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The crystal plastic theory was used to examine the effect of film-cooling hole arrangements on mechanical properties of cooled turbine blade. The finite element method was used to analyze the maximum von Mises stress and resolved shear stress of an octahedral slip system considering the number of rows, diameter, spacing, and tangential-to-longitudinal hole spacing (h/l) ratio. The different arrangements were found to have a significant influence on the maximum von Mises stress and resolved shear stress. For the triangular arrangement, the von Mises stress and resolved shear stress were highest with double rows, followed by a single row and then triple rows. For the quadrilateral arrangement, the stresses were highest with double rows, followed by triple rows and then a single row. Increasing the spacing or decreasing the diameter reduced the maximum von Mises stress and weakened the multi-hole interference effect. Both the maximum von Mises stress and resolved shear stress decreased with the h/l ratio.
In this study, continuous contact problem in the functionally graded (FG) layer loaded with two rigid flat blocks resting on the elastic semi-infinite plane was analyzed by the finite element method. The two-dimensional numerical model of the FG layer was made with the software added to the ANSYS program. This software can be adapted to all contact problem types by making minor changes. The accuracy check of the program was performed by comparing with the analytical solution of the problem by homogeneous layer and its solution by the finite element method. So, fast and practical solutions can be obtained by the developed finite element method on many applications such as; automotive, aviation and space industry applications. The comparisons made showed that the proposed solution gave good results at acceptable levels. In the problem, it was thought that all surfaces were frictionless. The external loads P and Q were transmitted to the FG layer via two flat rigid blocks. Normal stresses between the FG layer and the elastic plane, initial separation loads, initial separation distances and contact stresses under the blocks were investigated for various dimensionless quantities.
This chapter covers the computation of synthetic seismograms, or theoretical seismograms. This involves predicting, via computation, what seismic traces might look like for a given subsurface medium model. The relatively simple case of vertically traveling waves in a sequence of flat horizontal layers is discussed in relative detail, including how to compute wave amplitude losses due to reflection, transmission, geometrical spreading of wavefronts, and absorption. The generally more complicated case of nonvertically traveling waves is also briefly summarized. More complete methods such as the finite difference and finite element methods are briefly mentioned. Also covered are the reflectivity function and the interference effects that occur for waves with nearly equal arrival times, such as the tuning effect. The chapter ends with an appendix showing examples of synthetic seismograms computed with the finite difference method.
This paper describes a method to analyze open or closed elliptical structures with constant axial ratio by a Body-of-Revolution (BoR) Finite Element Method (FEM). The method is based on Transformation Optics, a coordinate transformation that maps the elliptical shape to a circular shape, for which BoR-FEM represents a greatly efficient tool for the analysis.
Surface exfoliation was observed on single-crystal silicon surface under the action of compressed plasma flow (CPF). This phenomenon is mainly attributed to the strong transient thermal stress impact induced by CPF. To gain a better understanding of the mechanism, a micro scale model combined with thermal conduction and linear elastic fracture mechanics was built to analyze the thermal stress distribution after energy deposition. After computation with finite element method, J integral parameter was applied as the criterion for fracture initiation evaluation. It was demonstrated that the formation of surface exfoliation calls for specific material, crack depth, and CPF parameter. The results are potentially valuable for plasma/matter interaction understanding and CPF parameter optimization.
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The 𝕄-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. In addition to mesh adaptation, preservation of the maximum principle is also studied. Some new sufficient conditions for maximum principle preservation are developed, and a mesh quality measure is defined to server as a good indicator. Four different metric tensors are investigated: one is the identity matrix, one focuses on minimizing an error bound, another one on preservation of the maximum principle, while the fourth combines both. Numerical examples show that these metric tensors serve their purposes. Particularly, the fourth leads to meshes that improve the satisfaction of the maximum principle by the finite element solution while concentrating elements in regions where the error is large. Application of the anisotropic mesh adaptation to fractured reservoir simulation in petroleum engineering is also investigated, where unphysical solutions can occur and mesh adaptation can help improving the satisfaction of the maximum principle.
