of building structures are currently made based on the design criterion of life-safety and this requires that the structures do not collapse to compromise safety of people in the structure, but they can be designed to experience some damage. However, this design approach has allowed large economic losses primarily due to the damage to the nonstructural components at relatively moderate levels of seismic intensities. This led to a new thinking about design approach called performance-based design approach that satisfies the life-safety objective at the same time, reduces the economic loss to an acceptable level. The performance-based design approaches are multi-level design that addresses several different levels of structural performances under different levels of seismic intensities. In this study, we have investigated the use of energy dissipating damping devices to achieve the performance of a building structure in a desirable manner over all levels of seismic intensity. Since the initial motivation of performance-based design was reducing economic loss, the life-cycle cost-based optimization is considered in this study to obtain the optimal designs with different damping devices. For the optimal design, three types of devices are used in this study: fluid viscous dampers, solid visco-elastic dampers, and yielding metallic dampers. The combinations of two different types of dampers are also examined in this study. The genetic algorithm (GA) approach is adopted as an optimizer that searches for the optimal solution in an iterative manner. Numerical results from the application of the optimal design to the selected model building are presented to demonstrate the applicability of the developed approach and to estimate the effectiveness of the obtained optimal design with each device. It is shown in the results that the optimal design with each individual damping devices or the combination of two different types of damping devices are very effective in reducing the expected failure cost as well as the displacement response quantities and fragilities. The results also show that the optimal designs focus relatively more on reducing economic losses for the lower but more frequent excitation intensities as these intensities contribute most to the failure costs. / Ph. D.

A tool for analyzing and understanding the behavior of structural systems based on the principle of virtual work was developed by Dr. Finley Charney in the early 1990s. The program was called DISPAR, which stands for DISplacement PARticipation factors, and was written to work in accordance with SAP90 and ETABS. This program became outdated once newer versions of SAP90 and ETABS were released. Starting with version 11 of SAP2000, Computers and Structures released an Open Application Programming Interface (OAPI) which allowed programmers efficient access to the information in SAP2000. With this release came the motivation to update the program DISPAR to work with SAP2000 version 11 and other versions to follow. This thesis provides an overview of how the new version of DISPAR was programmed using VB.Net and OpenGL. This thesis starts off with an in depth discussion and literature review on the development of the principle of virtual work. The literature review covers how virtual work can be used as a tool to understand structural behavior as well as optimize structural performance. The updated version of DISPAR (DISPAR for SAP2000) was then used to analyze the behavior of metal building frames under various loadings. The focus of this study was to determine the effect modeling the column base connection as partially rigid has on wind drift in metal building frames. Before beginning the study, a literature review was conducted on the rotation stiffness provided by typical column base connections. The information obtain in the literature review was then used to create a finite element model of a typical column base connection in a metal building. Once the finite element model was completed, DISPAR for SAP2000 was used to conduct a study on the sensitivity of the rotational stiffness of the column base connection. / Master of Science

The optimization of complex structures is extremely time consuming. To obtain their optimization results, researchers often wait for several hours and even days. Then, if they have to make a slight change in their input parameters, they must run their optimization problem again. This iterative process of defining a problem and finding a set of optimized solutions may take several days and sometimes several weeks. Therefore, to reduce optimization time, researchers have developed various approximation-based models that predict the results of time-consuming analysis. These simple analytical models, known as “meta- or surrogate models,” are based on data available from limited analysis runs. These “models of the model” seek to approximate computation-intensive functions within a considerably shorter time than expensive simulation codes that require significant computing power. One of the limitations of metamodels (or interchangeably surrogate models) developed for the structural approximation of trusses and space frames is lack of generalizability. Since such metamodels are exclusively designed for a specific structure, they can predict the performance of only the structures for which they are designed. For instance, if a metamodel is designed for a ten-bar truss, it cannot predict the analysis results of another ten-bar truss with different boundary conditions. In addition, they cannot be re-used if the topology of a structure changes (e.g., from a ten-bar truss to a 12-bar truss). If designers change the topology, they must generate new sample data and re-train their model. Therefore, the predictability of these exclusive models is limited. From a combination of the analysis of data from structures with various geometries, the objective of this study is to create, test, and validate generalizable metamodels that predict the results of finite element analysis. Developing these models requires two main steps: feature generation and model creation. In the first step, involving the use of 11 features for nodes and three for members, the physical representation of four types of domes, slabs, and walls were transformed into numerical values. Then, by randomly varying the cross-sectional area, the stress value of each member was recorded. In the second step, these feature vectors were used to create, test, and verify various metamodels in an examination of four hypotheses. The results of the hypotheses show that with generalizable metamodels, the analysis of data from various structures can be combined and used for predicting the performance of the members of structures or new structures within the same class of geometry. For instance, given the same radius for all domes, a metamodel generated from the analysis of data from a 700-, 980-, and 1,525-member dome can predict the structural performance of the members of these domes or a new dome with 250 members. In addition, the results show that generalizable metamodels are able to more closely predict the results of a finite element analysis than metamodels exclusively created for a specific structure. A case study was selected to examine the application of generalizable metamodels for the early-stage exploration of structural design alternatives in a construction project. The results illustrates that the optimization with generalizable metamodels reduces the time and cost of the project, fostering more efficient planning and more rapid decision-making by architects, contractors, and engineers at the early stage of construction projects.

