اصلاح مدل بزرگ‌مقياس رانكين- هيل و الگوريتم حل آن براي تحليل غيرخطي ديوار‌هاي آجري

Modification to the Orthotropic Rankine-Hill Macro-Model and Proposed Algorithm to Accelerate the Nonlinear Analysis of Brick Walls

استفاده از مدل‌سازي بزرگ‌مقياس براي تحليل سازه‌هاي آجري با ابعاد و اندازه‌ي بزرگ اجتناب‌ناپذير است. در يك تحليل دقيق بزرگ‌مقياس سازه‌هاي آجري، ارايه‌ي مدلي كه مشخصات مصالح براي تمامي وضعيت‌هاي تنش را به دقت برآورد كند، بسيار حايز اهميت است، كه به‌دلايلي مانند عدم وجود نتايج آزمايشگاهي گسترده و پيچيدگي ذاتي فرمول‌بندي ناهمسان‌گرد رفتار غيركشسان، ارايه‌ي اين مدل با مشكلاتي همراه است. تعداد پژوهشگراني كه موفق شده‌اند مدل‌هاي بزرگ‌مقياس مناسبي براي تحليل سازه‌هاي آجري ارايه دهند كه در آن حالت كشساني ناهمسان‌گرد با رفتار ناهمسان‌گرد غيركشسان تركيب شده باشد، بسيار اندك است. در اين نوشتار، جزييات به‌كارگيري مدل بزرگ‌مقياس رانكين- هيل، كه براي پيشگيري از تكينه گي در به‌كارگيري منحني‌هاي تنش- كرنش معادل در كشش و فشار اصلاح شده است، با ارايه‌ي الگوريتم و برنامه‌ي روش حل سريع به منظور استفاده در تحليل غيرخطي سازه‌هاي آجري تهيه و ارايه شده است.

In order to analyze masonry structures with a large number of unit walls and joints, application of macro-modeling is compulsory for nonlinear analysis. An accurate nonlinear analysis of masonry structures from a macro-modeling perspective requires a material description for all stress states of behavior. Due to the lack of comprehensive experimental results corresponding to pre-peak and post-peak behavior, and the intrinsic complexity of formulating anisotropic in the inelastic behavior of masonry structures, there are special difficulties in the nonlinear analysis of such structural systems and/or components. The complex behavior of masonry is due to the effect of anisotropy, which arises from the geometrical arrangement of units and mortar; even the properties of these constituents are isotropic. The relatively complex yield surfaces proposed by many authors almost preclude the use of modern plasticity concepts and an accurate representation of inelastic behavior such as the hardening and softening rule. Only a few authors have tried to develop specific macro-models for the non-linear analysis of masonry structures, in which, anisotropic elasticity is combined with anisotropic inelastic behavior. In order to model such orthotropic material behavior, the standard multi-surface plasticity model was developed with Rankine yield criterion for tension and Hill yield criterion for compression, which was presented by Lourenço. The advantages of a combined yield surface, together with modern plasticity concepts, are strong representations of the behavior of anisotropic, which encompasses various softening/hardening behaviors parallel to the axis of the material. In this paper, formulation and implementation of the method used for the Rankine-Hill model are detailed in the plane-stress numerical code with two major promotions. In the first, the expedited method for nonlinear analysis in localized solutions (return-mapping algorithm) are described for this model, and in the second, for the prevention of numerical singularity, the equivalent stress-strain curvatures are modified using the exponential formulation in tension and compression states. Prototype models were studied for monitoring and verifying the numerical results of the software code with the experimental results of brick walls.