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An Adaptive Discretization of Incompressible Flow using Node-Based Local Meshes
Get PDFIn this paper, we derive an adaptive mesh generation method for discretizing the incompressible flow using node-based local grids. The flow problem is described by the Stokes equations which are solved by a stabilized low-order P1-P1 (linear velocity, linear pressure) mixed finite element method. The proposed node-based adaptive mesh generation method consists of four components: mesh size modification, a node placement procedure, a node-based local mesh generation strategy and an error estimation technique, which are combined so as to guarantee obtaining a conforming refined/coarsened mesh. The nodes are considered as particles with interaction forces, which are generated by dynamic simulation according to Newton’s second law of motion. Then the successive meshes in adaptive procedure are obtained by using Bubble-type Local Mesh Generation (BLMG) method. At each refinement level, the refining and coarsening are archived simultaneously by appropriately modifying the mesh size function, such that the resulting meshes can be refined in regions where the errors are relatively large and coarsened in regions where the errors are relatively small. Numerical results show that the nodebased adaptive strategy is applicable and efficient to approximate the true solution and detect local singularities in the flow problems
Geometrically Nonlinear Inelastic Analysis of Timoshenko Beams on Inelastic Foundation
Get PDFIn this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity (fiber) approach exploiting three-dimensional material constitutive laws and numerical integration over the cross-sections. An incremental–iterative solution strategy along with an efficient iterative process are employed, while the arising boundary value problem is solved employing the boundary element method. Numerical examples are worked out confirming the accuracy and the computational efficiency of the proposed beam formulation, as well as the significant influence of the geometrical nonlinearity and the shear deformation effect in the response of a beam-foundation system
Modeling Cell Spreading and Alignment on Micro-Wavy Surfaces
Get PDFMechanical behavior of cells plays a crucial role in response to external stimuli and environment. It is very important to elucidate the mechanisms of cellular activities like spreading and alignment as it would shed light on further biological concepts. In this study, a multi-scale computational approach is adopted by modeling the cytoskeleton of cell as a tensegrity structure. The model is based on the complementary force balance between the tension and compression elements, resembling the internal structure of cell cytoskeleton composed of microtubules and actin filaments. The effect of surface topology on strain energy of a spread cell is investigated by defining strain energy of the structure as the main criterion in the simulation process of the cell spreading. Spreading as a way to decrease internal energy toward a minimum energy state is the main hypothesis that is investigated. The cell model is placed at different positions along the wavy surface and the spreading and alignment behavior is observed. The implementation of the model illustrates the effect of topological factors on spreading and alignment of the cell. Experiments were conducted by seeding Bovine Aortic Endothelial Cells (BAECs) on poly (dimethylsiloxane) (PDMS) wavy surface to serve as a verification for the proposed model in the context of cellular behavior. Experimental observations are in general agreement with the computational results, which points out that the model can be explanatory in terms of understanding mechanical characteristics of cells
Hybrid Simulation and Observation of Human Vertebral Endplate Morphology
Get PDFFocal damage such as cartilaginous defects, erosions, micro-fractures, Schmorl nodes and thinning in the human vertebral endplate are thought to contribute to intervertebral disc degeneration by compromising the nutrition transport between the vertebral bone marrow and the disc nucleus pulposus. However, microfractures in the endplate are currently not detectable by conventional clinical radiographic methods. Nonetheless high quality visualisation of the human endplate is possible by means of advanced light microscopy and appropriate staining. The objective of this study focuses on efficient and inexpensive multi-scale protocols to prepare the surfaces of human endplate specimens for morphometric characterisations at the tissue and at the cell levels. Human vertebral endplate surfaces were observed under reflected and transmission light microscopy in the coronal, sagittal and transverse orientations. The observations were coupled to the relevant histological staining procedures for undecalcified and decalcified tissue samples to identify the following three regions: the intervertebral disc, the intervertebral cartilaginous and bony endplate, the subchondral and trabecular bone. At the tissue level, qualitative tissue identification based on relative stiffness was performed by nanoindentation. The mean±SD intervertebral endplate thickness was found to be 432.9±89.3 µm. At the cell level, a Fast Fourier Transform algorithm made it also possible to measure the orientation of chondrocytes in the cartilaginous endplate
Long-term Analyses of Concrete-Filled Steel Tubular Arches Accounting for Interval Uncertainty