This dissertation presents a synthesis of methods for structural optimization of aircraft wing boxes. The optimization problem considered herein is the minimization of structural weight with respect to component sizes, subject to stress constraints. Different aspects of structural optimization methods representing the current state-of-the-art are discussed, including sequential quadratic programming, sensitivity analysis, parameterization of design variables, constraint handling, and multiple load treatment. Shortcomings of the current techniques are identified and a B-spline parameterization representing the structural sizes is proposed to address them. A new configurable B-spline parameterization method for structural optimization of wing boxes is developed that makes it possible to flexibly explore design spaces. An automatic scheme using different levels of B-spline parameterization configurations is also proposed, along with a constraint aggregation method in order to reduce the computational effort. Numerical results are compared to evaluate the effectiveness of the B-spline approach and the constraint aggregation method. To evaluate the new formulations and explore design spaces, the wing box of an airliner is optimized for the minimum weight subject to stress constraints under multiple load conditions. The new approaches are shown to significantly reduce the computational time required to perform structural optimization and to yield designs that are more realistic than existing methods.

Nos tempos atuais, já existe um forte desenvolvimento computacional no que diz respeito a análise de estruturas com características geométricas, de cargas e vinculações previamente definidas. Assim como os processadores, tem-se investido bastante em pré e pós-processadores, os quais são responsáveis pela maior parte do tempo dedicado a um projeto. No entanto, pode-se dizer que a definição automática das características geométricas dos elementos estruturais deixa a desejar. Hoje, esta etapa ainda é feita pelo engenheiro, apenas com uma ajuda indireta da máquina. Este trabalho apresenta uma maneira ótima de fazer o pré-dimensionamento das vigas de um pavimento de concreto armado. Para isso, desenvolveu-se uma formulação de minimização do custo de uma seção transversal com a qual, através de um método de aproximações combinadas, obtém-se o mínimo custo do vigamento de um pavimento. As variáveis envolvidas na função que representa o custo são: a altura da viga e as áreas de aço. E as restrições do problema são: a taxa geométrica da armadura, a taxa de armadura de compressão em relação a de tração e a flecha máxima pré-estabelecida pelo usuário. / Nowadays, there is a continuous development in structural computational analysis for known geometrical, loading and boundary conditions. Much effort has been made on the pre and pos-processors, which is the main part of the time spent in designing. The automatic definition of the geometrical characteristics for the structural elements, however is poor yet. Today, this phase is still carried out by the engineer, only with an indirect machine help. This work presents an optimal method to automate the first draft design of the beams reinforced concrete floor. A formulation to achieve the cross-section minimum cost function is proposed and then extended to the whole floor by combined approximation methods. In order to obtain the cost function the following values have been considered: the beam depth and the steel area. As problem constraints, the steel geometric rate, the steel compression with the steel tension rate and the limit displacement have to be prescribed by the user.