This paper is devoted to the American option pricing problem governed by the Black-Scholes equation. The existence of an optimal exercise policy makes the problem a free boundary value problem of a parabolic equation on an unbounded domain. The optimal exercise boundary satisfies a nonlinear Volterra integral equation and is solved by a high-order collocation method based on graded meshes. This free boundary is then deformed to a fixed boundary by the front-fixing transformation. The boundary condition at infinity (due to the fact that the underlying asset's price could be arbitrarily large in theory), is treated by the perfectly matched layer technique. Finally, the resulting initial-boundary value problems for the option price and some of the Greeks on a bounded rectangular space-time domain are solved by a finite element method. In particular, for Delta, one of the Greeks, we propose a discontinuous Galerkin method to treat the discontinuity in its initial condition. Convergence results for these two methods are analyzed and several numerical simulations are provided to verify these theoretical results.
The pricing model for American lookback options can be characterised as a two-dimensional free boundary problem. The main challenge in this problem is the free boundary, which is also the main concern for financial investors. We use a standard technique to reduce the pricing model to a one-dimensional linear complementarity problem on a bounded domain and obtain a corresponding variational inequality. The inequality is discretised by finite differences and finite elements in the temporal and spatial directions, respectively. By enforcing inequality constraints related to the options using Lagrange multipliers, the discretised variational inequality is reformulated as a set of semi-smooth equations, which are solved by a primal-dual active set method. One of the major advantages of our algorithm is that we can obtain the option values and the free boundary simultaneously, and numerical simulations show that our approach is as efficient as some other methods.
We provide some computable error estimates in solving a nonsymmetric eigenvalue problem by general conforming finite element methods on general meshes. Based on the complementary method, we first give computable error estimates for both the original eigenfunctions and the corresponding adjoint eigenfunctions, and then we introduce a generalised Rayleigh quotient to deduce a computable error estimate for the eigenvalue approximations. Some numerical examples are presented to illustrate our theoretical results.
This paper is concerned with numerical method for a two-dimensional time-dependent cubic nonlinear Schrödinger equation. The approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time, respectively. We prove optimal L2 error estimates for two fully discrete schemes by using elliptic projection operator. Finally, a numerical example is provided to verify our theoretical results.
Hill’48 yield function has been widely used to describe the anisotropic behaviors of material in FE simulation of tube and sheet metal forming process. To obtain the material behaviors of small-sized H96 brass extrusion double-ridged rectangular tube (DRRT) in bending process, an inverse method combining response surface method and three-point bending was proposed to identify the parameters of Hill’48 yield function. It was found that comparing with Hill’48 yield function only considering the normal anisotropy and Mises yield function, Hill’48 yield function with the identified parameters performs the best in reproducing the material behavior of H96 brass DRRT in three-point bending process. And then Hill’48 yield function with the identified parameters was also adopted in the FE simulations of rotary draw bending of DRRT. It was observed that the prediction accuracy of cross sectional deformation of DRRT in rotary bending process was improved effectively by using Hill’48 yield function with the identified parameters. This proves that the proposed inverse method is suitable to the real forming process.
In this article, by applying the Stokes projection and an orthogonal projection with respect to curl and div operators, some new error estimates of finite element method (FEM) for the stationary incompressible magnetohydrodynamics (MHD) are obtained. To our knowledge, it is the first time to establish the error bounds which are explicitly dependent on the Reynolds numbers, coupling number and mesh size. On the other hand, The uniform stability and convergence of an Oseen type finite element iterative method for MHD with respect to high hydrodynamic Reynolds number Re and magnetic Reynolds number Rm, or small δ=1–σ with
(C0, C1 are constants depending only on Ω and F is related to the source terms of equations) are analyzed under the condition that . Finally, some numerical tests are presented to demonstrate the effectiveness of this algorithm.
In this paper, we propose a finite element method for the elasticity problems which have displacement discontinuity along the material interface using uniform grids. We modify the immersed finite element method introduced recently for the computation of interface problems having homogeneous jumps [20, 22]. Since the interface is allowed to cut through the element, we modify the standard Crouzeix-Raviart basis functions so that along the interface, the normal stress is continuous and the jump of the displacement vector is proportional to the normal stress. We construct the broken piecewise linear basis functions which are uniquely determined by these conditions. The unknowns are only associated with the edges of element, except the intersection points. Thus our scheme has fewer degrees of freedom than most of the XFEM type of methods in the existing literature [1,8,13]. Finally, we present numerical results which show optimal orders of convergence rates.
