نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان، اصفهان

2 موسسه تحلیل عددی سازه‌ها با کاربرد در فناوری کشتی، دانشگاه صنعتی هامبورگ، هامبورگ، آلمان

3 موسسه محاسبات در مهندسی، دانشگاه صنعتی مونیخ، مونیخ، آلمان

چکیده

مسائل تحلیل شده عبارتند از باریک‌شدگی در آزمون کشش ساده با نمونه‌های شیاردار و بدون شیار و فشارگذاری صفحه سوراخ‌دار. این تحلیل‌ها نشان می‌دهند که روش‌های اجزای محدود مرتبه بالا با فرمول‌بندی مبتنی بر جابه‌جایی توانایی فائق آمدن بر قفل‌شدگی حجمی را دارند. این روش‌ها همچنین واجد خصوصیت‌هایی نظیر نرخ همگرایی بالا و عدم حساسیت زیاد به تغییر شکل‌های بسیار زیاد المانی نیز هستند. تحلیل‌های معیار با روش سلول محدود همچنین نشان می‌دهند که این روش علاوه بر مزایای روش‌های مرتبه بالا، قابلیت تحلیل آسان هندسه‌های بسیار پیچیده را نیز فراهم می‌آورد. نتایج تحلیل‌های ارائه شده نیز با استفاده از نتایج یک روش اجزای محدود مرتبه پایین با نام F-bar<span lang="FA" style="letter-spacing: -0.3pt; font-family:;" dir="RTL" yes;"="" en-us;="" roman";="" new="" "times="" bold";="" roman="" 11pt;="" lotus";="" b="" fa;=""> به تأیید رسیده‌اند. مطالعات عددی انجام شده نشان می‌دهد که هر دو روش مورد بررسی را می‌توان برای تحلیل پلاستیک مواد و سازه‌های مهندسی ساخته شده از فلزات نرم، به ویژه مواردی که دارای هندسه پیچیده هستند، با اطمینان به‌کار برد.

کلیدواژه‌ها

عنوان مقاله [English]

Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells

نویسندگان [English]

  • Aliakbar Taghipour 1
  • J. Parvizian 1
  • S. Heinze 2
  • A. Duester 2
  • E. Rank 3

چکیده [English]

finite cell method, are employed to compute a series of benchmark problems in the finite strain von Mises or J2 theory of plasticity. The hierarchical (integrated Legendre) shape functions are used for the finite element approximation of incompressible plastic dominated deformations occurring in the finite strain plasticity of ductile metals. The computational examples include the necking under uniaxial tension with notched and un-notched samples and the compression of a perforated plate. These computations demonstrate that the high-order finite element methods can provide a locking-free behavior with a pure displacement-based formulation. They also provide high convergence rates and robustness against high mesh distortions. In addition, it is shown that the finite cell method, on the top of the aforementioned advantages, provides easy mesh generation capabilities for highly complex geometries. The computational results are verified in comparison with the results obtained using a standard low-order finite element method known as the F-bar method. The numerical investigations reveal that both methods are good candidates for the plasticity analysis of engineering materials and structures made up of ductile materials, particularly those involving complex geometries.

کلیدواژه‌ها [English]

  • High-order finite element method
  • Finite cell method
  • Finite strain plasticity
  • Incompressibility
  • Volumetric locking
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