Advances in multiscale methods are presented from two perspectives which address the issue of computational complexity of optimizing and inverse analyzing nonlinear composite materials and structures at multiple scales. The optimization algorithm provides several solutions to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales. We also present an adaptive variant of the measure-theoretic approach (MTA) for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are: identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin-hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC-12K-31E and epoxy #2510 material system from the NIAR report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open-hole laminates. Advances in Multiscale methods also provides us a unique tool to study and analyze human bones, which can be seen as a composite material, too. We used two multiscale approaches for fracture analysis of full scale femur. The two approaches are the reduced order homogenization (ROH) and the novel accelerated reduced order homogenization (AROH). The AROH is based on utilizing ROH calibrated to limited data as a training tool to calibrate a simpler, single-scale anisotropic damage model. For bone tissue orientation, we take advantage of so-called Wolff’s law. The meso-phase properties are identified from the least square minimization of error between the overall cortical and trabecular bone properties and those predicted from the homogenization. The overall elastic and inelastic properties of the cortical and trabecular bone microstructure are derived from bone density that can be estimated from the Hounsfield units (HU). For model validation, we conduct ROH and AROH simulations of full scale finite element model of femur created from the QCT and compare the simulation results with available experimental data.

水準集結構拓撲優化方法同傳統的基於材料的拓撲優化方法相比具有明顯的優勢。由於採用了隱式的邊界表達，水準集方法能方便地處理結構形狀和拓撲的變化，且在優化過程中可以保持邊界的光滑。但這種動態結構邊界需要一種有限元分析方法可以適應其動態變化且能夠獲得足夠的計算精度。本文對傳統水準集結構拓撲優化中有限元分析存在的關鍵問題進行研究，同時針對應力約束下的結構拓撲優化，提出了一種新的拓撲優化方法。 / 首先， 擴展有限元法作為一種相對精確和高效的結構分析方法，本文將其引入到水準集結構拓撲優化中。引入擴展有限元法主要是為了處理優化過程中結構邊界上出現的材料的高度不連續情況，從而避免耗時的網格重新劃分。如果結構邊界從有限元單元內部通過，為了獲得足夠的計算精度，該單元內需要採用特殊的數值積分方法。常用的方法是將這個單元內被材料填充的區域劃分成小的子單元去適應單元內部的邊界，然後在各個子單元內採用高斯數值積分來獲得該單元的剛度矩陣。對於二維問題，如果結構邊界從一個單元內部通過，將單元分成幾部分，首先把單元內部的實體區域劃分成子三角形，然後計算出每個子三角形內的高斯積分點，最後單元剛度矩陣通過把所有子三角形的高斯積分點處的數值積分迭加得到。對於三維問題，則是將一個六面體單元分解為幾個四面體，然後在每一個四面體內部通過結構上定義的水準集函數值得到邊界，對於實體的部分劃分為子四面體，在每一個子四面體內計算出高斯積分點，此四面體的單元剛度矩陣為所有子四面體剛度矩陣的迭加，因此，該六面體的單元剛度矩陣為所劃分的四面體單元剛度矩陣的迭加。 / 其次，本文研究了提高擴展有限元法的計算精度和效率的方法。採用擴展有限元法進行結構分析時，如果被結構邊界剖分的有限元單元中實體部分體積比小到一定程度，將會影響到計算精度，本論文給出了處理擴展有限元中這種小單元情形的具體辦法。擴展有限元法作為一種結構分析計算方法，除了必須考慮精度外，效率也是一個重要的指標，尤其對於拓撲優化問題，因拓撲優化問題通常需要多步的反覆運算來獲取最優或局部最優解。為提高擴展有限元法的計算效率，相對於前面的基於剖分單元為子單元進行積分的辦法，本文提出了一種更高效的積分方法，即去除積分單元剖分，通過直接積分來計算被結構邊界剖分的單元的剛度矩陣。這種直接積分的方法不僅能保證結構分析的精度，更能顯著的提高計算效率，這對於水準集結構拓撲優化是非常有意義的。同時高階單元被用來從另一個角度分析擴展有限元法計算精度與效率之間的關係，換言之，可以用高階單元在相對粗的網格上來獲取同低階單元在相對密的網格上相同的分析結果精度，從而提高計算效率。但是這個問題需要找出計算精度在網格密度和單元階次之間的關係。 / 第三，本文以二維和三維結構的柔度最小化問題為例驗證了上述擴展有限元演算法在結構拓撲優化問題中應用的有效性。 / 最後，本文研究了基於應力約束的結構拓撲優化問題，並採用前面提出的擴展有限元法與水準集結合的拓撲優化方法。由於採用擴展有限元法進行結構分析可以獲得較準確的應力計算結果，特別是在結構邊界附近，這對於基於應力的拓撲優化問題有很大的優勢。而且，本文提出了一種形狀等效約束法來有效地控制局部應力約束，數值算例也證明擴展有限元法與形狀等效約束方法相結合對處理應力約束問題是一種非常有效的。同時，本文還提出了一種全新的通過拓撲優化來實現應力隔離結構設計的方法。通過在拓撲優化問題中不同區域施加不同的應力約束來有效地模擬這種應力隔離的問題。最終數值算例證明，該方法可以通過改變力的傳播途徑來達到有效地形成結構的應力隔離。 / Level set method is an elegant approach for structural shape and topology optimization, compared to the conventional material based topology optimization methods. The structural boundary is implicitly represented by a moving level set function. Thus, the shape and topology optimization can be processed simultaneously while maintaining a smooth boundary. The moving structural boundary demands a finite element analysis adaptable to the dynamic boundary changes and meeting required accuracy. In this thesis, the key issues of finite element methods of structural analysis for level set optimization method are investigated and an approach to stress-constrained topology optimization is presented. / Firstly, the extended finite element method (XFEM) is introduced into the level set method structural shape and topology optimization for obtaining a considerably accurate and efficient result of finite element analysis. In fact, the XFEM is employed as a structural analysis method to solve the problems of strong discontinuities between material