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Hybrid Elements for Modelling Squeeze Film Effects Coupled with Structural Interactions in Vibratory MEMS Devices
Get PDFWe present a hybrid finite element based methodology to solve the coupled fluid structure problem of squeeze film effects in vibratory MEMS devices, such as gyroscopes, RF switches, and 2D resonators. The aforementioned devices often have a thin plate like structure vibrating normally to a fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping. For accurate modelling of such devices the squeeze film effects must be incorporated. Extensive literature is available on squeeze film modelling, however only a few studies address the coupled fluid elasticity problem. The majority of the studies that account for the plate elasticity coupled with the fluid equation, either use approximate mode shapes for the plate or use iterative solution strategies. In an earlier work we presented a single step coupled methodology using only one type of displacement based element to solve the coupled problem. The displacement based finite element models suffer from locking issues when it comes to modelling very thin structures with the lateral dimensions much larger than the plate thickness as is typical in MEMS devices with squeeze film effects. In this work we present another coupled formulation where we have used hybrid elements to model the structural domain. The numerical results show a huge improvement in convergence and accuracy with coarse hybrid mesh as compared to displacement based formulations. We further compare our numerical results with experimental data from literature and find them to be in good accordance
Construction of an Edge Finite Element Space and a Contribution to the Mesh Selection in the Approximation of the Second Order Time Harmonic Maxwell System
Get PDFThis work is concerned with the development of the so-called Whitney and Nédélec edge finite element method for the solution of the time-harmonic Maxwell equations. Initially, the second order time harmonic Maxwell systems, as well as their variational formulation, are presented. In the sequence, Whitney and Nédélec element spaces, whose functions present continuous tangential components along the interface are built of adjacent elements. Then, numerical experiments validate the performance of Whitney and Nédélec first order elements in a two-dimensional domain. The discrete dispersion relation for the elements shows that the numerical phase velocity can be used as an error estimator. Consequently, it becomes possible to define an initial parameter to the mesh refinement that, by its turn, can make the phase difference negligible
Titin (Visco-) Elasticity in Skeletal Muscle Myofibrils
Get PDFTitin is the third most abundant protein in sarcomeres and fulfills a number of mechanical and signaling functions. Specifically, titin is responsible for most of the passive forces in sarcomeres and the passive visco-elastic behaviour of myofibrils and muscles. It has been suggested, based on mechanical testing of isolated titin molecules, that titin is an essentially elastic spring if Ig domain un/refolding is prevented either by working at short titin lengths, prior to any unfolding of Ig domains, or at long sarcomere (and titin) lengths when Ig domain un/refolding is effectively prevented. However, these properties of titin, and by extension of muscles, have not been tested with titin in its natural structural environment within a sarcomere. The purpose of this study was to gain insight into the Ig domain un/refolding kinetics and test the idea that titin could behave essentially elastically at any sarcomere length by preventing Ig domain un/refolding during passive stretch-shortening cycles. Although not completely successful, we demonstrate here that titin’s visco-elastic properties appear to depend on the Ig domain un/refolding kinetics and that indeed, titin (and thus myofibrils) can become virtually elastic when Ig domain un/refolding is prevented
Effects of Equiaxial Strain on the Differentiation of Dental Pulp Stem Cells without Using Biochemical Reagents
Get PDFDuring orthodontic treatments, applied mechanical forces create strain and result in tooth movement through the alveolar bone. This response to mechanical strain is a fundamental biological reaction. The present study evaluated the effect of equiaxial strain within the range of orthodontic forces on the osteogenic differentiation of human dental pulp stem cells (hDPSCs). Following isolation and culture of hDPSCs, 3rd passage cells were transferred on a silicone membrane covered with collagen. Cell adhesion to the membrane was evaluated under scanning electron microscope (SEM). Cells were divided into three groups: the first group was placed in a conventional culture medium, transferred to an equiaxial stretching device (3% strain for 2 weeks). The positive control was placed in an osteogenic medium with no mechanical strain. The negative control group was placed in the conventional culture medium with no mechanical strain either. Study groups were evaluated for expression of osteogenic markers (Alkaline phosphatase and Osteopontin) with immunofluorescence and real time PCR. SEM images revealed optimal adhesion of cells to the silicone membrane. Immunofluorescence study demonstrated that osteocalcin expression occurred after 2 weeks in the two groups under mechanical and chemical signals. After application of equiaxial strain, level of expression of osteogenic markers was significantly higher than in the negative and positive control groups. Based on the study results, static equiaxial strain which mimics the types of orthodontic forces can result in differentiation of hDPSCs to osteoblasts. The results obtained may be used in cell therapy and tissue engineering
Fluid Structure Modelling of Blood Flow in Vessels
Get PDFThis paper describes the capabilities of fluid structure interaction based multi-physics numerical modelling in solving problems related to vascular biomechanics. In this research work, the onset of a pressure pulse was simulated at the entrance of a three dimensional straight segment of the blood vessel like circular tube and the resulting dynamic response in the form of a propagating pulse wave through the wall was analysed and compared. Good agreement was found between the numerical results and the theoretical description of an idealized artery. Work has also been done on implementing the material constitutive models specific for vascular applications
