نویسندگان
گروه مهندسی عمران، دانشکده مهندسی، دانشگاه صنعتی قوچان، قوچان
چکیده
استفاده از اعضای سازهای نامنشوری برای بهینه‌سازی هزینه و مقاومت در حال افزایش است. در شرایط یکسان، مقاطع اعضا در سازه‌های فولادی نازک‌تر از سازه‌های بتنی است، بنابراین تحلیل کمانشی در سازه‌های فولادی از اهمیت بیشتری برخوردار است. تعیین بار بحرانی ستون‌هایی که ممان اینرسی در طول آنها متغیر است با استفاده از روش تحلیلی، زمان زیادی از کاربر می‌گیرد. در این مقاله تحلیل کمانشی ستون‌های نامنشوری فولادی با ممان اینرسی متغیر در طول ستون با بهره‌جویی از روش بدون شبکه پتروف-گالرکین انجام شده است. در این روش نیازی به شبکه‌بندی مسئله نیست و با توزیع تعدادی گره به صورت منظم یا نامنظم، دامنه و مرزهای مسئله مشخص می‌شود. تغییرات ممان اینرسی در طول ستون با استفاده از یک تابع توانی با ضریب نامنشوری و توان متغیر مدل‌سازی شده است. برای گسسته‌سازی معادلات دیفرانسیل حاکم بر رفتار کمانشی ستون‌ها، از تابع درونیاب شعاعی و برای برقراری شرایط مرزی ستون از روش جریمه (پنالتی) استفاده شده است. مقایسه نتایج عددی روش پیشنهادی با نتایج روشهای تحلیلی نشان می‌دهد که روش بدون شبکه در محاسبه بار کمانشی ستون‌های نامنشوری، از دقت بسیار بالایی برخوردار است. در ادامه، به کمانش ستون‌های ماهیچه‌ای با بار محوری متغیر در طول ستون به‌عنوان یک نمونه ستون پرکاربرد در مهندسی عمران برای نشان دادن کارایی روش پیشنهادی پرداخته شده است. در پایان، اثر پارامترهای مختلف از جمله غیریکنواخت بودن بار و نحوه تغییرات تدریجی ممان اینرسی در طول ستون، روی بار کمانشی ستون بررسی شده است.
کلیدواژه‌ها
عنوان مقاله [English]
Buckling Analysis of Non-Prismatic Columns Subjected to Non-Uniform Loading Using the Meshless Local Petrov-Galerkin Method
نویسندگان [English]
- F. F. Heidargheitaghi
- M. H. M. H. Ghadiri Rad
- M. Kazemi
چکیده [English]
Continuously varying cross-section members have found wide applications in engineering for cost and resistance optimization. Since steel structures generally have more slender members compared to concrete structures, buckling analysis of steel members is of more importance. Determining the critical load of functionally varying cross-section columns using the analytical solution is a time-consuming process. In this paper, buckling analysis of non-prismatic steel columns is conducted using the meshless local Petrov-Galerkin (MLPG) method. In meshless methods, the scattered nodes are used rather than the elements to model the problem domain and its boundaries. The change of the inertia moment within the length of a column is characterized by introducing a power function with variable taper ratio and exponent. The radial basis function is used to discretize the differential equation governing the buckling. The penalty method is used for the imposition of the boundary conditions. Numerical examples of the critical buckling load for prismatic and non-prismatic columns using the proposed method are compared with the analytical solution, and the effectiveness of the MLPG method for buckling analysis of non-prismatic columns is validated. Also, buckling analysis of muscle column members subjected to non-uniform axial load is carried out to show the efficiency of the proposed method. The effect of several parameters such as non-uniformity of the load and variation of the cross-section on the buckling load of the column is discussed in details.
کلیدواژه‌ها [English]
- Non-Prismatic Columns
- Meshless Local Petrov-Galerkin (MLPG) Method
- Buckling
- Radial Basis Function
- Eigen-Value
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