Showing papers in "Engineering Analysis With Boundary Elements in 2011"

The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems

Abstract: In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented, and the interpolating moving least-squares (IMLS) method proposed by Lancaster is improved. Compared with the IMLS method proposed by Lancaster, a simpler formula of the shape function is given in the improved IMLS method in this paper so that the new method has higher computing efficiency. Combining the shape function constructed by the improved IMLS method with Galerkin weak form of the elasticity problems, the interpolating element-free Galerkin (IEFG) method for the two-dimensional elasticity problems is presented, and the corresponding formulae are obtained. In the IEFG method, the boundary conditions can be applied directly which makes the computing efficiency higher than the conventional EFG method. Some numerical examples are presented to demonstrate the validity of the method.

BEM analysis of crack onset and propagation along fiber–matrix interface under transverse tension using a linear elastic–brittle interface model

Abstract: The behavior of the fiber–matrix interface under transverse tension is studied by means of a new linear elastic–brittle interface model. Similar models, also called weak or imperfect interface models, are frequently applied to describe the behavior of adhesively bonded joints. The interface is modeled by a continuous distribution of linear-elastic springs which simulates the presence of a thin adhesive layer (interphase). In the present work a new linear elastic–brittle constitutive law for the continuous distribution of springs is introduced. In this law the normal and tangential stresses across the undamaged interface are, respectively, proportional to the relative normal and tangential displacements. This model not only allows for the study of crack growth but also for the study of crack onset. An important feature of this law is that it takes into account the variation of the fracture toughness with the fracture mode mixity of a crack growing along the interface between bonded solids, in agreement with previous experimental results. The present linear elastic–brittle interface model is implemented in a 2D boundary element method (BEM) code to carry out micromechanical analysis of the fiber–matrix interface failure in fiber-reinforced composite materials. It is considered that the behavior of the fiber–matrix interphase can be modeled by the present model although, strictly speaking, there is usually no intermediate material between fiber and matrix. A linear-elastic isotropic behavior of both fiber and matrix is assumed, the fiber being stiffer than the matrix. The failure mechanism of an isolated fiber under transverse tension, i.e., the onset and growth of the fiber–matrix interface crack, is studied. The present model shows that failure along the interface initiates with an abrupt onset of a partial debonding between the fiber and the matrix, caused by presence of the maximum radial stress at the interface, and this debonding further develops as a crack growing along the interface.

Buckling analysis of Reissner–Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method

Abstract: Buckling study of plates subjected to uniformly uniaxial, biaxial in-plane compression and pure shear loads using an efficient novel meshfree method is presented in this paper. The moving Kriging (MK) interpolation technique satisfying the Kronecker delta function property is employed to construct the shape functions. To allow for the effect of transverse shear deformation on thick plates, the first-order Reissner–Mindlin plate theory (FSDT) is adopted. The new formulation enables us to eliminate shear-locking demonstrated by various numerical examples involving both thin and moderately thick plates. It is found that the results achieved by the present approach match well with those obtained by other existing numerical approaches and analytical solutions, which illustrates the applicability, the effectiveness and the accuracy of the method.

Meshless local Petrov–Galerkin method for coupled thermoelasticity analysis of a functionally graded thick hollow cylinder

Abstract: In this article, coupled thermoelasticity (without energy dissipation) based on Green–Naghdi model is applied to functionally graded (FG) thick hollow cylinder. The meshless local Petrov–Galerkin method is developed to solve the boundary value problem. The Newmark finite difference method is used to treat the time dependence of the variables for transient problems. The FG cylinder is considered to be under axisymmetric and plane strain conditions and bounding surfaces of cylinder to be under thermal shock loading. The mechanical properties of FG cylinder are assumed to vary across thickness of cylinder in terms of volume fraction as nonlinear function. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a Heaviside test function. Nodal points are regularly distributed along the radius of the cylinder and each node is surrounded by a uni-directional subdomain to which a local integral equation is applied. The Green–Naghdi coupled thermoelasticity equations are valid in each isotropic subdomain. The temperature and radial displacement distributions are obtained for some grading patterns of FGM at various time instants. The propagation of thermal and elastic waves is discussed in details. The presented method shows high capability and efficiency for coupled thermoelasticity problems.

