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The Theory used in ADINA is richly documented in the following books by K.J. Bathe and co-authors



To Enrich Life
(Sample pages here)

To Download — Second Edition of the Book "Finite Element Procedures" (4th printing)

You are welcome to download the second edition of the book, 4th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hard-copy of the book.

Improved versions will be made available here, from time to time, as the 5th printing, and so on.

"Finite Element Procedures", 2nd Edition (.pdf)

Solutions to exercises in the book "Finite Element Procedures", 2nd Edition, 2014 are given in this manual (.pdf)

The Chinese translation of the 2nd edition is also available: Vol. 1 Vol. 2

Following are more than 700 publications — that we know of — with reference to the use of ADINA. The pages give the Abstracts of some papers published since 1986 referring to ADINA. The most recent papers are listed first. All these papers may be searched using the box:

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Shape Optimization and Fluid Dynamic Analysis of a Translating Flexible Body

S.L. Thomson

Brigham Young University, Provo, UT, 84663

Proc. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA 2010-1432, 2010

Abstract: The translation (swimming) of an oscillating, slender, flexible body through an initially stationary fluid was explored using computational models and optimization routines. The computational model included fully-coupled two-dimensional fluid and solid finite element domains. The body leading edge was subjected to a prescribed vertical sinusoidal displacement, whereas the entire body was free to move horizontally. Large body deformation resulted in thrust production and horizontal body translation. Gradient-based optimization methods were used to find the body shape that yielded the maximum horizontal displacement over one period of vertical oscillation. It is shown that a tapered body with a “rounded” leading edge achieved significantly greater horizontal velocity than a body of uniform thickness. The computational domains, numerical models, optimization routines, and model verification studies are described. The predicted responses of uniform and optimal bodies are compared, and the sensitivity of horizontal displacement to body shape is quantified.


Fluid Structure Interaction Analysis in Human Upper Airways to Understand Sleep Apnea

G. Mylavarapu1, M. Mihaescu1, E. Gutmark1,  S. Murugappan2 and M. Kalra3

1 Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH, 45221
2 Dept. of Otolaryngology, MSB, University of Cincinnati, Cincinnati, OH, 45267 and
3 Dept. of Pulmonary Division, Cincinnati Children’s Hospital Medical Center, OH, 45229

Proc. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA 2010-1264, 2010

Abstract: Sleep apnea is characterized by partial or complete obstruction of upper airway during sleep. Existing clinical therapies are not fool-proof. Understanding human upper airway mechanisms with flow and structure dynamics is hence, essential for designing better clinical therapies. In this study, two dimensional Fluid-Structure Interaction (FSI) simulations were carried on human upper airway models using ADINA 8.4, a finite element code. Baseline model (B) is reconstructed from a mid-sagittal Magnetic Resonance Image (MRI) of an adolescent. In-house developed MATLAB code is used to de-feature various structures on the MRI scan. Vertices information from MATLAB code is then imported into Gambit 2.2, where edges are reconstructed and exported in IGES format to ADINA. Fluid and Solid surfaces are reconstructed and discretized in ADINA. Flow was assumed laminar and incompressible. Plain Strain hypothesis and small strains were assumed with solid domain. Appropriate boundary conditions with wall and fluid structure interfaces were defined in both fluid and solid domains. Pressure drop across airway is varied incrementally with a user defined time function. Airway wall displacement and flow features are obtained. The displacement of tip of soft palate and critical closing pressures required for partial or complete closure of upper airways are computed and compared across different cases. For comparative studies between a normal, narrower and corrected airway models (A, B, C), Model B is reconstructed from Model A by moving its posterior airway wall in anterior direction and Model C is reconstructed from Model B by excising the length of soft palate by 30%. It was observed that airway is more susceptible to collapse during expiration phase than inspiration. Increasing the stiffness of soft palate as in a palatal implant clinical therapy showed significant improvement in airway potency as demonstrated in Models A and B. Model B demonstrates a case of complete obstruction for significantly lower closing pressures when compared to Model A. Model A demonstrated hypo-apnea or partial obstruction of airway. Model C with excised soft palate is less susceptible to airway collapse when compared to Model B. This study is step forward to our previous studies on upper airways where airway walls were assumed static.


