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Mixed-mode Fracture Mechanics Analysis of Large-scale Cracked Structures Using Partitioned Iterative Coupling Method
No full textFor large-scale fracture mechanics simulation, a partitioned iterative coupling method is investigated. In this method, an analysis model is decomposed into two domains, which are analyzed separately. A crack is introduced in one small domain, whereas the other large domain is a simple elastic body. Problems concerning fracture mechanics can be treated only in the small domain. In order to satisfy both geometric compatibility and equilibrium on the domain boundary, the two domains are analyzed repeatedly using an iterative solution technique. A benchmark analysis was performed in order to validate the method and evaluate its computational performance. The computed stress intensity factors were as accurate as those obtained using the conventional method and the theoretical solution, and the computational performance was comparable. Based on a benchmark, a cracked structural component model having three million degrees of freedom was analyzed. Mode-I, mode-II, and mode-III stress intensity factors were successfully obtained after several iteration steps
Computer Modeling Chemical Vapor Infiltration of SiC Composites
No full textA novel multiphase field model is formulated to simulate the complex microstructure evolution during chemical vapor infiltration (CVI) process, which is widely used technique to produce SiC matrix composites reinforced by SiC fibers in ceramic engineer. The model consists of a set of nonlinear partial differential equations by coupling Ginzburg-Landau type phase field equations with mass/heat balance equations as well as modified Navier-Stokes equations. The microstructure evolution of preferential codeposition of Si, SiC and C under high ratio of H2 to MTS is simulated. The simulation is in good agreement with experiments result. The potential risk of blockage of the premature pores is predicted. By investigating the effect of gas flow and chemical reaction on concentration field of MTS, it is found that the gas flow is in favor of the homogeneous distribution of MTS while this distribution is mainly dominated by chemical reaction. Meanwhile, the effect of thermal gradient on CVI process is investigated
Cauchy Problem for the Laplace Equation in 2D and 3D Doubly Connected Domains
No full textIn this paper, we propose an algorithm to solve a Cauchy problem of the Laplace equation in doubly connected domains for 2D and 3D cases in which the Cauchy data are given on the outer boundary. We want to seek a solution in the form of the single-layer potential and discrete it by parametrization to yield an ill-conditioned system of algebraic equations. Then we apply the Tikhonov regularization method to solve this ill-posed problem and obtain a stable numerical solution. Based on the regularization parameter chosen suitably by GCV criterion, the proposed method can get the approximate temperature and heat flux on the inner boundary. Numerical examples illustrate that the proposed method is reasonable and feasible
A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations
Get PDFA wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. To justify the present method, the coupled viscous Burgers’ equations are solved as examples, results demonstrate that the proposed wavelet algorithm have a much better accuracy and efficiency than many existing numerical methods, and the order of convergence of such a wavelet method can even reach about 5
Numerical Simulation of 2-D Transversal SeismicWaves by Network Method
Get PDFIn this paper, the propagation of 2-D, transversal elastic waves is simulated by using the network method. The spatially discretized wave equation is the basis for designing the model of the volume element which contains as many components as addends in the governing equation. The whole network model, including the boundary conditions, is run in a suitable circuit simulation code such as PSpice with a relatively small computational time. The rules for the design are very few since there is a special component in the libraries of such codes, named controlled source, that is capable of implementing any kind of non-linearity or coupled term in the equation. The design routines as well as those required for the subsequent post-processing of output data are carried out by MATLAB. After the study and simulation of a standard case, in order to compare the network solutions with those obtained by the finite-difference explicit method, two problems are presented using the known Ricker pulse as excitation
GDQFEM Numerical Simulations of Continuous Media with Cracks and Discontinuities
Get PDFIn the present paper the Generalized Differential Quadrature Finite Element Method (GDQFEM) is applied to deal with the static analysis of plane state structures with generic through the thickness material discontinuities and holes of various shapes. The GDQFEM numerical technique is an extension of the Generalized Differential Quadrature (GDQ) method and is based on the idea of conventional integral quadrature. In particular, the GDQFEM results in terms of stresses and displacements for classical and advanced plane stress problems with discontinuities are compared to the ones by the Cell Method (CM) and Finite Element Method (FEM). The multi-domain technique is implemented in a MATLAB code for solving irregular domains with holes and defects. In order to demonstrate the accuracy of the proposed methodology, several numerical examples of stress and displacement distributions are graphically shown and discussed