A coupled ES-FEM/BEM method for fluid–structure interaction problems

Abstract: The edge-based smoothed finite element method (ES-FEM) developed recently shows some excellent features in solving solid mechanics problems using triangular mesh. In this paper, a coupled ES-FEM/BEM method is proposed to analyze acoustic fluid–structure interaction problems, where the ES-FEM is used to model the structure, while the acoustic fluid is represented by boundary element method (BEM). Three-node triangular elements are used to discretize the structural and acoustic fluid domains for the important adaptability to complicated geometries. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and the gradient smoothing operation is applied over the edge-based smoothing domains. The global equations of acoustic fluid–structure interaction problems are then established by coupling the ES-FEM for the structure and the BEM for the fluid. The gradient smoothing technique applied in the structural domain can provide the important and right amount of softening effects to the “overly-stiff” FEM model and thus improve the accuracy of the solutions of coupled system. Numerical examples of acoustic fluid–structure interaction problems have been used to assess the present formulation, and the results show that the accuracy of present method is very good and even higher than those obtained using the coupled FEM/BEM with quadrilateral mesh.

Radial basis function approximation methods with extended precision floating point arithmetic

Abstract: Radial basis function (RBF) methods that employ infinitely differentiable basis functions featuring a shape parameter are theoretically spectrally accurate methods for scattered data interpolation and for solving partial differential equations. It is also theoretically known that RBF methods are most accurate when the linear systems associated with the methods are extremely ill-conditioned. This often prevents the RBF methods from realizing spectral accuracy in applications. In this work we examine how extended precision floating point arithmetic can be used to improve the accuracy of RBF methods in an efficient manner. RBF methods using extended precision are compared to algorithms that evaluate RBF methods by bypassing the solution of the ill-conditioned linear systems.

A comparison of three explicit local meshless methods using radial basis functions

Abstract: In this paper, three kinds of explicit local meshless methods are compared: the local method of approximate particular solutions (LMAPS), the local direct radial basis function collocation method (LDRBFCM) which are both first presented in this paper, and the local indirect radial basis function collocation method (LIRBFCM). In all three methods, the time discretization is performed in explicit way, the multiquadric radial basis functions (RBFs) are used to interpolate either initial temperature field and its derivatives or the Laplacian of the initial temperature field. The five-noded sub-domains are used in localization. Numerical results of simple diffusion equation with Dirichlet jump boundary condition are compared on uniform and random node arrangement, the accuracy and stabilities of these three local meshless methods are asserted. One can observe that the improvement of the accuracy with denser nodes and with smaller time steps for all three methods. All methods provide a similar accuracy in uniform node arrangement case. For random node arrangement, the LMAPS and the LDRBFCM perform better than the LIDRBFCM.

A local radial basis functions—Finite differences technique for the analysis of composite plates

Abstract: Radial basis functions are a very accurate means of solving interpolation and partial differential equations problems. The global radial basis functions collocation technique produces ill-conditioning matrices when using multiquadrics, making the choice of the shape parameter a crucial issue. The use of local numerical schemes, such as finite differences produces much better conditioned matrices. However, finite difference schemes are limited to special grids. For scattered points, a combination of finite differences and radial basis functions would be a possible solution. In this paper, we use a higher-order shear deformation plate theory and a radial basis function—finite difference technique for predicting the static behavior of thin and thick composite plates. Through numerical experiments on square and L-shaped plates, the accuracy and efficiency of this collocation technique is demonstrated, and the numerical accuracy and convergence are thoughtfully examined. This technique shows great potential to solve large engineering problems without the issue of ill-conditioning.

Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov–Galerkin (MLPG) method

Abstract: In this paper, three dimensional (3D) static and dynamic analysis of thick functionally graded plates based on the Meshless Local Petrov–Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains using a Heaviside step function as test function. In this case, governing equations corresponding to the stiffness matrix do not involve any domain integration or singular integrals. Nodal points are distributed in the 3D analyzed domain and each node is surrounded by a cubic sub-domain to which a local integral equation is applied. The meshless approximation based on the three-dimensional Moving Least-Square (MLS) is employed as shape function to approximate the field variable of scattered nodes in the problem domain. The Newmark time integration method is used to solve the system of coupled second-order ODEs. Effective material properties of the plate, made of two isotropic constituents with volume fractions varying only in the thickness direction, are computed using the Mori–Tanaka homogenization technique. Numerical examples for solving the static and dynamic response of elastic thick functionally graded plates are demonstrated. As a result, the distributions of the deflection and stresses through the plate thickness are presented for different material gradients and boundary conditions. The effects of the volume fractions of the constituents on the centroidal deflection are also investigated. The numerical efficiency of the proposed meshless method is illustrated by the comparison of results obtained from previous literatures.

Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems

Abstract: This article concerns an extension of the topological sensitivity (TS) concept for 2D potential problems involving insulated cracks, whereby a misfit functional J is expanded in powers of the characteristic size a of a crack. Going beyond the standard TS, which evaluates (in the present context) the leading O(a2) approximation of J, the higher-order TS established here for a small crack of arbitrarily given location and shape embedded in a 2-D region of arbitrary shape and conductivity yields the O(a4) approximation of J. Simpler and more explicit versions of this formulation are obtained for a centrally symmetric crack and a straight crack. A simple approximate global procedure for crack identification, based on minimizing the O(a4) expansion of J over a dense search grid, is proposed and demonstrated on a synthetic numerical example. BIE formulations are prominently used in both the mathematical treatment leading to the O(a4) approximation of J and the subsequent numerical experiments.

Boundary element analysis of nanoinhomogeneities of arbitrary shapes with surface and interface effects

Abstract: In this paper, a boundary element method (BEM) is proposed to analyze the stress field in nanoinhomogeneities with surface/interface effect. To consider this effect, the continuity conditions along the internal interfaces between the matrix and inhomogeneities are modeled by the well-known Gurtin–Murdoch constitutive relation. In the numerical analysis, the interface elastic moduli and the geometry of the nanoscale inhomogeneity are varied to show their influence on the induced stress field. The interaction between nanoscale inhomogeneities and the effect of different geometric shapes of inhomogeneities, including ellipse, triangle, and square are also investigated for different interface material parameters. It is shown that the elastic field can be greatly influenced by the interfacial energy and geometry of nanoscale inhomogeneities. The proposed BEM formulation is very general, including the complete Gurtin–Murdoch model and is further convenient for arbitrary shapes of inhomogeneity.

Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method

Abstract: For appropriate management of available groundwater, the flow behavior in the porous media has to be analyzed. The complex problem of groundwater flow can be studied by solving the governing equations analytically or by using numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used for field problems. Meshfree (MFree) method is an alternative numerical approach to solve complex groundwater problems in simple manner. MFree method eliminates the drawback of meshing and remeshing as in FDM and FEM which can translate to substantial cost and time savings in modeling. In this paper, a model using MFree point collocation method (PCM) with multi-quadric radial basis function (MQ-RBF) is proposed for 2D groundwater flow simulation. The accuracy of the developed model is verified with available analytical solution in literature. The developed model is applied initially for a hypothetical problem and further for a field problem to compute head distribution. The PCM model results for the hypothetical problem are compared with FEM simulations while that of field problem are compared with boundary element based model results. The PCM model results are found to be satisfactory showing the applicability of the present approach.

Boundary knot method for heat conduction in nonlinear functionally graded material

Abstract: This paper firstly derives the nonsingular general solution of heat conduction in nonlinear functionally graded materials (FGMs), and then presents boundary knot method (BKM) in conjunction with Kirchhoff transformation and various variable transformations in the solution of nonlinear FGM problems. The proposed BKM is mathematically simple, easy-to-program, meshless, high accurate and integration-free, and avoids the controversial fictitious boundary in the method of fundamental solution (MFS). Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of heat conduction in two different types of nonlinear FGMs.

Computing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions

Abstract: We propose a numerical method to compute the survival (first-passage) probability density function in jump-diffusion models. This function is obtained by numerical approximation of the associated Fokker–Planck partial integro-differential equation, with suitable boundary conditions and delta initial condition. In order to obtain an accurate numerical solution, the singularity of the Dirac delta function is removed using a change of variables based on the fundamental solution of the pure diffusion model. This approach allows to transform the original problem to a regular problem, which is solved using a radial basis functions (RBFs) meshless collocation method. In particular the RBFs approximation is carried out in conjunction with a suitable change of variables, which allows to use radial basis functions with equally spaced centers and at the same time to obtain a sharp resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented in which several different kinds of radial basis functions are employed. The results obtained reveal that the numerical method proposed is extremely accurate and fast, and performs significantly better than a conventional finite difference approach.