Application of Parallel Processing to the Simulation of Heart Mechanics

M.G. Doyle1, S. Tavoularis1, and Y. Bourgault1,2

1 Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada
2 Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

D.J.K. Mewhort et al. (Eds.): HPCS 2009, LNCS 5976, pp. 30-47, 2010

Abstract: Simulations of the mechanics of the left ventricle of the heart with fluid-structure interaction benefit greatly from the parallel processing power of a high performance computing cluster, such as HPCVL. The objective of this paper is to describe the computational requirements for our simulations. Results of parallelization studies show that, as expected, increasing the number of threads per job reduces the total wall clock time for the simulations. Further, the speed-up factor increases with increasing problem size. Comparative simulations with different computational meshes and time steps show that our numerical solutions are nearly independent of the mesh density in the solid wall (myocardium) and the time step duration. The results of these tests allow our simulations to continue with the confidence that we are optimizing our computational resources while minimizing errors due to choices in spatial or temporal resolution.

Keywords: Biomechanics - heart mechanics - fluid-structure interaction.


An efficient two-stage approach for image-based FSI analysis of atherosclerotic arteries

J.R. Leach1,2, V.L. Rayz2, M.R.K. Mofrad1, D.Saloner1,2

1 UC Berkeley/UC San Francisco Joint Graduate Group in Bioengineering, University of California San Francisco, San Francisco, CA, USA
2 Department of Radiology, UC San Francisco Medical Center, San Francisco, CA, USA

Biomech Model Mechanobiol, 9:213–223, 2010

Abstract Patient-specific biomechanical modeling of atherosclerotic arteries has the potential to aid clinicians in characterizing lesions and determining optimal treatment plans. To attain high levels of accuracy, recent models use medical imaging data to determine plaque component boundaries in three dimensions, and fluid–structure interaction is used to capture mechanical loading of the diseased vessel. As the plaque components and vessel wall are often highly complex in shape, constructing a suitable structured computational mesh is very challenging and can require a great deal of time. Models based on unstructured computational meshes require relatively less time to construct and are capable of accurately representing plaque components in three dimensions. These models unfortunately require additional computational resources and computing time for accurate and meaningful results.Atwo-stage modeling strategy based on unstructured computational meshes is proposed to achieve a reasonable balance between meshing difficulty and computational resource and time demand. In this method, a coarsegrained
simulation of the full arterial domain is used to guide and constrain a fine-scale simulation of a smaller region of interest within the full domain. Results for a patient-specific carotid bifurcation model demonstrate that the two-stage approach can afford a large savings in both time for mesh generation and time and resources needed for computation. The effects of solid and fluid domain truncation were explored, and were shown to minimally affect accuracy of the stress fields predicted with the two-stage approach.

Keywords Atherosclerosis - Vulnerable plaque - Mechanical analysis and characterization - Carotid - Patient-specific – FSI


Carotid Atheroma Rupture Observed In Vivo and FSI-Predicted Stress Distribution Based on Pre-rupture Imaging

J.R. Leach1,2,3,  V.L. Rayz2, B. Soares2, M. Wintermark2, M.R.K. Mofrad1, and D. Saloner1,2

1 UC Berkeley/UC San Francisco Joint Graduate Group in Bioengineering, Berkeley, CA, USA
2 Department of Radiology, Biomedical Imaging, University of California San Francisco Medical Center, San Francisco, CA, USA
3 Department of Radiology, Box 114D, San Francisco Veterans Affairs Medical Center, 4150 Clement St., San Francisco, CA 94121, USA

Annals of Biomedical Engineering, DOI: 10.1007/s10439-010-0004-8, 2010

Abstract: Atherosclerosis at the carotid bifurcation is a major risk factor for stroke. As mechanical forces may impact lesion stability, finite element studies have been conducted on models of diseased vessels to elucidate the effects of lesion characteristics on the stresses within plaque materials. It is hoped that patient-specific biomechanical analyses may serve clinically to assess the rupture potential for any particular lesion, allowing better stratification of patients into the most appropriate treatments. Due to a sparsity of in vivo plaque rupture data, the relationship between various mechanical descriptors such as stresses or strains and rupture vulnerability is incompletely known, and the patient-specific utility of biomechanical analyses is unclear. In this article, we present a comparison between carotid atheroma rupture observed in vivo and the plaque stress distribution from fluid–structure interaction analysis based on pre-rupture medical imaging. The effects of image resolution are explored and the calculated stress fields are shown to vary by as much as 50% with sub-pixel geometric uncertainty. Within these bounds, we find a region of pronounced elevation in stress within the fibrous plaque layer of the lesion with a location and extent corresponding to that of the observed site of plaque rupture.

