حل تحلیلی کمانش ورق‌های قطاعی حلقوی متخلخل

کامران فرد, محمدرضا; سعیدی, علیرضا; نادری, ابوصالح

حل تحلیلی کمانش ورق‌های قطاعی حلقوی متخلخل

نویسندگان

¹ دانشکده مهندسی مکانیک دانشگاه شهید باهنر کرمان

² دانشکده مهندسی مکانیک مجتمع آموزش عالی بم

چکیده

در این مقاله، یک حل تحلیلی برای کمانش ورقهای قطاعی حلقوی متخلخل ارائه شده است. ابتدا معادلات تعادل و شرایط مرزی ورق، طبق فرضیات تئوری برشی مرتبه اول ورق و با استفاده از اصل حداقل انرژی پتانسیل بهدست آمدهاند. سپس معادلات پایداری ورق برحسب جابجایی‌های بسیار کوچک و با استفاده از معیار تعادل همسایگی استخراج شدهاند. بهدلیل وابستگی شدید در معادلات دیفرانسیل پایداری حاصله، ارائه حل تحلیلی برای آنها به آسانی امکانپذیر نیست. از این رو، با تعریف چهار تابع کمکی و انجام یکسری عملیات ریاضی، معادلات بههم وابسته پایداری از هم جدا شده و به دو معادله دیفرانسیل مستقل از هم تبدیل شدهاند. پس از حل این معادلات مستقل، با درنظر گرفتن شرایط مرزی تکیهگاه ساده در لبههای شعاعی و شرایط مرزی دلخواه در لبه‌های محیطی بار بحرانی کمانش محاسبه شده است. در بخش نتایج عددی، تأثیر پارامترهای مختلف هندسی نظیر زاویه قطاع، ضخامت و شعاع داخلی ورق، همچنین تأثیر میزان تخلخل ورق بر بار بحرانی کمانش آن بهازای شرایط مرزی دلخواه روی لبههای محیطی مورد بررسی قرار گرفته است. نتایج حاصلشده نشان میدهد که اثر افزایش میزان تخلخل موجود در ورق در کاهش بار بحرانی کمانش، بهمراتب کمتر از اثر پارامترهای هندسی و شرایط مرزی است.

کلیدواژه‌ها

20.1001.1.26455323.1398.15.1.11.8

عنوان مقاله [English]

Analytical Solution for Buckling of Annular Sectorial Porous Plates

نویسندگان [English]

M K ¹
A S ¹
A N ²

چکیده [English]

In this article, an analytical solution for buckling of annular sectorial porous plates, is presented. At first, based on first order shear deformation plate theory, the governing equilibrium equations and boundary conditions are obtained using minimum total potential energy principle. Then, the stability equations of the plate, are derived in terms of infinitesimal displacements using adjacent equilibrium criterion. Since these equations are highly coupled, it is so difficult to find an analytical solution for them. So, by introducing four auxiliary functions and doing some mathematical manipulations, the stability equations are decoupled and converted to two independent differential equation which can be solved analytically. For this purpose, it has been assumed the simply supported boundary conditions for the radial edges and desired boundary conditions for the circumferential edges of the plate. Finally, the critical buckling load has been calculated for different conditions of the plate. In section of numerical results, the effect of different geometrical parameters, such as sector angle, thickness and inner radius of the plate, also effect of porosity of the plate upon the critical buckling load has been studied for different arbitrary boundary conditions on circumferential edges. The result show that the effect of increase in porosity of the plate upon decrease of the critical buckling load is significantly fewer than the effect of geometrical parameters and the boundary conditions.

کلیدواژه‌ها [English]

Buckling
Annular Sectorial Plate
First order Shear Deformation Plate Theory
Adjacent Equilibrium Criterion
Porosity

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