توسعه یک روش نیمه‌تحلیلی جدید برای حل مسائل الاستودینامیک در حوزه فرکانس

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 دانشکده مهندسی، دانشگاه قم

2 سازمان صنایع دریایی ایران

چکیده

هدف پژوهش حاضر، توسعه یک روش نیمه‌تحلیلی جدید به‌منظور آنالیز دینامیکی سدهای بتنی وزنی می‌باشد. در این روش، ماتریس‌های ضرایب دستگاه معادلات دیفرانسیل حاکم با استفاده از چندجمله‌ای‌های مرتبه بالای لاگرانژ (توابع نگاشت)، توابع شکل ویژه، روش انتگرال‌‌گیری عددی
Gauss-Lobatto- Legendre و روند تولید فرم انتگرالی با استفاده از روش باقی­مانده‌های وزن‌دار، به‌صورت قطری استخراج می‌شود. این امر و نیز گسسته‌سازی مسئله با یک بعد کم­تر از فضای اصلی، باعث کاهش قابل‌توجه حجم محاسبات نسبت به سایر روش‌ها می‌شود. در این پژوهش برای اولین بار به کمک ابزارهای مذکور، معادله حاکم بر مسائل الاستودینامیک با تحریک پایه (بار زلزله) در حوزه فرکانس با انتقال به فضای محلی استخراج و روند حل آن بیان شد. هم‌چنین به‌منظور سنجیدن توانایی و دقت روش حاضر در حل این دسته از مسائل، دو سد وزنی بتنی با مخزن خالی تحت تحریک هارمونیک پایه آنالیز گردید. مقایسه‌ نتایج این روش با سایر روش‌ها نشان می‌دهد که روش حاضر دارای دقتی بالا توأم با استفاده از حداقل درجات آزادی غیردرگیر برای آنالیز دینامیکی مسائل بزرگ‌مقیاس همچون سدها می‌باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Developing a New Semi- Analytical Method for Solving Elastodynamic Problems in the Frequency Domain

نویسندگان [English]

  • Reza Babaee 1
  • Ehsan Jabbari 1
  • Mohsen Khosravi Babadi 2
1 Faculty of Engineering, University of Qom, Qom, Iran
2 Iran Marine Industries Organization
چکیده [English]

In this paper, a new semi-analytical method is developed for analyzing concrete gravity dams in the frequency domain. Among different numerical methods, the finite element method (FEM), the boundary element method (BEM), and the scaled boundary finite element method (SBFEM) are more popular. BEM requires basically reduced surface discretization and may be considered as an appealing alternative to FEM for elastodynamic problems but requires fundamental solution of the governing differential equations. Although coefficient matrices of BEM are much smaller than those of FEM, they are routinely non-positive definite, non-symmetric, and fully populated. The SBFEM combines the advantages of the FEM and the BEM. The SBFEM is a semi-analytical method for solving partial differential equations by transforming the governing partial differential equations to ordinary differential equations. In the SBFEM, similar to the BEM, the boundary of the problem’s domain is discretized, while no fundamental solution is required. A modified form of the SBFEM with diagonal coefficient matrices has been proposed (Fakharian amd Khodakarami, 2015) for solving elastodynamic problems in the time domain. In this study, the semi-analytical approach for solving elastodynamic problems in the frequency domain has been applied, the governing equations in local coordinate system has been developed and two concrete gravity dams with rigid foundations and empty reservoir have been analyzed under the earthquake harmonic load.

کلیدواژه‌ها [English]

  • Elastodynamic problems
  • Diagonal coefficient matrix
  • Concrete gravity dam
  • Frequency domain

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