Effect of Gravitational Field and Temperature Dependent Properties on Two-Temperature Thermoelastic Medium with Voids under G-N Theory
No full textThis investigation is aimed to study the two dimensional problem of thermoelastic medium with voids under the effect of the gravity. The modulus of elasticity is taken as a linear function of the reference temperature and employing the two-temperature generalized thermoelasticity. The problem is studied in the context of Green-Naghdi (G-N) theory of types II and III. The normal mode analysis method is used to obtain the exact expressions for the physical quantities which have been shown graphically by comparison between two types of the (G-N) theory in the presence and the absence of the gravity, the temperature dependent properties and the two-temperature effect
Constitutive Modeling of Early-Age Concrete by a Stochastic Multi-scale Method
Get PDFA nonlinear viscoelastic constitutive model for early age concrete is presented in this paper. In this model, time-dependent properties, such as the elastic modulus, and thermal and autogenous shrinkage deformations, are computed by a stochastic multi-scale method, in which three different scales are specified according to the requirement of separation of scales, and different scales are linked by means of the asymptotic expansion theory with the help of specific representative volume elements (RVE). Thus, a cross-scale research from the cement paste to the macro structure of concrete is realized, and performance-based optimization of cement-based materials becomes possible. The developed constitutive model is implemented in commercial finite element software. Then, by means of a comparative study involving a numerical simulation and a full-scale experiment of a segment of the Hong Kong-Zhuhai-Macao immersed tunnel to obtain the temperature field and the strain field, the proposed constitutive model is validated. Thus a completely cross-scale constitutive model from the cement paste to the macro structure of concrete is realized, avoiding a variety of non-standardized and highly specialized test methods for concrete. After that, the stress field of the structure is analyzed. It is a prerequisite for structural analysis aimed at the investigation of cracking. Finally, taking different kinds of cement and aggregate as example, combinatorial optimization of material is conducted. And it is concluded that the type of cement and aggregate has an important influence on the early-age performance of investigated immersed tunnel. P.O.42.5 cement and limestone appears to be a good choice for control of cracking in engineering practice
Numerical Solution of System of N–Coupled Nonlinear Schrödinger Equations via Two Variants of the Meshless Local Petrov–Galerkin (MLPG) Method
Get PDFIn this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the MLS approximation have kronecker delta property. Also, we implement the local meshless Petrov-Galerkin (MLPG) and local RPIM (LRPIM) techniques for obtaining two full discretization schemes for the numerical solution of the mentioned equation in the two-dimensional case. In the meshless local weak forms for obtaining an approximate solution for the node i in every sub-domain we use the shape functions of the moving least squares (MLS) and RPIM meshless approximations. The main aim of this paper is to show that the meshless methods based on the global form i.e. radial basis functions collocation method and local weak form i.e. MLPG and LRPIM techniques are also simple in implementation and suitable for the treatment of the system of coupled nonlinear Schrödinger equations. We show that the RBFs collocation scheme provides a simple implementation for computing long-range solitary solutions considered by coupled nonlinear Schrödinger equations and the conserved quantities mass and energy almost are constant. Of course selecting small enough time step, obtains conserved quantities which are exactly fixed. Also several test problems including the two-dimensional case are given and numerical simulations are reported. We compare the obtained numerical results with together. The numerical results confirm the efficiency of the proposed schemes
Investigation of Squeezing Unsteady Nanofluid Flow Using the Modified Decomposition Method
Get PDFIn this paper, we use the modified decomposition method (MDM) to solve the unsteady flow of a nanofluid squeezing between two parallel equations. Copper as nanoparticle with water as its base fluid has considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell- Garnetts (MG) and Brinkman models, respectively. The effects of the squeeze number, the nanofluid volume fraction, Eckert number, δ on Nusselt number and the Prandtl number are investigated. The figures and tables clearly show high accuracy of the method to solve the unsteady flow
A Corrected 3D Parallel SPH Method for Simulating the Polymer Free Surface Flows Based on the XPP Model
Get PDFIn this work, a corrected three-dimensional smoothed particle hydrodynamics (CSPH-3D) method is proposed to simulate the polymer free surface flows in the filling process based on the eXtended Pom-Pom (XPP) model, and some complex deformation phenomena are also numerically predicted. The proposed CSPH-3D method is mainly motivated by a coupled concept that an extended kernel-gradient-corrected SPH (KGC-SPH) method is used in the interior of fluid flow and the traditional SPH (TSPH) method is used near the boundary domain. The present 3D particle method has higher accuracy and better stability than the TSPH-3D method. Meanwhile, a density diffusive term is introduced to restrain the pressure oscillations, and a new boundary treatment is proposed to deal with multi-complex-wall-boundaries, which is effective and convenient for enforcing. Moreover, the MPI parallelization means with a dynamic cells neighbor particle search method is also adopted for enhancing the computational efficiency. The advantages and ability of the present method combined with other techniques are first demonstrated by several bench tests and compared with other results. Then the filling processes confined in two type containers based on the XPP fluid are simulated using the proposed CSPH-3D method, which including the filling with two-inlets in a rectangle container and the complex filling of die casting in a ring container. Some interesting phenomena are observed for example the jet coiling and race track effect, and the shear thinning behavior of XPP fluid is also shown. Finally, the influences of macroscopic rheological parameters on the deformation of complex filling process are numerically predicted and analyzed