Application of Principal Stress Lines on Structural Optimization Design

• Main Authors: Meng-Sheng Chien, 簡孟笙
• Other Authors: 呂良正
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/38aj8u

碩士 === 國立臺灣大學 === 土木工程學研究所 === 107 === Shell structures are widely used in structure design due to the benefit of their load-carrying capacity. However, considering the large-span shells failure region, the issues of designing reinforcement for the thin shell or supporting structure optimally for the grid shell are coming to be essential to be sorted out. Therefore, this thesis focuses on using principal lines generation techniques to stiffen the large span shell structures, model the grid shell structures and integrates with free-form surface based on optimization theory to obtain a final design considering both aesthetics and mechanical behaviors. In this thesis, we suggest a computational algorithm to design and optimize ribs layout on given design domain to enhance the global structural and mechanical performance. The core concept of our method is to place ribs along the principal stress lines which demonstrate the paths of stress flow. Based on certain surface and external loads, Finite Element Analysis can be performed and solve the physical field numerically. With the post-processing from FEM results, directional vector field of principal stress on nodes can be obtained by eigenvalue calculation. We use the ideal of particle trajectories to generate the principal stress lines by numerical integration. Discussion of sensitivity, orthogonality, accuracy and other property of principal stress lines are all considered in this research. Besides ribs layouts, shape optimization and sizing optimization are also the major parts and typical types of structural optimization. Our thesis using NURBS, which is a parametric method to approach the free-form surface, to construct and control our design domain. This method contains geometric tuning factors, such as control points, knots factors, etc. that gives user a great flexibility to handle the shape analytically. In the both shape and sizing optimization problems, sequential quadratic programming(SQP) is chosen as the optimization method to find the final design. In our implementation, Demonstration of principal stress lines on shell structures are separated into two parts. Firstly, ribs play a reinforced role in the shell structure which can improve the overall structural performance and deflection. Secondly, some famous real grid shell structures are taken as examples and utilized as the initial models of optimization problems. After acquiring the optimal results, switch the grid with ribs along the stress flow to achieve better static performances. Mentioning about designing the real grid shell structure, some factors that may influence the shell structure must be considered, such as load cases, structural strength, maximum displacement, etc. Self-weight, live load and wind load are often considered as the essential load cases. Computational fluid dynamic (CFD) analysis will be used to attain the wind pressure among the complex shape of shell surface. After solving by CFD analysis, and then mapping as a distribution of wind pressure to the surface of shell structures. Furthermore, the constraints of optimization problems are defined by Taiwan construction specifications and limit conditions specified in the codes, such as limitation of strength and displacement. Through these considerations to real grid shell structure design, engineers and architects can get more practical optimal result as reference. This research develops Python program to control the finite element analysis commercial software ABAQUS. With the analysis results from ABAQUS, the program can carry out the optimization analysis and find the final optimal results. The Python program allows users to create free-form surface by previous parametric NURBS method and generate the principal stress lines by our numerical method.