تعيين مدل خرپايي بهينه براي نواحي كرنش آشفته‌ي بتن مسلح تحت بارگذاري چندگانه با استفاده از بهينه‌سازي توپولوژي

Determining Optimal Strut-and-Tie Model for Reinforced Concrete Disturbed Region under Multiple Load using Topology Optimization

بهينه‌سازي توپولوژي پيوسته از جديدترين روش‌هاي تعيين مدل خرپايي براي طراحي نواحي كرنش آشفته‌ي بتن مسلح است. در اين پژوهش، با استفاده از تابع هدف كمينه‌سازي مجموع انرژي كرنشي كشسان، راهكاري براي تعيين مدل خرپايي اعضا بتن مسلح تحت تركيب بار استاتيكي افقي و عمودي پيشنهاد شده است. براي بررسي كارايي روش پيشنهادي، دو مسيله‌ي عددي بررسي شده است. در مسيله‌ي اول با تحليل اجزا محدود غيرخطي به بررسي مدل‌هاي به ‌دست‌آمده با كسر حجمي متفاوت براي يك ديوار برشي تحت بار استاتيكي متقابل معكوس و در مسيله‌ي دوم با تعيين شرايط جديدي براي مدل خرپايي بهينه، به صورت كيفي به بررسي مدل‌هاي به دست‌آمده با شعاع فيلترينگ متفاوت براي يك كربل تحت تركيب بار استاتيكي افقي و عمودي پرداخته شده است. نتايج نشان مي‌دهد كه روش پيشنهادي زمان تحليل و طراحي را كاهش داده است و با انتخاب كسر حجمي و شعاع فيلترينگ مناسب مي‌توان مدل‌هاي بهينه‌تري به دست آورد.

In the last two decades, strut-and-tie model (STM) has been the most widely used method for design of reinforced concrete disturbed regions. Continuum topology optimization is the latest method for determining appropriate STM. This method does not have limitations of conventional methods. In this article, an efficient methodology is presented for development of STM for reinforced concrete members under multiple loading conditions. Solid isotropic material with penalization (SIMP) topology optimization algorithm is employed to minimize elastic strain energy of the models. In order to prevent checkerboard patterns and mesh dependency, the sensitivity filtering was applied and design variables were updated using the optimality criteria. Two numerical examples were used to investigate the effectiveness of the proposed methodology. The first example is a shear wall with asymmetric opening under reversed static loading. The ultimate load to steel weight ratio was used as the criteria to compare the models with different volume fractions. CAST software was used for analysis and design of models. Nonlinear Finite Element models were developed to obtain load-deflection curves for different models. In the second example, a new criterion was used to compare the STM of a corbel under horizontal and vertical static loads. Effects of different filtering radii were also investigated. The results of this example show that models obtained from topology optimization are efficient and require the minimal steel reinforcement when compared with conventional models. The results indicate that a volume fraction in the range of 0.35-0.45 leads to efficient and optimum models. A low filtering radius results in models with redundant members and a high filtering radius results in removal of members from model. It should be noted that using topology optimization under multiple loads also results in saving the CPU time for analysis and design.