Keywords: Patient-specific - Vulnerable plaque - Atherosclerosis - Image-based


Fluid–structure interaction analysis of flow and heat transfer characteristics around a flexible microcantilever in a fluidic cell

K. Khanafer1,2, A.Alamiri3, I. Pop4

1 Vascular Mechanics Laboratory, Biomedical Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA
2 Section of Vascular Surgery, University of Michigan, Ann Arbor, MI 48109, USA
3 Mechanical Engineering Department, United Arab Emirates University, United Arab Emirates
4 Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

International Journal of Heat and Mass Transfer (In press 2010)

Abstract: This study analyzes the effect of the flow conditions and the geometric variation of the microcantilever’s bluff body on the microcantilever detection capabilities within a fluidic using a finite element fluid–structure interaction (FSI) model. Periodic steady-state results of the current investigation show that the magnitude of the inlet fluid velocity, elasticity of the microcantilever, random noise, and the height of the bluff body has respective profound effect on deflection of the microcantilever. Low inlet fluid velocity condition exhibits no vortices around the microcantilever. However, the introduction of a random noise in the fluidic cell may cause the microcantilever to oscillate in a harmonic mode at low velocity. The results of this study show that microcantilevers excite earlier for large height compared with smaller heights of the bluff body at high inlet fluid velocity. This work paves the road for researchers in the area microcantilever to design ef.cient microcantilevers that display least errors in the measurements.

Keywords: Fluid-structure interaction - Fluidic cell - Heat transfer - Microcantilever


Effective dampings and frequency shifts of several modes of an inclined cantilever vibrating in viscous fluid

S.-M. Lin

Mechanical Engineering Department, Kun Shan University, 949, DaWan Road, Tainan, 710-03, Taiwan, ROC

Precision Engineering, Vol. 34, pp. 320–326, 2010

Abstract: In this study, one investigates the dynamic behavior of an inclined non-uniform cantilever vibrating in fluid and close to a sample’s surface. The closed-form solution of this beam model is presented. In fact, there must exist the hydrodynamic loading to the cantilever. Its effects include the viscous shear damping, the squeeze film damping and the added liquid mass attached to the cantilever. These depend on the material and geometrical properties and the operational conditions, e.g. the inclined angle of a cantilever to a sample’s surface. For simplicity, the effective damping and the added mass are usually expressed as some formula. It is found here that these conventional formula are inaccurate for the case of the cantilever close to a sample’s surface. For understanding the detailed mechanism of motion, Basak and Raman (2006) analyzed the 3D fluid-structure interaction of a cantilever vibrating in liquid and close to a solid surface. The Q-factors and the resonant frequencies of different modes were presented. But the effective damping and the added mass attached to the cantilever were not presented. Via the present solution method the effective damping and the added mass are easily determined. It is very helpful for constructing the mathematical model and understanding the AFM behavior clearly.

Keywords: Liquid - Inclined cantilever - Q-factor - Resonant frequency


FSI Analysis of the Coughing Mechanism in a Human Trachea

M. Malvé,1,2,3  A. Pérez Del Palomar,1,2,3  J.L. López-Villalobos,4  A. Ginel,4 and M. Doblaré,1,2,3

1 Group of Structural Mechanics and Materials Modeling, Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza (Spain), C/María de Luna 3, 50018 Zaragoza, Spain;
2 Centro de Investigacíon Biomédica en Red en Bioingeniería Biomateriales y Nanomedicina (CIBER-BBN), C/María de Luna 11, 50018 Zaragoza, Spain;
3 Instituto de Salud Carlos III, Madrid, Spain; and
4 Department of Thoracic Surgery, Hospital Virgen del Rocío, Seville, Spain

