ارزیابی عددی روش انرژی اصلاح‌شده در تحلیل مسائل سازه‌ای با هندسه غیرخطی

نوع مقاله : علمی - پژوهشی

نویسندگان

1 دانشجوی دکتری سازه، گروه عمران، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران

2 استادیار، گروه عمران، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

در بسیاری از مسائل سازه‌ای مانند تعیین بار خرابی و همچنین تحلیل مکانیزم کمانش باید از تحلیلی‌های غیرخطی هندسی بهره گرفت. بااین‌وجود، به علت ماهیت پیچیده این نوع از مسائل و عدم وجود یک راه‌حل تحلیلی جامع برای آن‌ها در عمل از روش‌های عددی برای تقریب پاسخ دقیق مسئله استفاده می‌گردد. از مشکلات روش‌های عددی نیز عدم همگرایی و یا یافتن مسیر صحیح تعادل خصوصاً در مواجه با نقاط انشعابی است. ازاین‌رو هدف از این تحقیق، به‌کارگیری روش انرژی اصلاح‌شده (که در دینامیک سازه‌ها معرفی شده است) در مسائل شبه-استاتیک با هندسه غیرخطی و دارای نقاط انشعابی است تا بتوان کارایی این روش را در مقایسه با سایر روش‌های موجود نظیر تکنیک‌های عددی نیوتنی و همچنین نیرو-تغییرمکان-قید موردبررسی قرار داد. برای رسیدن به اهداف این تحقیق، پس از مرور کوتاه بر روی روش‌های تحلیلی نیرو-مبنا موجود در عمل، روش انرژی برای این نوع از مسائل تشریح شده و در ادامه مراحل اجرای کامپیوتری آن در غالب یک روند گام‌به‌گام تشریح می‌گردد. سپس با کدنویسی در نرم‌افزار متلب و به‌کارگیری روش مذکور بر روی مثال‌های عددی به کار گرفته‌شده توسط دیگر محققین نظیر سازه‌های خرپایی و قابی، پاسخ‌های به‌دست‌آمده با حل تحلیلی و همچنین نتایج دیگر روش‌ها مانند نیوتن-رافسون و طول قوس مورد صحت سنجی واقع شده‌اند. درمجموع، تفسیر نتایج به‌دست‌آمده از شبیه‌سازی‌های عملی صورت گرفته بیانگر این موضوع بوده‌اند که روش عددی معرفی‌شده در تحلیل مسائل با غیرخطی هندسی دارای دقت بهتری در مقایسه با روش طول قوس بوده و همچنین نسبت روش نیوتن-رافسون نیز به‌خوبی می‌تواند از نقاط انشعابی در منحنی بار-تغییرمکان بدون واگرایی عبور کند.

کلیدواژه‌ها


عنوان مقاله [English]

Developing and Investigation the Numerical Efficiency of Modified Energy Method in Solid Mechanics With Geometric Nonlinearity and Bifurcation Points

نویسندگان [English]

  • Ahmad Razaghi 1
  • Jafar Asgari Marnani 2
  • Mohammad Sadegh Rohanimanesh 2
1 Ph.D. student, Department of Civil Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 Assistant professor, Department of Civil Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
چکیده [English]

Geometric nonlinear analyses are used in many structural problems, such as the determination of failure load, as well as the study of buckling mechanism. Nevertheless, due to the complex nature of this type of problems and the absence of a comprehensive analytical solution for them, numerical methods are utilized in practice to approximate the exact response of these systems. In the application of numerical methods, there are also some difficulties such as divergence or finding the correct path of equilibrium, especially in the case of bifurcation points. Hence, the main purpose of this research is to apply the modified energy method (introduced in the dynamics of structures) in quasi-static problems with geometric nonlinearity and bifurcation points so that the efficiency of this method can be compared to others, such as Newtonian numerical techniques and force-displacement-constraint approaches. To achieve the objectives of this research, after briefly reviewing the current force-based computational methods in practice, the energy method is described for such problems, and then the step-by-step process of its computer implementation will be presented. Afterward, by coding in MATLAB software and applying the method to numerical examples employed by other researchers such as truss and frame structures, the numerical results are verified by analytical solution as well as those obtained by other methods, such as Newton-Raphson and Arc Length techniques. Generally, the interpretation of the results obtained from performed simulations has shown that the presented numerical method in analyzing nonlinear geometric problems has better accuracy compared to the Arc Length method; moreover, it can well pass through bifurcation points in the force-displacement curve without divergence in comparison with the Newton-Raphson method.

کلیدواژه‌ها [English]

  • Numerical study
  • Modified energy method
  • Solid mechanics
  • Geometric nonlinearity
  • Bifurcation points
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