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How to Select the Value of the Convergence Parameter in the Adomian Decomposition Method
Get PDFIn this paper, we investigate the problem of selecting of the convergence parameter c in the Adomian decomposition method. Through the curves of the n-term approximations Φn(t;c) versus c for different specified values of n and t, we demonstrate how to determine the value of c such that the decomposition series has a larger effective region of convergence
Axisymmetric and 3-D Numerical Simulations of the Effects of a Static Magnetic Field on Dissolution of Silicon into Germanium
Get PDFNumerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a static magnetic field increased the amount of silicon transported into the melt. The magnetic field also induced a change in dissolution interface shape. This change indicates a change in flow structure in the melt. Both simulation models (axisymmetric and 3-D) predicted this change in flow structure.
In the absence of magnetic field, a flat and stable interface was observed in the experiments. In the presence of an applied field, the dissolution interface remains flat in the center but curves back into the source material near the wall. The application of the magnetic field gave rise to higher dissolution of silicon near the crucible wall. This enhanced dissolution near the wall was well predicted by the present 3-D simulation model, but not by the axisymmetric model. This indicates that this effect was due to the three-dimensionality of the melt flow
Symmetric Coupling of the Meshless Galerkin Boundary Node and Finite Element Methods for Elasticity
Get PDFCombining moving least square (MLS) approximations and boundary integral equations, a symmetric and boundary-only meshless method, the Galerkin boundary node method (GBNM), is developed in this paper for two- and threedimensional elasticity problems with mixed boundary conditions. Unlike other MLS-based meshless methods, boundary conditions in this meshless method can be applied directly and easily. In the GBNM, the stiffness matrices so obtained are symmetric. The property of symmetry is an added advantage in coupling the GBNM with the finite element method (FEM). Thus, a symmetric coupling of the GBNM and the FEM is also discussed for elasticity problems. Error analysis and convergence study of the GBNM and the coupled GBNM-FEM are given in Sobolev spaces. For demonstration purpose, some numerical examples are presented
Design Evaluation of a Particle Bombardment System Used to Deliver Substances into Cells
Get PDFThis work deals with the bombardment of a stream of particles possessing varying mean particle size, velocity and aspect ratio into a cell that has fixed (known) compliance characteristics. The particles are intended to penetrate the cell membrane causing zero or minimum damage and deliver foreign substances (which are attached to their surfaces) to the interior of the cell. We adopt a particle-based (discrete element method) computational model that has been recently developed by the authors to describe both the incoming stream of particles and the cell membrane. By means of parametric numerical simulations, treating the stream’s mean particle size, velocity and aspect ratio as random variables, we explore the synergy between these parameters and identify basic trends as to how changes in the input parameters affect the output results, and as to what are the best combinations of parameter values that lead to (i) the highest amount of particle delivery and (ii) the lowest level of membrane damage. Conclusions are drawn on this regard based on statistical assessment of the simulations results. Computational particle-based models render reliable and fast simulation tools. We believe they can be very useful to help advance the design of particle bombardment systems
A New Multi-objective Reliability-based Robust Design Optimization Method
Get PDFA new multi-objective reliability-based robust design optimization (M ORBRDO) model is proposed which integrats the multi-objective robustness, the reliability sensitivity robustness and the six sigma robustness design idea. The pure-quadratic polynomial functions are adopted to fit the performance objective functions (POF) and the ultimate limited state functions (ULSF) of the structure. Based on the ULSF and the checking point method, the equations of the first order reliability index are calculated. The mapping transformation method is employed when the non-normal distribution variables are included. According to the POF and the Taylor series expansion method, the equations of mean value and standard deviation of the performance objectives are deduced. In order to improve the efficiency of MORBRDO, a new reliability based design optimization strategy is proposed. The new strategy does not update the ULSF in the sub-cycle of reliability calculation process, so that the computational work is reduced remarkably. Then, the optimum design was obtained with the sequential quadratic programming method. Finally, three engineering projects, a I-beam structure, a pressure vessel and the turbine blade model lines are introduced to redesign their sizes by the new MORBRDO methodology proposed in this paper. The results prove that the new MORBRDO model and methods are correct, feasible and efficient, so it is valuable theoretically and applicative in engineering
Nonlinear Panel Flutter Analysis Based on an Improved CFD/CSD Coupled Procedure
