توسعه فرمول‌بندی گاوس-لژاندر-هرمیت-سه‌نقطه‌ای (GLH-3P) برای تحلیل خطی و غیرخطی ارتعاشات سازه‌ها تحت اثر تحریک زلزله

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده فنی و مهندسی، دانشگاه بناب، بناب، ایران

2 دانشکده مهندسی عمران و محیط زیست، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

پاسخ دینامیکی سازه‌ها تحت اثر زلزله یکی از مسائل مهم مهندسی عمران است که نیازمند روش‌های تحلیلی دقیق و کارآمد است. روش‌های تحلیل تاریخچه زمانی غیرخطی، ابزاری قدرتمند برای ارزیابی پاسخ دینامیکی سازه‌ها تحت اثر زلزله ارائه می‌دهند. اساساً، این روش‌ها نیازمند فرض یک مدل برای تغییرات شتاب در طول گام و یک روش انتگرال‌گیری مؤثر عددی برای حل معادلات غیرخطی هستند. در این پژوهش، فرمول‌بندی کارآمدی برای تحلیل دینامیکی غیرخطی سازه‌ها تحت عنوان روش گاوس-لژاندر-هرمیت-سه نقطه‌ای ارائه می‌گردد که مبتنی بر قاعده انتگرال‌گیری ضمنی سه-نقطه‌ای گاوس می‌باشد که از درون‌یابی مرتبه سوم به روش هرمیت برای تقریب میان‌گام‌ها استفاده می‌کند. فرمول ارائه‌شده قابلیت تحلیل سیستم‌های غیرخطی هندسی و مصالح را دارا بوده و انواع مختلفی الگوهای بارگذاری را پوشش می‌دهند. متعاقباً، جهت بررسی عملکرد فرمول‌بندی پیشنهادی، تعدادی از سیستم‌های خطی و غیرخطی تحت اثر بارگذاری رکورد زلزله ال-سنترو قرار گرفته‌ و مورد بررسی قرار گرفتند. نتایج به‌دست‌آمده از تحلیل‌های روش جدید، با نتایج روش‌های رایج دیگر مانند روش نیمه‌تحلیلی انتگرال دوهامل و روش شبه تحلیلی نیومارک-بتا و روش ویلسون-تتا مورد مقایسه قرار گرفته است. فرمول‌بندی ارائه‌شده از نظر دقت، پایداری، هم‌گرایی و هزینه محاسباتی برتری قابل‌توجهی نسبت به سایر روش‌ها دارد و می‌توان آن را در نرم‌افزارهای اجزای محدود پیاده‌سازی و برای تحلیل تاریخچه زمانی غیرخطی سازه‌های یک درجه آزادی استفاده کرد.

کلیدواژه‌ها

عنوان مقاله [English]

Development of Gauss-Legendaire-Hermite-3Point (GLH-3P) Formulation for Linear and Nonlinear Analysis of Earthquake-Affected Structures

نویسندگان [English]

  • Mehdi Babaei 1
  • Mohammad Reza Hanafi 2
  • Alireza Rahaei 2
1 Department of Civil Engineering, University of Bonab, Bonab, Iran
2 Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
چکیده [English]

The dynamic behavior of structures under seismic loading is a critical consideration in civil engineering, requiring accurate and efficient analytical methods. Nonlinear time history analysis methods, which involve solving the structure's motion equations over time, serve as valuable tools in this regard. These methods consist of two key components: an acceleration model for each step and a numerical integration technique for tackling nonlinear equations. This research presents an effective formulation for nonlinear dynamic analysis of structures, referred to as the Gauss-Legendre-Hermit-3P Method. It's based on the implicit three-point Gauss integration rule and employs third-order Hermite interpolation for approximating intermediate steps. The proposed formula can analyze nonlinear geometric and material systems and handle various loading patterns. To evaluate the performance of this formulation, a series of linear and nonlinear systems were subjected to the El-Centro earthquake record and analyzed. The results obtained from the analyses of the new method were compared with those of other commonly used methods, including the semi-analytical Duhamel integral method, the pseudo-analytical Newmark-beta method, and the Wilson-theta method. The proposed formulation exhibits a significant advantage over other methods in terms of accuracy, stability, convergence, and computational cost. It can be seamlessly implemented into finite element software and employed for nonlinear time history analysis of single-degree-of-freedom and multi-degree-of-freedom structures.

کلیدواژه‌ها [English]

  • Time-History Analysis
  • Nonlinear Analysis
  • Newmark Method
  • Gauss-Legendre Quadrature
  • Hermite Interpolation

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نشریه مهندسی عمران امیرکبیر
دوره 57، شماره 10
دی 1404
صفحه 1725-1748

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