بهينه سازي توپولوژي و شكل سازه هاي پيوسته غيرخطي با روش بهينه سازي تكاملي سازه ها

Optimization of form and topology of Nonlinear Continuous Structures Using Evolutionary Structural Optimization (ESO)

روش هاي بهينه سازي توپولوژي قادرند طرح هايي را با بهترين طرح سازه براي عملكردهاي سازه اي مورد نياز پيدا كنند. يكي از اين روش ها، بهينه سازي تكاملي سازه هاست. بهينه سازي ﺗﮑﺎﻣﻠﻲ سازه ها ﺑه معناي ﺣﺬﻑ ﻣﻮﺍﺩ ناﮐﺎﺭﺁﻣﺪ ﺍﺯ ﺳﺎﺯﻩ است به طوري كه ﻧﺘﺎﻳﺞ به دست آمده ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﺑﻪ ﺳﻤﺖ ﻃﺮﺡ ﺑﻬﻴﻦ ﭘﻴﺶ مي روند. بهينه سازي ﺗﮑﺎﻣﻠﯽ سازه ها ﺑﺎ ﺭﺍﻫﺒﺮﺩ دو جهتي ﺷﮑﻞ بهبوديافته ي ﺭﻭﺵ بهينه سازي تكاملي سازه ها ﺍﺳﺖ ﮐﻪ ﻋﻼﻭﻩ ﺑﺮ ﺣﺬﻑ ﺍﻟﻤﺎﻥ، قابليت ﺍﺿﺎﻓﻪ ﮐﺮﺩﻥ ﺍﻟﻤﺎﻥ ﺭﺍ ﻫﻢ ﺩﺍﺭﺩ. تاكنون ﻓﺮﺍﻳﻨﺪ ﺣﺬﻑ ﻭ ﺍﺿﺎﻓﻪ ﮐﺮﺩﻥ ﺍﻟﻤﺎﻥ ﺑﺎ روش هاي ﻣﺨﺘﻠﻒ ﻭ ﺑﺮﺍﻱ ﺍﻧﻮﺍﻉ ﻣﻌﻴﺎﺭﻫﺎﻱ بهينه سازي انجام شده ﺍﺳﺖ. در اين پژوهش مسئله بهينه سازي با معيار سفتي براي سازه هاي غيرخطي هندسي، غيرخطي وابسته به ماده و تركيب غيرخطي هندسي و مادي انجام شده است. براي اثبات صحت و كارايي الگوريتم، عمل بهينه سازي روي چند سازه در دو حالت خطي و غيرخطي انجام شده و نتيجه هاي به دست آمده با طرح هاي بهين پيشنهادشده با استفاده از روش هاي ديگر مقايسه شده است. شكل بهين در دو حالت خطي و غيرخطي به طور محسوسي متفاوت و براي تحليل غيرخطي نامتقارن به دست مي آيد. زمان اجراي برنامه در حالات غيرخطي بيشتر از حالت خطي است ولي با تحليل غيرخطي سازه ها يك طرح بهين با سفتي بيشتر به دست مي آيد. در ادامه به تحليل خطي و غيرخطي در بهينه سازي شكل سازه ها پرداخته شده است. هدف پيدا كردن بهترين شكل فيلت و حفره است به گونه اي كه تنش بيشينه به كمترين مقدار خود برسد. نتيجه ها نشان مي دهد كه بهينه سازي تكاملي سازه ها توانايي خوبي در بهينه سازي شكل فيلت ها در سازه هاي غيرخطي دارد.

Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient elements from the structure after each finite element analysis, so that the obtained design is gradually evolved to an optimum. The bidirectional evolutionary structural optimization (BESO) method is a new version of the ESO method in which simultaneous removing and adding elements is allowed. The procedures of removing and adding elements are performed using various criteria. Due to the importance of nonlinear structural analysis, in this study the BESO approach is used. The nonlinearity is assumed for the geometry, 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. The complementary work for the optimized shapes are compared. It is concluded that using BESO results in a more optimized shape. Optimized shapes for this case were obtained from linear and nonlinear analysis using BESO, and nonlinear analysis using Solid Isotropic Material, with Penalization for intermediate densities (SIMP). In the next example, 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. The nonlinear analysis with BESO also results in a stiffer design. Furthermore, the effectiveness of ESO is proved by applying them to some shape optimization problems. The aim is to find the best circular hole 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. 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. 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. Results show that ESO has a superior capability for shape optimization of holes in nonlinear structures, and in this case maximum stress is reduced by 28%.