Get PDFNonlinear aeroelasticity, caused by the interaction between nonlinear fluid and geometrically nonlinear structure, is studied by an improved CFD and CSD coupled program. An AUSMpw+ flux splitting scheme, combined with an implicit time marching technology and geometric conservation law, is utilized to solve unsteady aerodynamic pressure; The finite element co-rotational theory is applied to model geometrically nonlinear two-dimensional and three-dimensional panels, and a predictor-corrector program with an approximately energy conservation is developed to obtain nonlinear structure response. The two solvers are connected by Farhat’s second order loosely coupled method and the aerodynamic loads and structural displacements are transferred by boundary element method. With the application on the solution of panel flutter problems for supersonic, transonic and subsonic Mach numbers, representative limited cycle oscillations appear when geometric nonlinearity and aerodynamic nonlinearity are considered. The flutter boundary and amplitude of limit cycle oscillation are discussed and compared with the work of Dowell and Gordnier. The program is also used to compute the nonlinear elastic response of AGARD 445.6 wing, and the results show that improved procedure presents a better stability than conventional method
Stochastic Finite Element Method Reliability Analysis of the Corrugated I-beam Girder
Get PDFThe main issue in this paper is to present stochastic analysis of the steel plate girder with the corrugated web subjected to Gaussian random fluctuations in its web thickness. Such an analysis is carried out using the Stochastic Finite Element Method based on the generalized stochastic perturbation technique and discretization of structure with the quadrilateral 4-noded shell finite elements. It is numerically implemented using the FEM system ABAQUS and the symbolic algebra system MAPLE, where all the probabilistic procedures are programmed. We compare the perturbation-based results with these obtained from traditional Monte-Carlo simulation and, separately, analytical solution calculated by a symbolic integration carried out in MAPLE. We calculate probabilistic characteristics of up to the fourth order for the static deformations and stresses, critical loads and eigenfrequencies to verify their distributions affected by the Gaussian dispersion of the web thickness itself resulting from an extensive corrosion, for instance. The reliability index for deformations is calculated according to the First Order Reliability Method (FORM) and can be further used in durability prediction of such structures
Numerical Study on Mechanical Properties of Steel Fiber Reinforced Concrete by Statistical Second-order Two-scale Method
No full textThe present study aims to evaluate the mechanical properties of steel fiber reinforced concrete (SFRC) by the statistical second-order two-scale (SSOTS) method. At first, the representation for microstructure of SFRC is described by a concept of statistical screen. According to the microstructure representation, the SSOTS method is displayed in a concise way. This method is on the basis of asymptotic expansion homogenization and Monte Carlo method, and can calculate the local strain and stress field through the two-order displacement solution. As the classical homogenization method, the expression of homogenized elastic modulus is derived analytically. Then combined with the appropriate strength criterion and correspondence principle, the homogenized strength and viscoelastic properties of SFRC are obtained respectively. The validity of the SSOTS method is confirmed by the comparison between numerical results and the available experiment data. Results show that the SSOTS method is effective to evaluate the elastic, strength and viscoelastic properties of SFRC. In addition, the influence of distribution of steel fibers on the macroscopic mechanical properties of SFRC is discussed
Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method
Get PDFIn this paper, we construct the Lane–Emden–Fowler type equations of higher orders. We study the linear and the nonlinear Lane–Emden–Fowler type equations of the third and fourth orders, where other forms can be treated in a similar manner. We use the systematic Adomian decomposition method to handle these types of equations with specified initial conditions. We confirm that the Adomian decomposition method provides an efficient algorithm for exact and approximate analytic solutions of these equations. We corroborate this study by investigating several numerical examples that emphasize initial value problems
A Regularized Method of Fundamental Solutions for 3D and Axisymmetric Potential Problems
Get PDFThe Method of Fundamental Solutions (MFS) is investigated for 3D potential problem in the case when the source points are located along the boundary of the domain of the original problem and coincide with the collocation points. This generates singularities at the boundary collocation points, which are eliminated in different ways. The (weak) singularities due to the singularity of the fundamental solution at the origin are eliminated by using approximate but continuous fundamental solution instead of the original one (regularization). The (stronger) singularities due to the singularity of the normal derivatives of the fundamental solution are eliminated by solving special auxiliary subproblems (desingularization). The desingularization idea is similar to a previously published technique and is completely independent of the applied regularization technique. The presented method produces well-conditioned or moderately ill-conditioned matrices in the resulting linear system of algebraic equations, while the accuracy remains acceptable. No boundary mesh structure is needed. The method is generalized to 3D axisymmetric potential problems in a natural way, despite in this case the fundamental solution does not remain a radial function. The use of extremely ill-conditioned matrices is still avoided