and void domain during the level set optimization process in order to avoid the time cost remeshing. To achieve a reasonably accurate result of finite element analysis in the element intersected by structural boundary, special numerical integral schemes of XFEM are studied. The partition method is adopted to divide the integral domain into sub-cells, in which Gauss quadrature is utilized to calculate the element stiffness matrix. For two-dimensional (2D) problems, the integral domain is divided into sub-triangles, and the Gauss quadrature points in each sub-triangle are used to evaluate the element stiffness matrix which is the sum of all contributions of these sub-triangles. For three-dimensional (3D) problems, the hexahedral element is decomposed into multiple tetrahedra, and the integral domain in each tetrahedron is divided into sub-tetrahedra for obtaining the Gauss quadrature points. Therefore, the stiffness of each tetrahedron is obtained by summing all contributions of the sub-tetrahedra, which means the hexahedral element stiffness matrix is the accumulation of element stiffness matrixes with all these tetrahedra. / Secondly, the methods for improving the computational accuracy and efficiency of XFEM are studied. First of all, the practical solutions for dealing with the small volume fraction element of the proposed XFEM are provided since this kind of situation may result in the accuracy losing of finite element analysis. Besides computational accuracy of structural analysis, the efficiency is another sufficiently important issue of structural optimization problem. Therefore, a new XFEM integral scheme without quadrature sub-cells is developed for improving the computational efficiency of XFEM compared to the XFEM integral scheme with partition method, which can yield similar accuracy of structural analysis while prominently reducing the computational cost. Numerical experiments indicate that this performance is excellent for level set method shape and topology optimization. Moreover, XFEM with higher order elements are involved to improve the accuracy of structural analysis compared to the corresponding lower order element. Consequently, the computational cost is increased, therefore, the balance of computational cost between FE system scale and the order of element is discussed in this thesis. / Thirdly, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely employed in the recent literature of structural topology optimization. / Finally, the stress-based topology optimization problems with the proposed XFEM schemes are investigated. Due to the accuracy of structural analysis, XFEM schemes have natural advantages for solving the stress-based topology optimization problems using the level set method. Moreover, the shape equilibrium constraint approach is developed to effectively control the local stress constraint. Some numerical examples are solved to prove the high-performance of the proposed shape equilibrium constraint approach and XFEM schemes in the stress-constrained topology optimization problem. Meanwhile, a new approach of stress isolation design is presented through topology optimization. The stress isolation problem is modeled into a topology optimization problem with multiple stress constraints in different regions. Numerical experiments demonstrate that this approach can change the force transmission paths to successfully realize stress isolation in the structure. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Li, Li. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 113-123). / Abstract also in Chinese. / Abstract --- p.I / 摘要 --- p.IV / Acknowledgement --- p.VI / Contents --- p.VII / List of Figures --- p.XI / List of Tables --- p.XV / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Related Works --- p.3 / Chapter 1.3 --- XFEM for Structural Optimization --- p.4 / Chapter 1.4 --- Topology Optimization with Stress Constraint --- p.7 / Chapter 1.5 --- Contributions and Organization of the Dissertation --- p.10 / Chapter 2 --- Level Set Method for Structural Optimization --- p.12 / Chapter 2.1 --- Structural Optimization Problem --- p.12 / Chapter 2.2 --- Implicit Level Set Representation --- p.14 / Chapter 2.3 --- Evolution of the Level Set Function --- p.15 / Chapter 2.4 --- Level Set Surface Reinitialization --- p.16 / Chapter 2.5 --- Velocity Extension --- p.17 / Chapter 3 --- Extended Finite Element Method (XFEM) --- p.19 / Chapter 3.1 --- Global Enrichment --- p.19 / Chapter 3.2 --- Local Enrichment --- p.20 / Chapter 3.3 --- Enrichment Function --- p.22 / Chapter 3.3.1 --- Enrichment for Strong Discontinuity --- p.22 / Chapter 3.3.2 --- Enrichment for Weak Discontinuity --- p.23 / Chapter 3.4 --- XFEM used in Structural Optimization --- p.23 / Chapter 4 --- Implementation of XFEM for Structural Optimization --- p.25 / Chapter 4.1 --- 2D XFEM Scheme --- p.26 / Chapter 4.1.1 --- Numerical Integral Scheme in 2D --- p.26 / Chapter 4.1.2 --- Evaluation of the 2D XFEM Scheme --- p.27 / Chapter 4.2 --- 3D XFEM Scheme --- p.30 / Chapter 4.2.1 --- Numerical Integral Scheme in 3D --- p.30 / Chapter 4.2.2 --- Evaluation of the 3D XFEM Scheme --- p.33 / Chapter 5 --- Computational Accuracy and Efficiency Aspects of XFEM --- p.36 / Chapter 5.1 --- XFEM Scheme for Small Volume Fraction Element --- p.38 / Chapter 5.1.1 --- Problem Definition --- p.39 / Chapter 5.1.2 --- Numerical Example --- p.41 / Chapter 5.2 --- Stress Smoothing in XFEM --- p.46 / Chapter 5.3 --- XFEM Integral Scheme without Quadrature Sub-cells --- p.50 / Chapter 5.3.1 --- 2D XFEM Integral Scheme without Quadrature Sub-cells --- p.50 / Chapter 5.3.2 --- 3D XFEM Integral Scheme without Quadrature Sub-cells --- p.53 / Chapter 5.4 --- Higher Order Elements with XFEM Scheme --- p.55 / Chapter 5.4.1 --- Higher Order Elements --- p.55 / Chapter 5.4.2 --- Numerical Example --- p.57 / Chapter 6 --- Minimum Compliance Optimization using XFEM --- p.64 / Chapter 6.1 --- Level Set Formulation of the Optimization Problem --- p.64 / Chapter 6.2 --- Finite Element Analysis with XFEM --- p.65 / Chapter 6.3 --- Shape Sensitivity Analysis --- p.65 / Chapter 6.4 --- Numerical Examples --- p.68 / Chapter 6.4.1 --- A 2D Short Cantilever Beam --- p.68 / Chapter 6.4.2 --- A 3D Short Cantilever Beam --- p.75 / Chapter 6.4.3 --- A Michell-type Structure in 3D --- p.77 / Chapter 7 --- Stress-Constrained Topology Optimization using XFEM --- p.81 / Chapter 7.1 --- Shape Equilibrium Approach to Stress Constraint --- p.81 / Chapter 7.1.1 --- Problem Formulation of Stress-Constrained Topology Optimization --- p.81 / Chapter 7.1.2 --- Shape Equilibrium Constraint Approach --- p.82 / Chapter 7.1.3 --- Material Derivatives of Stress Constraint --- p.83 / Chapter 7.1.4 --- Shape Sensitivity Analysis --- p.85 / Chapter 7.2 --- Finite Element Analysis with XFEM --- p.87 / Chapter 7.3 --- Minimal Weight Design with Stress Constraint --- p.88 / Chapter 7.3.1 --- Problem Definition --- p.88 / Chapter 7.3.2 --- Numerical Example --- p.89 / Chapter 7.4 --- Stress Isolation design --- p.94 / Chapter 7.4.1 --- Problem Definition --- p.94 / Chapter 7.4.2 --- Shape Sensitivity Analysis --- p.95 / Chapter 7.4.3 --- Numerical Examples --- p.97 / Chapter 8 --- Conclusions and Future Works --- p.109 / Chapter 8.1 --- Conclusions --- p.109 / Chapter 8.2 --- Future Works --- p.110 / Chapter 8.2.1 --- Adaptive XFEM --- p.111 / Chapter 8.2.2 --- Extend Shape Equilibrium Constraint Approach to 3D --- p.112 / Chapter 8.2.3 --- Extend the Stress Isolation Design Method into Industrial Applications --- p.112 / Bibliography --- p.113

A finite element (FE) based level set method is proposed for structural topology optimization problems in this thesis. The level set method has become a popular tool for structural topology optimization in recent years because of its ability to describe smooth structure boundaries and handle topological changes. There are commonly two stages in the optimization process: the stress analysis stage and the boundary evolution stage. The first stage is usually performed with the finite element method (FEM) while the second is often realized by solving the level set equation with the finite difference method (FDM). The first motivation for developing the proposed method is the desire to unify the techniques of both stages within a uniform framework. In addition, there are many problems involving irregular design domains in practice, the FEM is more powerful than the FDM in dealing with these problems. This is the second motivation for this study. / Numerical examples are involved in this thesis to illustrate the reliability of the proposed method. Problems on both regular and irregular design domains are considered and different