Reference : A one point integration rule over star convex polytopes
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
http://hdl.handle.net/10993/41945
A one point integration rule over star convex polytopes
English
Francis, Amrita[Indian Institute of Technology, Madras, Chennai 600036, India > Integrated Modelling and Simulation Lab, Department of Mechanical Engineering]
Natarajan, Sundararajan[Indian Institute of Technology, Madras, Chennai 600036, India > Integrated Modelling and Simulation Lab, Department of Mechanical Engineering]
Atroshchenko, Elena[University of Chile, Santiago, Chile > Department of Mechanical Engineering]
Bordas, Stéphane[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit > ; School of Engineering, Cardiff University, CF24 3AA Wales, UK > > > ; Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang, Viet Nam]
[en] Linear consistency ; Polygonal finite element method ; Wachspress shape functions ; Numerical integration ; One point integration
[en] In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor’s expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. The convergence properties, the accuracy and the efficacy of the one point integration scheme are discussed by solving few benchmark problems in elastostatics.
Researchers ; Professionals ; Students ; General public ; Others
[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit > ; School of Engineering, Cardiff University, CF24 3AA Wales, UK > > > ; Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang, Viet Nam]
