Mastan Abadi, M., Alijani, A., Darvizeh, A., Mottaghian, F. (2016). Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 8(4), 295-309.
M. Mastan Abadi; A. Alijani; A. Darvizeh; F. Mottaghian. "Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model". Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 8, 4, 2016, 295-309.
Mastan Abadi, M., Alijani, A., Darvizeh, A., Mottaghian, F. (2016). 'Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model', Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 8(4), pp. 295-309.
Mastan Abadi, M., Alijani, A., Darvizeh, A., Mottaghian, F. Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2016; 8(4): 295-309.
Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model
1MSc Student, Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran
2Assistant Prof., Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
3Professor, Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
4MSc Student, Department of Mechanical Engineering, University of Guilan, Rasht, Iran
Abstract
In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using the Dirac’s delta function. In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams
مدلسازی ناپیوستگی تیرها با دو تحلیل فرم قوی و ضعیف به کمک مدل فنر پیچشی
Authors [Persian]
مصطفی مستان آبادی, علی علی جانی, ابوالفضل درویزه, فاطمه متقیان
Abstract [Persian]
در این مقاله ناپیوستگی در تیرها با استفاده از یک فنر پیچشی مدلسازی می‌شود که شدت این ناپیوستگی توسط میزان سفتی فنر تنظیم می‌گردد. با دو تحلیل فرم قوی و ضعیف به ترتیب معادله دیفرانسیل حاکم اصلاح شده و ماتریس سفتی سازه بهبود یافته برای تیرهای ناپیوسته استخراج می‌شوند. در فرم قوی، با در نظرگرفتن تئوری تیر اویلر-برنولی و تیموشنکو و با استفاده از دو روش تحلیل متفاوت، تاثیر تغییر شکل برشی در تیرهای دارای ناپیوستگی ارائه شده است. در این فرم، سفتی خمشی تیر ناپیوسته به کمک تابع دلتای دیراک اصلاح می‌شود. در فرم ضعیف، ماتریس سفتی کاهش یافته از درون معادله انرژی کرنشی استخراج که این معادله نیز به کمک سه معادله پیوستگی، سینماتیک و ساختاری ساخته می‌شود. فرض خطی بودن هندسه و ماده به ترتیب برای تشکیل معادلات سینماتیک و ساختاری در نظر گرفته شده است. در این فرم، شرایط پیوستگی دو بخش گسسته شده‌ی تیر اویلر-برنولی را به یکدیگر مربوط می‌کند که در آن یک تابع شکل هرمیتی بهبود یافته برای درونیابی میدان جابجایی بکار گرفته می‌شود. یک مثال کاربردی، مقایسه و صحت سنجی جواب‌های دو فرم قوی و ضعیف و همچنین رفتار استاتیکی تیر ناپیوسته را نشان می‌دهد
Keywords [Persian]
ناپیوستگی، تیر، فرم‌های قوی و ضعیف، تئوری‌های اویلر- برنولی و تیموشنکو
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