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A DMLPG Refinement Technique for 2D and 3D Potential Problems
Get PDFMeshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations (PDE). MLPG techniques are nowadays used for solving a huge number of complex, real–life problems. While MLPG aims to approximate the solution of a given differential problem, its “dual” Direct MLPG (DMLPG) technique relies upon approximating linear functionals. Assume adaptive methods are to be implemented. When using a mesh–based method, inserting and/or deleting a node implies complex adjustment of connections. Meshless methods are more apt to implement adaptivity, since they does not require such adjustments. Nevertheless, ad–hoc insertion and/or deletion algorithms must be devised, in order to attain a good accuracy. In this paper we introduce a fresh refinement technique for DMLPG methods. Nodes are inserted in a discretization cloud where the local variation in the solution is supposed to be “large”. The variation is estimated using the (local) Total Variation (TV). DMLPG allows to directly estimate the partial derivatives, in order to compute the TV. MLPG must rely upon approximating the derivatives of the shape functions, hence MLPG refinement results to be more involved than its DMLPG counterpart. We show that our DMLPG refinement procedure allows one to efficiently solve a given diffusion problem whose solution undergoes large variations on a small portion of the domain. The accuracy afforded by a fine uniform cloud can be attained by using far less non–uniformly arranged nodes
Boundary Element Analysis of Thin Anisotropic Structures by a Self-regularization Scheme
Get PDFIn the conventional boundary element method (BEM), the presence of singular kernels in the boundary integral equation or integral identities causes serious inaccuracy of the numerical solutions when the source and field points are very close to each other. This situation occurs commonly in elastostatic analysis of thin structures. The numerical inaccuracy issue can be resolved by some regularization process. Very recently, the self-regularization scheme originally proposed by Cruse and Richardson (1996) for 2D stress analysis has been extended and modified by He and Tan (2013) to 3D elastostatics analysis of isotropic bodies. This paper deals with the extension of the technique developed by the latter authors to the elastostatics analysis of 3D thin, anisotropic structures using the self-regularized displacement boundary integral equation (BIE). The kernels of the BIE employ the double Fourier-series representations of the fundamental solutions as proposed by Shiah, Tan and Wang (2012) and Tan, Shiah and Wang (2013) recently. Numerical examples are presented to demonstrate the veracity of the scheme for BEM analysis of thin anisotropic bodies
Modelling of Landslides: An SPH Approach
Get PDFThis paper presents a model (mathematical, rheological and numerical) for triggering and propagation of landslides presenting coupling between the solid skeleton and the pore fluid. The model consists of two sub models, a depth integrated model incorporating the propagation equations, and a 1D model describing pore pressure evolution. The depth integrated sub model is discretized using a set of SPH nodes, each one having an associated finite difference mesh for discretizing the pore pressure evolution. The model we propose differs from other depth integrated models with coupled pore pressures proposed in the past in the way pore pressures are described in the soil mass. Here, we will not restrict the analysis to an assumed shape function fulfilling boundary conditions, but we will rather use a full approximation of pore pressures inside the landslide
A RIM-based Time-domain Boundary Element Method for Three-Dimensional Non-homogeneousWave Propagations
Get PDFThis paper presents a three-dimensional (3-D) boundary element method (BEM) scheme based on the Radial Integration Method (RIM) for wave propagation analysis of continuously non-homogeneous problems. The Kelvin fundamental solutions are adopted to derive the boundary-domain integral equation (BDIE). The RIM proposed by Gao (Engineering Analysis with Boundary Elements 2002; 26(10):905-916) is implemented to treat the domain integrals in the BDIE so that only boundary discretization is required. After boundary discretization, a set of second-order ordinary differential equations with respect to time variable are derived, which are solved using the Wilson-q method. Main advantages of the proposed method are that 1) it can treat wave propagations in non-homogeneous domains with only boundary mesh required, and that 2) coefficient matrices arising from the BEM are evaluated and stored only once so that solving large-scale problems with huge time steps is possible. In the numerical examples, the present method is tested in terms of accuracy, capacity to treat non-homogeneous problems and large-scale potentials
3D Fluid-Structure Interaction Canine Heart Model with Patch to Quantify Mechanical Conditions for Optimal Myocardium Stem Cell Growth and Tissue Regeneration
Get PDFRight ventricular (RV) dysfunction is a common cause of heart failure in patients with congenital heart defects and often leads to impaired functional capacity and premature death. Myocardial tissue regeneration techniques are being developed for the potential that viable myocardium may be regenerated to replace scar tissues in the heart or used as patch material in heart surgery. 3D computational RV/LV/Patch models with fluid-structure interactions (FSI) were constructed based on data from a healthy dog heart to obtain local fluid dynamics and structural stress/strain information and identify optimal conditions under which tissue regeneration techniques could achieve best outcome. RV/LV/Patch geometry and blood pressure data were obtained from a dog following established procedures. Four FSI models were used to quantify the influence of different patch materials (Dacron scaffold, treated pericardium) on local environment around the patch area, especially focusing on the thickness and stiffness of the patch. Our results indicated that changes in patch stiffness had little impact on the ejection fraction of the right ventricle because the total patch area was small. However, patch stiffness had huge impact on local RV maximum principal stress (Stress-P1) and strain (Strain-P1) around the patch area. Compared to the no-patch model, patch models had increased Stress-P1 and decreased Strain-P1 values in the patch area. Softer patches were associated with greater stress/strain variations. Thinner patch led to complex local flow environment which may have impact on myocytes seeding and RV remodeling. Our multi-physics RV/LV/Patch FSI model can serve as a useful tool to investigate cellular biology and tissue regeneration under localized flow and structural stress environment