Get PDFCreep and shrinkage of the concrete core of a concrete-filled steel tubular (CFST) arch under sustained loading are inevitable, and cause a long-term change of the equilibrium configuration of the CFST arch. As the equilibrium configuration changes continuously, the long-term radial and axial displacements of the CFST arch, stress distributions as well as the internal forces in the steel tube and the concrete core change substantially with time. Creep and shrinkage of the concrete core are related to a number of its material parameters such as its creep coefficient, aging coefficient, and shrinkage strain. The values of these parameters differ significantly from one experiment to another, highlighting that these parameters experience certain amounts of uncertainty, which needs to be considered in the long-term analysis of a CFST arch. Although stochastic methods can be used to account for such uncertainties, their statistical variations are presumed being known, which have to be inferred from laboratory tests. However, the available data from creep and shrinkage tests of the concrete core of CFST members are quite limited and scattered, and so the stochastic method is of little use. This paper presents a long-term analysis of CFST circular arches by accounting for interval uncertainties in these parameters by interval modelling, and derives the upper and lower bounds for the long-term structural responses. It is shown that the uncertainties of creep and shrinkage of the concrete core have significant long-term effects on the structural behaviour of CFST arches
Dynamic Anti-plane Crack Analysis in Functional Graded Piezoelectric Semiconductor Crystals
Get PDFThis paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It is noted that the stresses and electric displacement field in functionally graded piezoelectric semiconductors exhibit the same singularities at crack tips as in a homogeneous piezoelectric solid. The influence of the initial electron density on the intensity factors and energy release rate is also investigated
Analytical Models for Sliding Interfaces Associated with Fibre Fractures or Matrix Cracks
Get PDFAnalytical stress transfer models are described that enable estimates to be made of the stress and displacement fields that are associated with fibre fractures or matrix cracks in unidirectional fibre reinforced composites. The models represent a clear improvement on popular shear-lag based methodologies. The model takes account of thermal residual stresses, and is based on simplifying assumptions that the axial stress in the fibre is independent of the radial coordinate, and similarly for the matrix. A representation for both the stress and displacement fields is derived that satisfies exactly the equilibrium equations, the required interface continuity equations for displacement and tractions, and all stress-strain equations except for the one that relates to axial deformation. In addition, the representation is such that the Reissner energy functional has a stationary value provided that averaged axial stress-strain relations for the fibre and matrix are satisfied. The improved representation is fully consistent with variational mechanics and provides both the stress and displacement distributions in the fibre and the matrix. For isolated or interacting fibre fractures or matrix cracks, interface sliding is considered where two types of condition are investigated. Firstly, it is assumed that the shear stress is uniform within the sliding region, and a small transition zone is included in the model in order that essential zero traction conditions can be satisfied on the crack surfaces. Secondly, it is assumed that stress transfer in the sliding region is controlled by Coulomb friction. Illustrative predictions are made for an example polymer composite, although the methodology presented is equally applicable to other types of composite (e.g. metal and ceramic matrix composites)
Forced Vibration of the Pre-Stressed and Imperfectly Bonded Bi-Layered Plate Strip Resting on a Rigid Foundation
Get PDFWithin the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the influence of the shear-spring type imperfection of the contact conditions between the layers of the pre-stressed bi-layered plate strip resting on the rigid foundation, on the frequency response of this plate strip is investigated. The corresponding mathematical problem is solved numerically by employing FEM and numerical results illustrating the influence of the parameter characterizing the degree of the mentioned imperfectness, on the frequency response of the normal stress acting on the interface planes between the layers and between the plate and rigid foundation are presented and discussed. In particular, it is established that an increase in the value of the shear-spring parameter the absolute values of the compressed normal stress decrease, but the values of the stretched normal stress increase and this parameter has an influence also on the character of the action of the initial stresses on the frequency response under consideration
The Cell Method: an Enriched Description of Physics Starting from the Algebraic Formulation
Get PDFIn several recent papers studying the Cell Method (CM), which is a numerical method based on a truly algebraic formulation, it has been shown that numerical modeling in physics can be achieved even without starting from differential equations, by using a direct algebraic formulation. In the present paper, our focus will be above all on highlighting some of the theoretical features of this algebraic formulation to show that the CM is not simply a new numerical method among many others, but a powerful numerical instrument that can be used to avoid spurious solutions in computational physics
Bandgap Opening in Metallic Carbon Nanotubes Due to Silicon Adatoms
Get PDFControlling the bandgap of carbon nanostructures is a key factor in the development of mainstream applications of carbon-based nanoelectronic devices. This is particularly important in the cases where it is desired that the carbon nanostructures are the active elements, as opposed to being the conductive leads between other elements of the device. Here, we report density functional theory calculations of the effect of silicon impurities on the electronic properties of carbon nanotubes (CNTs). We have found that Si adatoms can open up a bandgap in intrinsically metallic CNTs, even when the linear density of Si atoms is low enough that they do not create an adatom chain along the tube. The bandgap opened in metallic CNTs can range up to approximately 0.47 eV, depending on adsorption site, on the linear density of Si adatoms, and on the chirality of the nanotube. We have found that a lower spatial symmetry of the charge transfer between adatom and CNT leads to a higher value of the bandgap opened, which indicates that the physical origin of the bandgap lies in the reduced spatial symmetry of the charge transferred