Annals of Biomedical Engineering, Vol. 38, No. 4, pp. 1556–1565, 2010

Abstract: The main physiological function of coughing is to remove from the airways the mucus and foreign particles that enter the lungs with respirable air. However, in patients with endotracheal tubes, further surgery has to be performed to improve cough effectiveness. Thus, it is necessary to analyze how this process is carried out in healthy tracheas to suggest ways to improve its efficacy in operated patients. A finite element model of a human trachea is developed and used to analyze the deformability of the tracheal walls under coughing. The geometry of the trachea is obtained from CT of a 70-year-old male patient. A fluid structure interaction approach is used to analyze the deformation of the wall when the fluid (in this case, air) flows inside the trachea. A structured hexahedral-based grid for the tracheal walls and an unstructured tetrahedral-based mesh with coincident nodes for the fluid are used to perform the simulations with the finite element-based commercial software code (ADINA R&D Inc.). Tracheal wall is modeled as an anisotropic fiber reinforced hyperelastic solid material in which the different orientation of the fibers is introduced. The implantation of an endotracheal prosthesis is simulated. Boundary conditions for breathing and coughing are applied at the inlet and at the outlet surfaces of the fluid mesh. The collapsibility of a human trachea under breathing and coughing is shown in terms of flow patterns and wall stresses. The ability of the model to reproduce the normal breathing and coughing is proved by comparing the deformed shape of the trachea with experimental results. Moreover the implantation of an endotracheal prosthesis would be related with a decrease of coughing efficiency, as clinically seen.

Keywords: Trachea - Finite element method - Fluid–solid interaction - Coughing - Fiber reinforced material


An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex
of Arterial Bifurcations

Z. Zeng, B.J. Chung, M. Durka, and A.M. Robertson

Department of Mechanical Engineering and Materials Science, McGowan Institute for Regenerative Medicine, Center for Vascular Remodeling and Regeneration (CVRR); University of Pittsburgh, Pittsburgh, PA 15261, USA

R. Rannacher, A. Sequeira (eds.), Advances in Mathematical Fluid Mechanics, Springer-Verlag Berlin Heidelberg, 2010

Abstract Intracranial aneurysms (ICA) are abnormal dilations of the cerebral arteries, most commonly located at the apices of bifurcations. The ability of the arterial wall, particularly the endothelial cells forming the inner lining of the wall, to respond appropriately to hemodynamic stresses is critical to arterial health. ICA initiation is believed to be caused by a breakdown in this homeostatic mechanism leading to wall degradation. Due to the complex nature of this process, there is a need for both controlled in vitro and in vivo studies. Chung et al. developed an in vitro chamber for analyzing the response of biological cells to the hemodynamic wall shear stress fields generated by the impinging flows found at arterial bifurcations. Here, we build on this work and design an in vitro flow chamber that can be used to reproduce specific magnitudes of wall shear stress (WSS) and gradients of wall shear stress. Particular attention is given to reproducing spatial distributions of these functions that have been shown to induce pre-aneurysmal changes in vivo. We introduce a measure of the gradient of the wall shear stress vector (WSSVG) which is appropriate for complex 3D flows and reduces to expected measures in simple 2D flows. The WSSVG is a scalar invariant and is therefore appropriate for use in constitutive equations for vessel remodeling in response to hemodynamic loads.

Keywords:  Intracranial aneurysm - Wall shear stress gradient - Flow chamber – Bifurcation


Direct methanol fuel cell bubble transport simulations via thermal lattice Boltzmann and volume of fluid methods

K. Fei, T.S. Chen, C.W. Hong

Department of Power Mechanical Engineering, National Tsing Hua University, 101, Sec. 2, Kwang Fu Road, Hsinchu 30013, Taiwan

Journal of Power Sources 195 (2010) 1940–1945

Abstract: Carbon dioxide bubble removal at the anode of a direct methanol fuel cell (DMFC) is an important technique especially for applications in the portable power sources. This paper presents numerical investigations of the two-phase flow, CO2 bubbles in a liquid methanol solution, in the anode microchannels from the aspect of microfluidics using a thermal lattice Boltzmann model (TLBM). The main purpose is to derive an efficient and effective computational scheme to deal with this technical problem. It is then examined by a commercially available software using Navier–Stokes plus volume of fluid (VOF) method. The latter approach is normally employed by most researchers. A simplified microchannel simulation domain with the dimension of 1.5mm in height (or width) and 16.0mm in length has been setup for both cases to mimic the actual flow path of a CO2 bubble inside an anodic diffusion layer in the DMFC. This paper compares both numerical schemes and results under the same operation conditions from the viewpoint of fuel cell engineering.