Topology optimization of composite material plate with respect to sound radiation

Abstract: In this paper, topology optimization of composite material plate with respect to minimization of the sound power radiation has been studied. A new low noise design method based on topology optimization is proposed, which provides great guidance for acoustic designers. The structural vibrations are excited by external harmonic mechanical load with prescribed frequency and amplitude. The sound power is calculated using boundary element method. An extended solid isotropic material with penalization (SIMP) model is introduced for acoustic design sensitivity analysis in topology optimization, where the same penalization is applied for the stiffness and mass of the structural volume elements. Volumetric densities of stiffer material are chosen as design variables. Finally, taking a simple supported thin plate as a simulation example, the sound power radiation from structures subjected to forced vibration can be considerably reduced, leading to a reduction of 20 dB. It is shown that the optimal topology is easy to manufacture at low frequency, while as the loading frequency increases, the optimal topology shows a more and more complicated periodicity which makes it difficult to manufacture.

BEM simulations of potential flow with viscous effects as applied to a rising bubble

Abstract: A model for the unsteady rise and deformation of non-oscillating bubbles under buoyancy force at high Reynolds numbers has been implemented using a boundary element method. Results such as the evolution of the bubble shape, variations of the transient velocity with rise height and the terminal velocity for different size bubbles have been compared to recent experimental data in clean water and to numerical solutions of the unsteady Navier–Stokes equation. The aim is to capture the essential physical ingredients that couple bubble deformation and the transient approach towards terminal velocity. This model requires very modest computational resources and yet has the flexibility to be extended to more general applications.

New variable transformations for evaluating nearly singular integrals in 2D boundary element method

Abstract: This work presents a further development of the distance transformation technique for accurate evaluation of the nearly singular integrals arising in the 2D boundary element method (BEM). The traditional technique separates the nearly hypersingular integral into two parts: a near strong singular part and a nearly hypersingular part. The near strong singular part with the one-ordered distance transformation is evaluated by the standard Gaussian quadrature and the nearly hypersingular part still needs to be transformed into an analytical form. In this paper, the distance transformation is performed by four steps in case the source point coincides with the projection point or five steps otherwise. For each step, new transformation is proposed based on the approximate distance function, so that all steps can finally be unified into a uniform formation. With the new formulation, the nearly hypersingular integral can be dealt with directly and the near singularity separation and the cumbersome analytical deductions related to a specific fundamental solution are avoided. Numerical examples and comparisons with the existing methods on straight line elements and curved elements demonstrate that our method is accurate and effective.

Bending and vibration responses of laminated composite plates using an edge-based smoothing technique

Abstract: In this paper, bending and vibration analysis of laminated composite plates is carried out using a novel triangular composite plate element based on an edge-based smoothing technique. The present formulation is based on the first-order shear deformation theory, and the discrete shear gap (DSG) method is employed to mitigate the shear locking. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and edge-based smoothing domains are used for the numerical integration to improve the accuracy and the convergence rate of the method. The present formulation is coded and used to solve various example problems of bending and free vibration of laminated composite plates. It is found that the present method can provide excellent results with a wide range of thickness and is free of shear locking.

3-D boundary element-finite element method for the dynamic analysis of piled buildings

Abstract: A boundary element–finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler–Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs. Soil–foundation–structure interaction is rigorously taken into account with an affordable number of degrees of freedom. The code allows the direct analysis of multiple piled buildings, so that the influence of other constructions can be taken into account in the analysis of a certain element. The formulation is outlined before presenting validation results and an application example.

A dual reciprocity BEM approach using new Fourier radial basis functions applied to 2D elastodynamic transient analysis

Abstract: In this paper, a new boundary element analysis for two-dimensional (2D) transient elastodynamic problems is proposed. The dual reciprocity method (DRM) is reconsidered by employing new radial basis functions (RBFs) to approximate the domain inertia terms. These new RBFs, which are in the form of ζ+κ sin (ωr+α), are called Fourier RBFs hereafter. Using the method of variation of parameters, the particular solution kernels of Fourier RBFs corresponding to displacement and traction, whose a few terms are singular, has been explicitly derived. Therefore, a new simple smoothing trick has been employed to resolve the singularity problem. Moreover, the limiting values of the particular solution kernels have been evaluated. In order to find the unknown parameters of Fourier RBFs, an optimization problem seeking for the optimum value of the Houbolt scheme parameter β that minimizes the mean squared error (MSE) function of the problem is established. Since the MSE function of the proposed RBFs is a function of five unknown parameters (i.e., ζ, κ, ω, α, and β), the genetic algorithm (GA) has been used to solve the necessary optimization problem. In order to illustrate the validity, accuracy, and superiority of the present study, several numerical examples are examined and compared to the results of analytical and other RBFs reported in the literature. Compared to other RBFs, Fourier RBFs show more accurate and stable results. Moreover, these results are obtained using less degree of freedom without any additional internal points that are commonly used to improve the accuracy of the results.

