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تحليل پلاستيك قاب‌ها با استفاده از تئوري گراف‌ها

كارشناسي ارشد

مهندسي عمران- مهندسي سازه

1399

1402/6/11

علي كاوه

مهندسي عمران

در اين پايان نامه مباني تئوري گراف‌ها شرح داده شده است. سپس مباني و روش هاي تحليل پلاستيك به همراه تاريخچه تحليل پلاستيك بيان شده است. در ادامه روش ماتريسي تحليل پلاستيك قاب‌هاي مسطح،با استفاده از تئوري گراف‌ها برمبناي قضيه ايمن ذكر شده و شيوه تشكيل ماتريس هاي سازه‌اي و تركيب آنها جهت تشكيل ماتريس ضرايب و نيز كاربرد روش برنامه ريزي رياضي براي حل اين مسائل بيان شده است. همچنين روش توليد پايه سيكلهاي كمينه و تاثير آنها در روند حل مسائل مورد بررسي قرار گرفته است و در ادامه با استفاده از كد كامپيوتري نوشته شده در محيط برنامه MATLAB، چند مثال با شرايط هندسي و تكيه‌گاهي مختلف، با استفاده از روشهاي فوق حل شده و تاثير استفاده از پايه سيكلهاي كمينه و شبه كمينه در تعدادي از اين مثال ها درمقايسه با حالتي كه از سيكلهاي پايه تصادفي غيركمينه استفاده شده بود، مقايسه و بررسي شده‌است.

1402/10/03

Plastic analysis of frame structures using theory of graphs

9/1/2024 12:00:00 AM

In this thesis, optimal plastic analysis and design of frames is investigated using the combinatorial force method. For this purpose, the graph theoretical methods are employed for improving the sparsity of the flexibility matrices of the structures. The main aim of this thesis is to optimize the plastic analysis and design of planar frame structures using the theory of graphs utilizing minimal cycle basis corresponding to sparse flexibility matrices. For this purpose, first, the concepts and definitions of graph theory are presented, and then a number of matrices associated with graphs have been introduced. Then the force method for the plastic analysis and design of frame structures is described. In the process of optimal plastic analysis and design of frames, flexibility matrices with special properties are needed, which is being called well-structured matrices. These types of matrices reduce the computational time needed to perform analysis and design problems, while increasing the accuracy of the solution. The points necessary for this should be recognized and applied before the formation of flexibility matrices. This is done by forming cycles with special characteristics in the graph equivalent to the structural model. For this purpose, the effective factors in the formation of good matrices and the necessary methods for this work in the process of plastic analysis and design of frames are all mentioned in a practical way along with related examples. Then, some examples with different geometry, loading and support conditions have been solved using MATLAB code to show the effectiveness of the presented method. Finally, the results showed that the use of minimal cycle bases compared to fundamental cycles bases will significantly increase the sparsity of the flexibility matrices and reduce the computational time required for the plastic analysis and design of the frame structures.

تحليل پلاستيك , تحليل بهينه , طراحي پلاستيك , تئوري گراف‌ها , قضيه ايمن , برنامه‌ريزي خطي رياضي , روش نيرو

Plastic Analysis , Optimal Analysis , plastic design , Graph theory , Safe theorem , Linear programming , Force method

Abdolrahman Hosseini

Dr. Ali Kave