The metadynamic recrystallization (MDRX) behavior of a Nb–V microalloyed nonquenched and tempered steel was investigated by isothermal hot compression tests on Gleeble-1500 thermal-mechanical simulator. Compression tests were performed using double hit schedules at temperatures of 1273–1423 K, strain rates of 0.01–5 s−1, initial grain sizes of 92–149 μm and an inter-pass time of 0.5–10 s. The experimental results show that MDRX softening fraction increases with the increasing of deformation temperature, strain rate, and inter-pass time, while it decreases with the increasing of initial grain size. Based on the experimental results, the MDRX softening fraction kinetic model and recrystallized grain size model of the tested steel was established. Besides, using the above mathematic models, a finite element model was built to simulate the MDRX process of the tested steel. The simulation results show good agreement with the experimental ones, which indicates that finite element method is an effective approach to analyze the MDRX behavior and the established that mathematic models of the tested steel are reliable and accurate.
Among the different energy storage technologies under study, lithium–oxygen batteries are one of the most promising due to their great gravimetric energies and capacities 6–10 times greater than other technologies such as conventional lithium-ion cells. The current study provides a comprehensive understanding of how the anodic (e.g., dendrites) and cathodic designs (e.g., porosity of the carbon cathode and mass fraction of oxygen) affect the discharge characteristics of lithium–oxygen cells. When comparing all changes in dendrite surface, porosity and oxygen restriction, it is concluded that although the changes in porosity and oxygen decrease the performance of the cells, the dendrites led to the greatest decrease in performance of the battery when examining the capacity of the cell. This comprehensive understanding will aid in the design of a cyclable and commercially viable lithium–oxygen battery that could be used for a wide range of energy storage applications.
In this paper, the compressive behaviors of Zr-based bulk metallic glass (BMG) were experimentally studied under different testing conditions. To deeply reveal the inherent deformation mechanisms, numerical study was systematically conducted to analyze the shear banding evolution in BMGs, and the effect of testing machine stiffness, contact friction, and sample parallelism on the compressive ductility was therefore elucidated. Among them the effect of contact friction was carefully studied experimentally and the inherent deformation mechanisms was numerically analyzed in terms of the formation of shear bands. Free-volume theory was incorporated into ABAQUS finite element method code as a user material subroutine UMAT. The numerical method was firstly compared with the corresponding experimental results, and then parameter analyses were performed to discuss the impacts of testing conditions on the malleability of the BMG samples. The present work will shed some light on the interpretation of failure mechanisms in BMGs under different loading conditions.
ArbiTER (Arbitrary Topology Equation Reader) is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models. The primary application area envisioned is boundary plasma physics in magnetic confinement devices; however ArbiTER should be applicable to other science and engineering fields as well. The code permits a variable numbers of dimensions, making possible application to both fluid and kinetic models. The use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.
Since last decades, microwaves have received tremendous attention as an interesting tool for material characterization. In general, standard microwave measurement methods require cutting and polishing of samples to put it in a suitable waveguide or cavity. However, several methods have been developed in order to permit a non-destructive measurement. A well-known method is based on coaxial open-ended waveguide, which is used as a sensor for dielectric characterizations. Moreover, with the requirement of new forms, developing mathematical model for each one is not convenient. Indeed, the complex structures required in the industrial field can be perfectly designed with high-performance three-dimensional software. Many attempts have been done to solve the conversion problem by proposing different algorithms. Nevertheless, they are sensitive for complex structure that contains transition part. In this paper, we propose a dielectric measurement method based on the use of coaxial waveguide. A novel algorithm for dielectric characterization of complex structures is also presented, which is based on the joint use of artificial neuronal networks and finite element method. The proposed algorithm aims to find the dielectric characterization for complex structures. Experimental evaluations applied to solid and liquid dielectrics confirm the validation of the proposed algorithm.
A multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value problems. In this scheme, obtaining the optimal approximation for the ground state solution of Bose-Einstein condensates includes a sequence of solutions of the linear boundary value problems by the multigrid method on the multilevel meshes and some solutions of nonlinear eigenvalue problems some very low dimensional finite element space. The total computational work of this scheme can reach almost the same optimal order as solving the corresponding linear boundary value problem. Therefore, this type of multigrid scheme can improve the overall efficiency for the simulation of Bose-Einstein condensations. Some numerical experiments are provided to validate the efficiency of the proposed method.
We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.