تحلیل قاب‌های صفحه‌ای دوبُعدی با روش تحلیلی ترکیب نیرو- جابجایی

نوع مقاله : پژوهشی

نویسندگان

دانشکده‌ی مهندسی و فناوری، دانشگاه مازندران، مازندران.

چکیده

در پژوهش حاضر به ‌بررسی کارایی یک روش پیشنهادی برای حل قاب‌های صفحه‌ای نامعین پرداخته شده است، که از ترکیب روابط نیرو و جابجایی براساس رفتار تغییرشکل محوری و خمشی تیر به طور هم‌زمان بهره می‌برد. در روش پیشنهادی، ابتدا معادله‌های دیفرانسیلی اعضاء سازه‌ای براساس تئوری کلی تیر اویلر- برنولی با درنظرگرفتن آثار محوری تعیین شده و سپس با کمک حل تحلیلی و اعمال شرایط مرزی، ثابت‌های انتگرالی معادله‌های مرتبط با قاب‌ها به‌دست آمده‌اند. برای میزان کارآیی روش پیشنهادی، سه مثال از قاب‌های صفحه‌ای متداول تحلیل و با کمک روش اجزاء محدود اعتبارسنجی انجام شده‌اند. نتایج نشان داده‌اند که پاسخ‌های تعیین‌شده از دو روش مذکور، تطابق خوبی دارند. از مزیت‌های روش ترکیبی نیرو- جابجایی، تعیین حل پارامتریک و همچنین قابلیت دستیابی به پاسخ‌ها در هر نقطه‌ی دلخواه از سازه با دقت بالاست.. علاوه‌بر آن، برای یافتن کمیت پاسخ سینماتیکی و استاتیکی نیازی به پس‌پردازش ندارد.  لذا روش ترکیبی نیرو- جابجایی می‌تواند به‌عنوان یک رویکرد جایگزینی برای روش‌های رایج در حل قاب‌های صفحه‌ای چندمحوری استفاده شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of Plane Multi-Span Frames with the Analytical Method of Force-Displacement Combination

نویسندگان [English]

  • Amirhosein Bahreini
  • Ali Asgari
  • Alireza Khabiri
  • Reza Taghipour
Faculty of Engineering and Technology, University of Mazandaran, Mazandaran, Iran.
چکیده [English]

This paper investigates the effectiveness of the mixed forced-displacement method for solving indeterminate plane frames that combine force and displacement relations based on the beam’s axial and bending deformation behavior simultaneously. In this method, the differential equations of all structural members are determined based on the general theory of the Bernoulli beam by considering the axial effects. In the following, with the help of an analytical solution and application of boundary conditions, the integral constants of the equations related to the uniaxial frames of the structure are obtained. For the effectiveness of the proposed method, three examples of common frames have been analyzed and validated with the finite element method. The results show that the answers determined by the two methods are completely consistent. One of the advantages of the combined displacement-force method is determining the parametric solution as well as the high accuracy of this method. In addition, it does not need post-processing to find the quantity of kinematic and static responses. Therefore, this method can be used as an alternative approach to the finite element method in solving multi-axial plane frames. Moreover, its capability to handle intricate loading and various boundary condition configurations highlights the method's efficiency. Furthermore, the method simplifies the simultaneous influences of material and geometric nonlinearities in the analysis process. Material nonlinearities, such as yielding and hardening, are accommodated by adjusting the stiffness matrix. In contrast, geometric nonlinearities arising from significant displacements are addressed through iterative updates of the displacement field until convergence is achieved. In summary, the mixed displacement-force method is a comprehensive and efficient tool for 2D frame analysis. The ability to provide accurate results without the need for complex numerical simulations increases the importance of this method in the range of structural analysis techniques. Future research efforts could examine developing the process to three-dimensional frames and investigating its application in the performance-based design and analysis areas.

کلیدواژه‌ها [English]

  • Plane frames
  • indeterminate structures
  • mixed force-displacement method
  • Euler–Bernoulli beam equation
  • analytical method

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