meshes are tested and compared. / Solving the level set equation with the standard Galerkin FEM might produce unstable results because of the hyperbolic characteristic of this equation. Therefore, the streamline diffusion finite element method (SDFEM), a stabilized method, is employed to solve the level set equation. In addition to the advantage of simplicity, this method generates a system of equations with a constant, symmetric, and positive defined coefficient matrix. Furthermore, this matrix can be diagonalized by virtue of the lumping technique in structural dynamics. This makes the cost in solving and storing quite low. It is more important that the lumped coefficient matrix may help to improve the stability under some circumstance. / The accuracy of the finite element based level set method (FELSM) is compared with that of the finite difference based level set method (FDLSM). The FELSM is a first-order accurate algorithm but we prove that its accuracy is enough for structural optimization problems considered in this study. Even higher-order accurate FDLSM schemes are used, the numerical results are still the same as those obtained by FELSM. It is also shown that if the Courant-Friedreichs-Lewy (CFL) number is large, the FELSM is more robust and accurate than FDLSM. / The reinitialization equation is also solved with the SDFEM and an extra diffusion term is added to improve the stability near the boundary. We propose a criterion to select the factor of the diffusion term. Due to numerical errors and the diffusion term, boundary will drift during the process of reinitialization. To constrain the boundary from moving, a Dirichlet boundary condition is enforced. Within the framework of FEM, this enforcement can be conveniently preformed with the Lagrangian multiplier method or the penalty method. / Velocity extension is discussed in this thesis. A natural extension method and a partial differential equation (PDE)-based extension method are introduced. Some related topics, such as the "ersatz" material approach and the recovery of stresses, are discussed as well. / Xing, Xianghua. / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0628. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 102-113). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese.

Engineers have utilized CAE technique as an analysis tool to refine the engineering design over decades. However, CAE alone is not the key to open the door for the final goal. In order to achieve the practical solution to the real-time engineering problem, we need to integrate CAD, CAE and optimization techniques into a single framework. / In the optimization algorithm part, apart from the general parametric steepest descent (ST) algorithm, we also study the least square (LSQ) based optimization algorithm. As a result, we can solve the problem arisen from the variant dimensional sizes of the different design variables by using the weighted sensitivity information. / In the problem of the structural optimizations, three categories of the approaches can be identified: size, shape and topology optimizations. For size optimization, explicit dimensions are usually chosen as the design variables, for example, the thickness of a beam or the diameter of a cylinder. For shape optimization, the shape related parameters of the geometrical boundary are always considered to be the design variables, like the positions of the control points for a Bezier curve. However, these two methods are lack of the capability to handle the topological changes of the geometry. On the contrary, topology optimization is the generalization of size and shape optimizations, which offers a more flexible and powerful tool to determine the best layout of the materials and the topology to the design problem, and it is becoming increasingly important in the conceptual design phase. In other words, topology optimization gives one the inspiration for the locations where we put holes to reach the best design. / In this thesis, we put forward the algebraic level set (ALS) model with the consideration of the constructive solid geometry (CSG) model so that it is consistent with half-space primitive concept in CSG. Based on general shape derivative, we propose the general shape design sensitivity analysis (SDSA) formulations for general geometric primitives that are represented implicitly, such