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Application of isogeometric approach to dynamics of curved beam

Łasecka-Plura Magdalena, Białasik Jan, Kuczma Mieczysław, Tabrizikahou Alireza

Vibrations in Physical Systems

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2023

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Vol. 34, nr 1

art. no. 2023117

EN

In the paper dynamics of a free-form Timoshenko curved beam is investigated. The considered problem is solved using isogeometric analysis. Non-uniform rational B-spline (NURBS) basis functions are applied to describe both geometry and displacement field of the considered beam. The Timoshenko beam theory is used to derive the element stiffness and mass matrices. The application of the presented method is shown in numerical examples. The correctness of the presented approach is proved by comparing the obtained results to those available in the literature and calculated by the finite element method. Analysis of convergence is presented for different orders of NURBS basis functions.

2

Prediction of random vibration fatigue damage using isogeometric modelling

Wang Shubiao, Khalij Leila, Troian Renata, Shi Lujie

Computer Assisted Methods in Engineering and Science

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2021

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Vol. 28, no. 3

193--223

EN

The finite element analysis (FEA) method is indispensable in simulation technology, as itcan help engineers predict results to avoid the cost of experimental testing. However, thefinite element mesh generation process can be time-consuming, and the approximate meshmodel can lead to inaccurate stress results. Improving the accuracy of stress estimationleads to a better assessment of damage or life of mechanical components. In this study, weapplied the isogeometric analysis (IGA) implemented in LS-DYNA software to study twospecimens subjreted to the stationary Gaussian random loads. These geometric modelswere represented by non-uniform rational B-spline (NURBS) to assess the damage andfatigue life in the frequency domain by using Dirlik’s distribution and cumulative damage.A comparison with FEA was conducted to highlight the main differences. Experimentalfatigue tests with an electrodynamic shaker were also carried out to check if the fatiguelives predicted by numerical models are consistent. The study showed that IGA predictssimilar results to FEA with an acceptable relative error and reduced the time for meshgeneration, requiring fewer integration points and mesh elements.

3

Three-dimensional simulations of the airborne COVID-19 pathogens using the advection-diffusion model and alternating-directions implicit solver

Łoś Marcin, Woźniak Maciej, Muga Ignacio, Paszynski Maciej

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 4

art. no. e137125

EN

In times of the COVID-19, reliable tools to simulate the airborne pathogens causing the infection are extremely important to enable the testing of various preventive methods. Advection-diffusion simulations can model the propagation of pathogens in the air. We can represent the concentration of pathogens in the air by “contamination” propagating from the source, by the mechanisms of advection (representing air movement) and diffusion (representing the spontaneous propagation of pathogen particles in the air). The three-dimensional time-dependent advection-diffusion equation is difficult to simulate due to the high computational cost and instabilities of the numerical methods. In this paper, we present alternating directions implicit isogeometric analysis simulations of the three-dimensional advection-diffusion equations. We introduce three intermediate time steps, where in the differential operator, we separate the derivatives concerning particular spatial directions. We provide a mathematical analysis of the numerical stability of the method. We show well-posedness of each time step formulation, under the assumption of a particular time step size. We utilize the tensor products of one-dimensional B-spline basis functions over the three-dimensional cube shape domain for the spatial discretization. The alternating direction solver is implemented in C++ and parallelized using the GALOIS framework for multi-core processors. We run the simulations within 120 minutes on a laptop equipped with i7 6700 Q processor 2.6 GHz (8 cores with HT) and 16 GB of RAM.

4

Heuristic algorithm to predict the location of C0 separators for efficient isogeometric analysis simulations with direct solvers

Paszyńska A., Jopek K., Woźniak M., Paszyński M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 6

907--917

EN

We focus on two and three-dimensional isogeometric finite element method computations with tensor product Ck B-spline basis functions. We consider the computational cost of the multi-frontal direct solver algorithm executed over such tensor product grids. We present an algorithm for estimation of the number of floating-point operations per mesh node resulting from the execution of the multi-frontal solver algorithm with the ordering obtained from the element partition trees. Next, we propose an algorithm that introduces C0 separators between patches of elements of a given size based on the stimated number of flops per node. We show that the computational cost of the multi-frontal solver algorithm executed over the computational grids with C0 separators introduced is around one or two orders of magnitude lower, while the approximability of the functional space is improved. We show O(NlogN) computational complexity of the heuristic algorithm proposing the introduction of the C0 separators between the patches of elements, reducing the computational cost of the multi-frontal solver algorithm.