عنوان مقاله
کمانش و فراکمانش حرارتی تیرهای اویلر برنولی تثبیت شده مفصلی روی فونداسیون الاستیک
فهرست مطالب
چکیده
مقدمه
فرمولهای ریاضی
روش عددی و نتایج آن
نتیجه گیری
بخشی از مقاله
روش عددی و نتایج آن
یافتن هرگونه را حل تحلیلی برای مسئله پیچیده حد مرزی (1) - (4) به علت شمول غیر خطی قوی و مسئله مزدوج سازی داخل آن کار مشکلی است، لذا برای یافتن راه حل های عددی مسئله از روش پاشش استفاده می شود. ایده حمایت کننده از روشshooting عبارت است از جایگزینی مسئله ارزش مرزی دو نقطه با یک سری مسائل ارزش اولیه. لذا مقادیر نامعلوم توابع نامعلوم در نقطه شروع اساسا بر آورد میشوند تا روش محاسبه شروع شود.
کلمات کلیدی:
Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation Xi Song, Shi-Rong Li * Department of Engineering Mechanics, Lanzhou University of Technology, Lanzhou, Gansu 730050, PR China Available online 27 June 2006 Abstract In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the postbuckling temperature compared with the linear one. 2006 Elsevier Ltd. All rights reserved. Keywords: Beam; Elastic foundation; Thermal buckling; Mode transition; Numerical results 1. Introduction Thermal buckling may be an undesired phenomenon in many structures such as railroad tracks, pipelines, and concrete roads. Some cases cannot be avoided under special conditions. So, in recent years, many researchers have paid close attention to finding the regularity of thermal buckling to ensure the safety of structures. A number of papers on thermal buckling of beams have been published in recent years. Jekot (1996) examined the thermal post-buckling of a beam made of physically non-linear thermo-elastic material, in which he considered a simplified form of axial strain rather than the geometric non-linearity of the curvature of deformed central axis. By accurately considering the formulation of the axial strain and the curvature, Coffin and Bloom (1999) first presented an elliptic integral solution for the symmetric post-buckling response of alinear-elastic and hygrothermal rod with two ends pinned. However, a numerical solution to two coupled elliptical equations is necessary for the final post-buckling solution. Assuming that thermal strain temperature is non-linear, Vaz and Solano (2003a,b) also examined thermal post-buckling of rods and came up with a closedform solution via uncoupled elliptical integrals. But, due to the limit of the elliptical integral to the boundary conditions, only the case of pinned–pinned ends was considered. In the light of the exact non-linear geometric theory, Li and Cheng (2000), Li et al. (2002) and Li and Xi (2006) presented accurate mathematical formulations for post-buckling of Euler–Bernoulli beams and Timoshenko beams with different boundary conditions. When a static increasing temperature was applied the strongly non-linear differential equations with various boundary conditions were solved numerically by using a shooting method. The strongly non-linear differential equations with various boundary conditions were solved numerically by using the shooting method. Raju and Rao (1993), Rao and Raju (2002) and Rao and Neetha (2002) did a series of investigations on thermal postbuckling of uniform columns as well as tapered columns by Raleigh–Ritz method, finite element method and intuitive method. The effects of elastic foundation parameter on the critical temperature and post-buckling temperature rise were also considered, but they did not take into account the non-linearity of the curvature of the deformed central axis
