تحلیل دینامیکی اندرکنش خاک و سازه با استفاده از روش اجزای محدود مرزی مقیاس‌شده مجزا

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی عمران، دانشگاه صنعتی خواجه‌نصیرالدین طوسی، تهران، ایران

2 دانشکده مهندسی عمران و محیط‌زیست، دانشگاه تربیت مدرس، تهران، ایران

3 دانشکده مهندسی، دانشگاه اراک، اراک، ایران

چکیده

در سال­های اخیر، توسعه روش­های عددی برای تحلیل لرزه­ای سازه­ها به‌عنوان یک موضوع تحقیقاتی مهم شناخته شده است. هدف از انجام این تحقیق، توسعه روش نیمه­تحلیلی اجزای محدود مرزی مقیاس‌شده مجزا برای در نظر گرفتن اثرات اندرکنش خاک و سازه است. در این تحقیق، روند حل مسائل اندرکنش دینامیکی خاک و سازه با استفاده از روش اجزای محدود مرزی مقیاس­شده مجزا برای اولین بار، توسعه یافته است. برای غیر درگیر کردن معادلات حاکم بر مسائل اندرکنش، یک فرض اولیه ترکشن بر روی مرز اندرکنش اعمال شده است. برای حل این مسائل لازم است که از دو نقطه مرجع جداگانه برای گسسته­سازی محیط خاک و محیط سازه استفاده شود. بدین‌صورت که ابتدا محیط خاک با استفاده از روش اجزای محدود مرزی مقیاس­شده مجزا مورد تحلیل قرار گرفته، سپس از نتایج به‌دست‌آمده، برای تحلیل محیط سازه به کمک روش حاضر، استفاده شده است. در نهایت، به‌منظور بررسی صحت نتایج به‌دست‌آمده از روش حاضر، به حل چندین مثال عددی، با مقادیر متفاوت مدول الاستیسیته برای محیط خاک پرداخته شده است که نتایج به‌دست‌آمده در مقایسه با نتایج حاصل از روش اجزای محدود، حاکی از دقت و انعطاف­پذیری بالای روش حاضر برای در نظر گرفتن اثرات اندرکنش خاک و سازه است. علاوه بر این، تعداد المان­های مورد استفاده در روش حاضر به‌مراتب کمتر از تعداد المان­های به کار رفته در روش اجزای محدود است که این امر منجر به کاهش هزینه­های محاسباتی خواهد شد.

کلیدواژه‌ها


عنوان مقاله [English]

Dynamic Analysis of Soil-Structure Interaction Using Decoupled Scaled Boundary Finite Element Method

نویسندگان [English]

  • Amin Ghazanfari Tehran 1
  • Naser Khaji 2
  • Mahdi Yazdani 3
1 K.N. Toosi University of Technology, Tehran, Iran
2 Tarbiat Modares University, Tehran, Iran
3 Arak University, Arak, Iran
چکیده [English]

Structures are subjected to different loadings during their lifetime. Most of these loads are time dependent and change over the time. Therefore, it is important to evaluate structures under dynamic loads. On the other hand, dynamic response of structures is affected by several factors that results in many complexities to structural analysis. Thus, numerical methods are used for seismic analysis of structures. In this article, a new semi analytical method with high efficiency is developed for soil-structure interaction (SSI) analysis, which is called decoupled scaled boundary finite element method (DSBFEM). This method has analytical solution in radial direction and uses a specific shape functions as the interpolation function in the circumferential direction. In addition, the boundaries of the problem are discretized by specific new non-isoparametric elements. In these elements, new special shape functions as well as higher-order Chebyshev mapping functions are implemented. For the shape functions, Kronecker Delta property is satisfied for displacement function, simultaneously. Moreover, the first derivatives of shape functions are assigned to zero at any given control point. In fact, to model the geometry of the problems, we consider a local coordinate origin (LCO) for transportation of the geometric characteristics of global coordinate and local coordinate. Consequently, using a form of weighted residual method and implementing Clenshaw-Curtis numerical integration, coefficient matrices of the system of equations are converted into diagonal ones, which leads to a set of decoupled partial differential equations for solving the whole system. This means that the governing partial differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. Due to the soil flexibility effect on structural responses, in this paper, SSI problem has been investigated considering different values of modulus of elasticity for soil domain. To achieve this, two different LCOs have been used to discretize the soil domain and the structure domain. Thus, a three-step algorithm is proposed, which consists of: (1) considering an initial stress on the interaction boundary, (2) analysis of soil domain, and (3) analysis of structure domain. Therefore, after the initial assumption of stress on the interaction boundary, the soil domain will be completely analyzed by two-stage traction redistribution and the results on interaction boundary will be used as boundary conditions of structure domain. It should be noted that in the proposed algorithm, only one-stage traction redistribution will be used to analyze the structure domain. Finally, validity and accuracy of DSBFEM are fully demonstrated through some benchmark examples with different values of modulus of elasticity for the soil domain, and the results are compared with Finite Element Method (FEM). The results indicate that the proposed method has high accuracy and flexibility to consider the SSI effect, determine the resonant frequency and the maximum displacement amplitude of the structure. In addition, the number of elements used in the DSBFEM is much less than the FEM, which will lead to a reduction in computational costs.

کلیدواژه‌ها [English]

  • Decoupled Scaled Boundary Finite Element Method (DSBFEM)
  • Soil-Structure Interaction (SSI)
  • Dynamic Analysis
  • Frequency Domain
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