Keywords: Direct methanol fuel cell (DMFC) - Bubble dynamics - Thermal lattice Boltzmann method (TLBM) - Volume of fluid (VOF)

A Numerical Study with FSI Mode on the Characteristics of Pressure Fluctuation and Discharge Valve Motion in Rotary Compressors with Single and Dual Muffler

H. M. Chae1 and C.Nyung Kim2

1 Department of Mechanical Engineering, Graduate School of Kyunghee University, Yongin, Korea, 446-701
2 Department of Mechanical Engineering, College of Engineering, Kyunghee University, Yongin, Korea, 446-701

International Journal Of Precision Engineering And Manufacturing, 11( 4):589-596, 2010

Rotary compressors in air-conditioners have been considered for the efficiency enhancement and noise reduction. To perceive the characteristics of noise in a rotary compressor, the features of discharge valve motion and pressure fluctuation in compressors have to be examined. This study has been conducted to investigate the characteristics of discharge valve motion and pressure fluctuation in association with refrigerant flow in rotary compressors with single and dual muffler. The current study has been performed with the FSI mode since the discharge valve oscillates in association with periodic compression of refrigerants in the compressors. For the case of dual muffler, it has been observed that the displacement of discharge valve is smaller than that in the case of single muffler since the compressor with dual muffler has larger inner resistance to the refrigerant flow than that in the case of single muffler. Also, the standard deviation and the energy spectrum of the pressure fluctuation with the dual muffler are smaller than those with the single muffler. Therefore, the use of the dual muffler is expected to contribute to the noise reduction. To the contrary, it has been found that the efficiency of the compressor with dual muffler is smaller with the diminution of volume flow rate compared to the case of single muffler. This study may supply a basis for the design of rotary compressors with higher efficiency and lower noise.

Keywords: Rotary compressor -  Single muffler - Dual muffler - Discharge valve - Pressure fluctuations – FSI

Modeling and Simulation of Human Upper Airway

Z. Liu1, X. Xu1, F. F.J. Lim2, X. Luo3, A. Van Hirtum4, and N.A. Hill3

1 Institute of High Performance Computing, Fusionopolis Way, #16-16 Connexis, Singapore 138632
2 Engineering Science Programme, National University of Singapore, Singapore 117576
3 Department of Mathematics, University of Glasgow, Glasgow, G12 8QW UK
4 Département Parole et Cognition, GIPSA-Lab, University of Grenoble, CNRS 5216, 46 Av. Felix Viallet, 38031 Grenoble, France

WCB 2010, IFMBE Proceedings 31, pp. 686–689, 2010

Abstract: Snoring might indicate the first stage of the Obstructive Sleep Apnea (OSA) syndrome, and has received much attention in recent years. Previous studies on snoring have shown that upper airway narrowing, collapse, and resistance are predisposing factors for snoring and OSA. However, further research work is needed to understand the mechanisms of snoring. Although there have been many CFD studies modeling nasal turbulence, the larynx and vocal folds, most are limited to lumped one- or two-dimensional cases, or three-dimensional problems with over-simplified physics, e.g. rigid rather than flexible walls. In this study, we address the impact of fluid-structure interactions by using a three-dimensional numerical simulation of an experimental upper airway model, which is constructed to mimic the interaction of the deformation of the soft palate and adjacent tissues with a pressurized airflow (breathing) during sleep. The model consists of a deformable structure domain and its associated airflow domain. The results of the numerical simulation are compared with the experimental data. In addition, Interesting flow fields and pressure distributions are revealed. The fluid structure interaction model can be developed further to study the more realistic human upper airway problems.

Keywords: Snoring - upper airway - fluid structure interaction - Obstructive Sleep Apnea


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