A Direct Forcing Immersed Boundary Method Employed With Compact Integrated RBF Approximations For Heat Transfer and Fluid Flow Problems
Get PDFIn this paper, we present a numerical scheme, based on the direct forcing immersed boundary (DFIB) approach and compact integrated radial basis function (CIRBF) approximations, for solving the Navier-Stokes equations in two dimensions. The problem domain of complicated shape is embedded in a Cartesian grid containing Eulerian nodes. Non-slip conditions on the inner boundaries, represented by Lagrangian nodes, are imposed by means of the DFIB method, in which a smoothed version of the discrete delta functions is utilised to transfer the physical quantities between two types of nodes. The velocities and pressure variables are approximated locally on Eulerian nodes using 3-node CIRBF stencils, where first- and second-order derivative values of the field variables are also included in the RBF approximations. The present DFIB-CIRBF scheme is verified through the solution of several test problems including Taylor-Green vortices, rotational flow, lid-driven cavity flow with multiple solid bodies, flow between rotating circular and fixed square cylinders, and natural convection in an eccentric annulus between two circular cylinders. Numerical results obtained using relatively coarse grids are in good agreement with available data in the literature
The Far-field Green’s Integral in Stokes Flow from the Boundary Integral Formulation
Get PDFIn boundary integral methods for Stokes flow, the far-field Green’s integral is usually taken to be zero without proof. However, this is not obviously the case, the reason being that Stokes flow is a near-field approximation and breaks down in the far-field. Here, we show that it is zero as expected by matching it to a far-field Green’s integral in Oseen flow. Hence, there are similarities to the matched asymptotic procedure matching a near-field Stokes flow to a far-field Oseen flow, except in this case a different and new procedure is required to deal with the Green’s integrals. In particular, the velocity is represented in the near-field by an integral distribution of stokeslets, and in the far-field by an integral distribution of oseenlets, and the two integral distributions are matched together by equating the stokeslets with the oseenlets in the matching region. A boundary integral representation is then obtained which holds throughout the whole flow region, enabling the velocity in the boundary integral scheme to be determined everywhere in the flow region
The Use of the BE SBS Algorithm to Evaluate Boundary and Interface Stresses in 3D Solids
Get PDFIn this paper, the BE SBS (subregion-by-subregion) algorithm, a generic substructuring technique for the BEM, is applied to evaluate stresses at boundary and interfacial points of general 3D composites and solids. At inner points, regular boundary integration schemes may be employed. For boundary or interfacial points, the Hooke’s law along with global-to-local axis-rotation transformations is directly applied. In fact, in thin-walled domain parts, only boundary stresses are needed. As the SBS algorithm allows the consideration of a generic number of subregions, the technique applies to the stress analysis in any composite and solid, including the microstructural (grain-by-grain) modeling of materials. The independent assembly and algebraic manipulation of the BE matrices for the many substructures involved in the model, makes the formulation very suitable for dealing with large-order models, as it typically happens in the 3D microstructural analysis of general composites. For that, Krylov solvers were incorporated into the SBS algorithm. To show the performance of the technique, stresses are calculated in beams, and 3D representative volume elements (RVEs) of carbon-nanotube (CNT)
Two Dimensional Nonlocal Elasticity Analysis by Local Integral Equation Method
Get PDFIn this paper, a Local Integral Equation Method (LIEM) is presented for solving two-dimensional nonlocal elasticity problems . The approach is based on the Eringen’s model with LIEM and the interpolation using the radial basis functions to obtain the numerical solutions for 2D problems. A weak form for the set of governing equations with a unit test function is transformed into the local integral equations. The meshless approximation technique with radial basis functions is employed for the implementation of displacements. A set of the local domain integrals is obtained in analytical form for the local elasticity and by using a standard integral scheme for the nonlocal elasticity. Three examples are presented to demonstrate the convergence and accuracy of LIEM including a rectangular plate, disk and a plate containing a circular hole subjected to a uniformly distributed displacement or tensile load. Comparisons have been made with the solutions of one dimension problems and other numerical techniques including the finite integration method, the finite/boundary element methods