as line and circle primitives in two-dimensional space and plane primitive in three-dimensional space. We then extend the relevant formulations into corresponding parametrically represented primitives as they are widely used in today's mainstream CAD systems. / The material density method and the boundary-variation method are the popular methods adopted in both academia and industrial community. Even though the former method is dominant in industry, the latter method is more preferable these years owing to its boundary description nature. Undoubtedly, the level set based method is the most promising technique of the boundary-variation type. Scientists successfully developed the optimization algorithms based on the level set method (LSM) in the past few years. With the implicit representation of the LSM, topological changes of the design can be handled easily and the geometrical complexity is then reserved. / The numerical examples for the design optimization problem are successfully implemented with both the implicit geometric representation (2D cases) and the parametric geometric representation (3D cases), which proves the feasibility of the proposed framework. The results show that both shape and topology optimizations of a design could be accomplished in a natural way. / The optimal result given by conventional topology optimization usually involves tedious post-processing to form CAD geometry. Using our parameterizations with basic primitives and the proposed optimization algorithms, we can deliver comparatively complicated shapes with rich topological information. Therefore, the detail design could be conducted directly later. / Zhang, Jiwei. / "December 2010." / Adviser: Yu Michael Wang. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 119-129). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Lui, Fung Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 83-92). / Abstracts in English and Chinese. / Acknowledgement --- p.iii / Abbreviation --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Related Work --- p.6 / Chapter 1.2.1 --- Parametric Optimization Method and Radial Basis Functions --- p.6 / Chapter 1.3 --- Contribution and Organization of the Dissertation --- p.7 / Chapter 2 --- Level Set Method for Structure Shape and Topology Optimization --- p.8 / Chapter 2.1 --- Primary Ideas of Shape and Topology Optimization --- p.8 / Chapter 2.2 --- Level Set models of implicit moving boundaries --- p.11 / Chapter 2.2.1 --- Representation of the Boundary via Level Set Method --- p.11 / Chapter 2.2.2 --- Hamilton-Jacobin Equations --- p.13 / Chapter 2.3 --- Numerical Techniques --- p.13 / Chapter 2.3.1 --- Sign-distance function --- p.14 / Chapter 2.3.2 --- Discrete Computational Scheme --- p.14 / Chapter 2.3.3 --- Level Set Surface Re-initialization --- p.16 / Chapter 2.3.4 --- Velocity Extension --- p.16 / Chapter 3 --- Structure Topology Optimization with Discrete Level Sets --- p.18 / Chapter 3.1 --- A Level Set Method for Structural Shape and Topology Optimization --- p.18 / Chapter 3.1.1 --- Problem Definition --- p.18 / Chapter 3.2 --- Shape Derivative: an Engineering-oriented Deduction --- p.21 / Chapter 3.2.1 --- Sensitivity Analysis --- p.23 / Chapter 3.2.2 --- Optimization Algorithm --- p.28 / Chapter 3.3 --- Limitations of Discrete Level Set Method --- p.30 / Chapter 4 --- RBF based Parametric Level Set Method --- p.32 / Chapter 4.1 --- Introduction --- p.32 / Chapter 4.2 --- Radial Basis Functions Modeling --- p.33 / Chapter 4.2.1 --- Inverse Multiquadric (IMQ) Radial Basis Functions --- p.38 / Chapter 4.3 --- Parameterized Level Set Method in Structure Topology Optimization --- p.39 / Chapter 4.4 --- Parametric Shape and Topology Structure Optimization Method with Radial Basis Functions --- p.42 / Chapter 4.4.1 --- Changing Coefficient Method --- p.43 / Chapter 4.4.2 --- Moving Knot Method --- p.45 / Chapter 4.4.3 --- Combination of Changing Coefficient and Moving Knot method --- p.46 / Chapter 4.5 --- Numerical Implementation --- p.48 / Chapter 4.5.1 --- Sensitivity Calculation --- p.48 / Chapter 4.5.2 --- Optimization Algorithms --- p.49 / Chapter 4.5.3 --- Numerical Examples --- p.52 / Chapter 4.6 --- Summary --- p.65 / Chapter 5 --- Conclusion and Future Work --- p.80 / Chapter 5.1 --- Conclusion --- p.80 / Chapter 5.2 --- Future Work --- p.81 / Bibliography --- p.83