| Author: | Zhang, Zixin |
| Title: | Development and application of isogeometric analysis and topology optimization for future structural design |
| Advisors: | Usmani, Asif Sohail (BEEE) |
| Degree: | Ph.D. |
| Year: | 2024 |
| Subject: | Isogeometric analysis Computer-aided design Structural design Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Building Environment and Energy Engineering |
| Pages: | xx, 181 pages : color illustrations |
| Language: | English |
| Abstract: | In the context of rapid development in construction technology, civil engineers have greater design freedom for pursuing efficient yet aesthetic structures. The conceptual design phase may often produce a complex structure and prove challenging for structural safety requiring multiple revisions and negotiations between the architect and structural engineer in order to obtain a practical, economical, and safe design. This thesis presents a framework to facilitate better communication between architects and structural engineers by establishing an isogeometric analysis and topology optimization platform that may also explicitly account for constructability constraints. Isogeometric analysis (IGA) is an emerging numerical approach for simulating the structural response, which aims at integrating Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) into a consistent mathematical expression. Benefiting from its precise boundary description and high-order continuity, IGA is recognized to have great application potential in various industrial scenarios. To explore the application value of IGA-based structural optimization for the construction industry, an isogeometric optimization approach of the post-tensioned concrete beam, a typical construction component, was developed. This approach uses NURBS curves for the geometric description and interpolation, which incorporates the SIMP method to generate the optimized topology and enables simultaneous optimization of prestress tendon shape and concrete beam topology for pursuing optimal structural performance. With a Drucker-Prager criterion, unequal tension and compression stress constraints are adopted for the use of concrete material. The isogeometric description of the concrete beam not only enhances the accuracy of stress calculation but also gives a simplified and straightforward prestress mapping scheme. To avoid the existence of slim components, a NURBS-based minimum width control approach is adopted in a consistent isogeometric framework. To standardize and continuously maintain the structural analysis and topology optimization process under the isogeometric framework, an integrated structural simulation tool shall be based on open-source software and facilitated by a specially developed tool to consider various construction demands. This includes an isogeometric analysis module in OpenSees for simulating the structural response, as well as a corresponding topology optimization package. In this thesis, the development of IGA module begins from the IGAQuad and IGABrick elements with NURBS-based shape functions and geometric descriptions in OpenSees, a widely used finite element modelling framework. The reliability and modelling capabilities of these IGA solid elements have been verified from the 2D and 3D benchmark problems. The isogeometric optimization package includes two classical topology optimization models that are the minimum compliance model with volume constraint and the minimum volume model with unequal stress constraint. The base of development and maintenance is the opensource and modular infrastructure of OpenSees and its extensive library of material models and solution methods that provides strong code support for pursuing the futural construction-oriented design. With the computational platform established, various construction considerations can be integrated. In the context of the still-developing construction printing technology, prefabrication technology is relatively more economical and reliable at the current stage. From the structural design perspective, periodic topology optimization addresses the prefabricability, regularity aesthetic, and assemblability, which fits the demands of the construction-oriented design. However, due to the strict geometric constraint, full periodic structure over-sacrifices structural performance like compliance. To trade-off the manufacturability of full-periodic structures with the high structural performance of free-form design, it is effective to combine the advantages of both by assembling the free-form and periodic components according to a rational scheme, which is called multi-pattern design. Herein, we proposed a new multi-pattern topology optimization method for allowing user-defined periodic groups between the individual unit-cells, several unit-cells are grouped with the same periodic configurations (type 1 to n) to find the possible designs between full-periodic and free-form structures. To automatically define a more beneficial scheme of the periodic group with a huge number of unit cells in case no preferred scheme, a new clustering-based multi-pattern selection approach is also proposed. It can be found that the multi-pattern design performs the merits of regularity from full-periodic design and efficient structural performance from free-form design, users can simply control the optimization tendency to determine the solution closer to free-form or periodic design. |
| Rights: | All rights reserved |
| Access: | open access |
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