Quick Construction of Femoral Model Using Surface Feature Parameterization
Get PDFTo facilitate the modifying of femoral surface model, by dividing the femoral mesh into surface feature units bearing medical significance based on surface feature technology, a new approach of constructing femoral models using surface feature technology is proposed. Firstly, considering of femoral anatomy, the femoral triangle mesh model generated from the averaged point-clouds is divided into several specific regions, which are called feature regions; Secondly, feature parameters are defined and the constraints among them are set up, and feature surfaces are created by skinning the contours; Finally, the adjacent feature surfaces are connected by transition surfaces, and the parametric CAD surface model of femur is constructed. Experimental results show that, with the proposed method, the surface feature model can be intuitively constructed and edited with high-level parameters. Therefore, the proposed method provides a basic tool for the design of implants and the digital restoration of incomplete femurs
Evaluation of Mechanical and Chemical Stimulations on Osteocalcin and Runx2 Expression in Mesenchymal Stem Cells
Get PDFThe osseous tissue repair and regeneration have great importance in orthopedic and maxillofacial surgery. Tissue engineering makes it possible to cure different tissue abnormalities using autologous grafts. It is now obvious that mechanical loading has essential role in directing cells to differentiation.
In this study, the influence of cyclic uniaxial loading and its combination with chemical factors on expression of osteogenic markers was investigated. Rat bone marrow-derived stem cells were isolated and cultured. In one group cells were maintained in chemical induction medium. In another group cells were subjected to cyclic uniaxial strain with 3% amplitude and 0.3 Hz frequency for 24 hours and in the last group cells were affected by induction medium and physical stimulation. TaqMan Real time PCR and immunocytochemistry were done to evaluate gene expression variations. Moreover, a small incision was made to access the bone of the cranium and induced cells were seeded on collagen based scaffolds and finally the cell seeded scaffolds were implanted.
Results indicated that mechanical loading alone caused a phenomenal increase in Runx2 and osteocalcin expression. Remarkable increment in gene expression was gained when induction medium were added to mechanical stimulation. The order of chemical and mechanical stimulation caused different effects and results were much better when the cells were affected by mechanical strain at first. Histological analysis showed mechanical stimulation could promote bone ingrowth in vivo. These evidences demonstrated that combination of chemical factors with mechanical strain was much more effective for directing osteogenesis since these elements have synergistic effects
On the Vortex Formation Effect During the Application of a Nitrogen-Gas Assisted Laser-Fusion Cutting Technique to Stainless Steel
Get PDFThis paper focuses on the vortex formation effect during the application of a laser-fusion cutting technique. This industrial technique is typically associated with the ejection of a film of molten stainless steel blown off by a subsonic laminar jet of nitrogen gas used to assist the process. Without taking into account the transverse movement of the workpiece, we consider a 4 mm thick stainless steel plate. The resulting molten metal flow is assumed to be laminar, steady, viscous and incompressible. The numerical results reveal vortex structures adjacent to the walls at the entrance of the kerf, and a pair of eddies outside the kerf. Remarkably, these vortex structures can produce a separation point in the molten film, and thereby they can affect the surface quality of the processed material. The problem is investigated in the framework of a numerical technique available in the Fluent software, based on a volume of fluid (VOF) surface-tracking strategy and the enthalpy method to account for material solidification or melting
Natural Convection in a Square Cavity Filled with Nanofluids
No full textThe present paper deals with a numerical study of natural convection in a square cavity filled with a nanofluid. The left and right vertical walls of the cavity are maintained at a local temperature Th (heat source) and a local cold temperature TC, respectively. Horizontal walls are assumed to be adiabatic. The governing equations are discretized by using the finite volume method and solved by the SIMPLER algorithm. Our computer fortran code is validated through comparison with numerical results found in the literature. Results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for the Rayleigh number (103 ≤ Ra ≤ 106), solid volume fraction of nanoparticles (0 ≤ Ø ≤ 0.10), type of nanofluids (Cu, Ag, Al2O3 and TiO2), and dimensionless length of the heat source (0.50 ≤ B ≤ 1)
Modeling the Axial Splitting and Curling of Metal Tubes under Crush Loads
Get PDFPlastic deformation and splitting are two important mechanisms of energy dissipation when metal tubes undergo axial crushing. Isotropic J2 plasticity theory combined with a failure criterion is used to model axial splitting and curling of metal tubes undergoing axial crush. The proposed material model is implemented within a finite element (FE) framework using the user material subroutine VUMAT option available in the commercial code ABAQUS. Experimental results from literature are used to validate the model. The predicted splitting and curling patterns as well as the load-displacement response agree well with the experimental observations. The present material model is also used to predict the number of axial cracks in splitting the tube