بهینه‌سازی توپولوژی و شکل سازه‌های پیوسته غیرخطی با روش بهینه‌سازی تکاملی سازه‌ها

نویسندگان
یاسر علوی نیا 1
محمد حسین ابوالبشری 2
1 دانش آموخته کارشناسی ارشد
2 گروه مکانیک، دانشگاه فردوسی مشهد
چکیده
روش‌های بهینه‌سازی توپولوژی قادرند طرح‌هایی را با بهترین طرح سازه برای عملکردهای سازه‌ای مورد نیاز پیدا کنند. یکی از این روش‌ها، بهینه‌سازی تکاملی سازه‌هاست. بهینه‌سازی ﺗﮑﺎﻣﻠﻲ سازه‌ها ﺑه معنای ﺣﺬﻑ ﻣﻮﺍﺩ ناﮐﺎﺭﺁﻣﺪ ﺍﺯ ﺳﺎﺯﻩ است به طوری که ﻧﺘﺎﻳﺞ به دست آمده ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﺑﻪ ﺳﻤﺖ ﻃﺮﺡ ﺑﻬﻴﻦ ﭘﻴﺶ می‌روند. بهینه‌سازی ﺗﮑﺎﻣﻠﯽ سازه‌ها ﺑﺎ ﺭﺍﻫﺒﺮﺩ دو جهتی ﺷﮑﻞ بهبودیافته‌ی ﺭﻭﺵ بهینه‌سازی تکاملی سازه‌ها ﺍﺳﺖ ﮐﻪ ﻋﻼﻭﻩ ﺑﺮ ﺣﺬﻑ ﺍﻟﻤﺎﻥ، قابلیت ﺍﺿﺎﻓﻪ ﮐﺮﺩﻥ ﺍﻟﻤﺎﻥ ﺭﺍ ﻫﻢ ﺩﺍﺭﺩ. تاکنون ﻓﺮﺍﻳﻨﺪ ﺣﺬﻑ ﻭ ﺍﺿﺎﻓﻪ ﮐﺮﺩﻥ ﺍﻟﻤﺎﻥ ﺑﺎ روش‌های ﻣﺨﺘﻠﻒ ﻭ ﺑﺮﺍﻱ ﺍﻧﻮﺍﻉ ﻣﻌﻴﺎﺭﻫﺎﻱ بهینه‌سازی انجام‌شده ﺍﺳﺖ. در این پژوهش مسئله بهینه‌سازی با معیار سفتی برای سازه‌های غیرخطی هندسی، غیرخطی وابسته به ماده و ترکیب غیرخطی هندسی و مادی انجام‌شده است. برای اثبات صحت و کارایی الگوریتم، عمل بهینه‌سازی روی چند سازه در دو حالت خطی و غیرخطی انجام‌شده و نتیجه‌های به دست آمده با طرح‌های بهین پیشنهادشده با استفاده از روش‌های دیگر مقایسه شده است. شکل بهین در دو حالت خطی و غیرخطی به طور محسوسی متفاوت و برای تحلیل غیرخطی نامتقارن به دست می‌آید. زمان اجرای برنامه در حالات غیرخطی بیشتر از حالت خطی است ولی با تحلیل غیرخطی سازه‌ها یک طرح بهین با سفتی بیشتر به دست می‌آید. در ادامه به تحلیل خطی و غیرخطی در بهینه‌سازی شکل سازه‌ها پرداخته‌شده است. هدف پیدا کردن بهترین شکل فیلت و حفره است به گونه‌ای که تنش بیشینه به کمترین مقدار خود برسد. نتیجه‌ها نشان می‌دهد که بهینه‌سازی تکاملی سازه‌ها توانایی خوبی در بهینه‌سازی شکل فیلت‌ها در سازه‌های غیرخطی دارد.

کلیدواژه‌ها

عنوان مقاله English

Optimization of Nonlinear Structures Using Evolutionary Structural Optimization (ESO)

نویسنده English

Mohammad Hossein Abolbashari 2
2 Mechanical Engineering Department
چکیده English

Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. The bidirectional evolutionary structural optimization (BESO) method is a new version of the ESO method in which simultaneously removing and adding elements is allowed. Due to the importance of nonlinear structural analysis, in this study the BESO approach is used for nonlinear analysis of structures. The problems nonlinearity is assumed for the geometry, for the material, and for both geometry and material. In the first example, the BESO is applied to maximize the stiffness of a cantilever beam with a time dependent loading. Next, the BESO is applied to optimize the stiffness of a plate with the material nonlinearity. The results show that the nonlinear analysis leads to a much stiffer design. In the third example, a cantilever beam with both material and geometry nonlinearity is considered. The beam is also to be optimized for stiffness. The optimized shapes are compared for linear and nonlinear analysis against the SIMP.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.

کلیدواژه‌ها English

Evolutionary structural optimization
Nonlinear Analysis
shape optimization
Stiffness Maximization
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مهندسی عمران مدرس
دوره 17، شماره 1
خرداد و تیر 1396
صفحه 157-167