نویسندگان
دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان
چکیده
تحلیل پراکندگی شبکه یکی از معیارهای بررسی کارآیی روش اجزای محدود در شبیه سازی انتشار امواج صوتی یا امواج الاست یک است. مشکلی که معمولا در استفاده از این روش درشبیه سازی مسائل انتشار موج به وجود می آید به ناپیوستگی های میدانی برمی گردد که نهایتاً منجر به تغییر در اندازه و جهت بردار سرعت موج از یک جزء به جزء مجاور می شوند. برای حل این مشکل و بهبود دقت پاسخ ها دو راه حل پیشنهاد شده اند که عبارتند ازتغییر روش انتگرالگیری و تغییر توابع شکل. در این تحقیق از روش اجزای محدود ایزوجئومتریک استفاده شده- است. در این روش از توابع شکل بی-اسپلاین و نربز استفاده می شود که باعث بهبود دقت پاسخ ها خصوصاً در مسائل دینامیک سازهای یک بعدی شده اند. درجه پیوستگی این توابع شکل در مرز دو جزء مجاور می تواند بزرگتر از صفر باشد. در این تحقیق، تحلیل دو بعدی پراکندگی شبکه درانتشار موج در حالت کرنش صفحه ای برای اولین بار ارائه شده است. نتایج نشان می دهند که پراکندگی شبکه در درجات آزادی یکسان، در مقایسه با روش اجزای محدود کلاسیک، به نصف کاهش می ییابد.
کلیدواژه‌ها
عنوان مقاله [English]
Two Dimensional Complex Wavenumber Dispersion Analysis using B-Spline Finite Elements Method
نویسندگان [English]
- Y. Mirbagheri
- H. Nahvi
- J. Parvizian
چکیده [English]
Grid dispersion is one of the criteria of validating the finite element method (FEM) in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA) is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS) functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.
کلیدواژه‌ها [English]
- Grid dispersion
- elastic wave
- b-spline and NURBS shape functions
- phase velocity of wave
- group velocity of wave
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