نویسنده
گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه ایلام
چکیده
در این مقاله کمانش استاتیکی تیرهای همگن پوشیده شده با لایه تشکیل شده از مواد مدرج تابعی متخلخل، با شرایط مرزی مختلف بر اساس تئوری تیر تیموشنکو بررسی شده است. از اصل کار مجازی برای به دست آوردن روابط حاکم بر مسئله استفاده شده است و سپس دو روش حل تحلیلی دقیق و حل عددی برای به دست آوردن نیروی کمانش و حل روابط مورد استفاده قرار گرقته‌اند. روابط حاکم به صورت یک سری رابطه دیفرانسیل معمولی جفت شده هستند. در حل تحلیلی ابتدا این روابط با استفاده از یک سری عملیات ریاضی جدا می‌شوند و سپس حل می‌شوند. حل به دست آمده دارای یک سری پارامترها و ثابت‌های مجهول است. با استفاده از روابط شرایط مرزی در دو انتهای تیر یک دستگاه رابطه همگن استخراج می‌شود که از رویه حل نابدیهی آن، مقدار نیروی کمانش محوری تیر به دست می‌آید. در حل عددی از روش مربعات دیفرانسیلی تعمیم یافته برای حل روابط استاتیکی استفاده شده است. در پایان، نتایج عددی ارائه شده است و تأثیر پارامترهای مختلف از جمله نسبت ضخامت به طول تیر، ضخامت لایه متخلخل، مقدار پارامتر تخلخل بر روی میزان نیروی کمانش مطالعه شده است. مقایسه نتایج به دست آمده از دو روش حل تحلیلی و عددی، صحت و اعتبار هر دو روش را تایید می‌کند.
کلیدواژه‌ها
عنوان مقاله [English]
Analytical and Numerical Study on the Buckling of Homogeneous Beams Coated by a Functionally Graded Porous Layer with Different Boundary Conditions
نویسنده [English]
- H. Salehipour
چکیده [English]
In this paper, static buckling of homogeneous beams coated by a functionally graded porous layer with different boundary conditions is investigated based on the Timoshenko beam theory. The principle of virtual work has been used to obtain the governing equations. Two different methods, namely analyticalsolution and numerical solution are used to solve the governing equations and extract the buckling force. The governing equations are coupled as a series of ordinary differential equations. In the analytical solution, these equations are first uncoupled using a series of mathematical operations, and are then solved. The obtained solution has a series of parameters and unknown constants. Using the boundary conditions at the boundaries of the beam, a homogeneous system of equations is extracted, from which the axial buckling force is obtained. In the numerical solution, the generalized differential quadrature method is used to solve the static equations. Finally, the numerical results are presented and the effects of various parameters such as thickness to beam length ratio, porous layer thickness, porosity parameter, etc. on the buckling of the beam are investigated. Comparison of the results obtained from the two analytical and numerical solution methods confirms the accuracy and validity of both methods.
کلیدواژه‌ها [English]
- Static buckling
- Timoshenko beam
- Functionally graded porous material
- Exact analytical solution
- Generalized differential quadrature method
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