Shape variable radial basis function and its application in dual reciprocity boundary face method

Abstract: The radial basis functions (RBFs) is an efficient tool in multivariate approximation, but it usually suffers from an ill-conditioned interpolation matrix when interpolation points are very dense or irregularly spaced. The RBFs with variable shape parameters can usually improve the interpolation matrix condition number. In this paper a new shape parameter variation scheme is implemented. Comparison studies with the constant shaped RBF on convergence and stability are made. Results show that under the same accuracy level, the interpolation matrix condition number by our scheme grows much slower than that of the constant shaped RBF interpolation matrix with increase in the number of interpolation points. As an application example, the dual reciprocity method equipped with the new RBF is combined with the boundary face method to solve boundary value problems governed by Poisson equations. Numerical results further demonstrate the robustness and better stability of the new RBF.

Using analytical expressions in radial integration BEM for variable coefficient heat conduction problems

Abstract: In this paper, a new approach using analytical expressions in the radial integration boundary element method (RIBEM) is presented for solving variable coefficient heat conduction problems. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. The fourth-order spline RBF is employed to approximate unknowns appearing in domain integrals arising from the varying heat conductivity. The radial integration method is utilized to convert domain integrals to the boundary resulting in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented approach.

A boundary elements formulation for 3D fretting-wear problems

Abstract: Computational wear modeling is an extremely time-consuming problem, especially the 3D cases. In this work, a 3D boundary element method (BEM) formulation for wear modeling is proposed and applied to simulate 3D fretting-wear problems under gross sliding and partial slip conditions. The present formulation applies the BEM to approximate the elastic response of solids, and an augmented Lagrangian formulation to solve the contact problem. Contact restrictions fulfilment is established by a set of projection functions, and wear on contact surfaces is computed using the Archard wear law. The BEM proves to be a very suitable numerical method for this kind of mechanical interaction problems, considering only the boundary degrees of freedom involved in the problem and obtaining a very good approximation of contact tractions with a low number of elements. This is very interesting in terms of computational cost reductions of wear modeling, specially in 3D problems. In that regard, an acceleration strategy is applied to the proposed algorithm. It allows to obtain very important reductions on wear simulation times. The proposed methodology is therefore an efficient numerical tool for 3D fretting-wear problems modeling.

A new semi-analytical method with diagonal coefficient matrices for potential problems

Abstract: In this paper, a new semi-analytical method is proposed for solving boundary value problems of two-dimensional (2D) potential problems. In this new method, the boundary of the problem domain is discretized by a set of special non-isoparametric elements that are introduced for the first time in this paper. In these new elements, higher-order Chebyshev mapping functions and new special shape functions are used. The shape functions are formulated to provide Kronecker Delta property for the potential function and its derivative. In addition, the first derivative of shape functions are assigned to zero at any given control point. Finally, using weighted residual method and implementing Clenshaw–Curtis quadrature, the coefficient matrices of equations system become diagonal, which results in a set of decoupled governing equations for the whole system. This means that the governing equation for each degree of freedom (DOF) is independent from other DOFs of the domain. Validity and accuracy of the present method are fully demonstrated through four benchmark problems.

Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method

Abstract: This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and hypersingular boundary integrals contained in the equations are evaluated as the Cauchy principal values and Hadamard finite parts for constant element discretization without using any regularization technique in this study. The present boundary integral equations are more efficient to use than the usual ones based on any other singularity subtraction technique and can be applied to the fast multipole boundary element method more readily and efficiently. The effectiveness and accuracy of the present equations are demonstrated through some numerical examples.

A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM)

Abstract: In this paper, a three-dimensional (3-D) adaptive analysis procedure is proposed using the meshfree node-based smoothed point interpolation method (NS-PIM) Previous study has shown that the NS-PIM works well with the simplest four-node tetrahedral mesh, which is easy to be implemented for complicated geometry In contrast to the displacement-based FEM providing lower bound solutions, the NS-PIM possesses the attractive property of providing upper bound solutions in strain energy norm In the present adaptive procedure, a novel error indicator is devised for NS-PIM settings, which evaluates the maximum difference of strain energy values among four nodes in each of the tetrahedral cells A simple h-type local refinement scheme is adopted and coupled with 3-D mesh automatic generator based on Delaunay technology Numerical results indicate that the adaptive refinement procedure can effectively capture the stress concentration and solution singularities, and carry out local refinement automatically The present adaptive procedure achieves much higher convergence in strain energy solution compared to the uniform refinement, and obtains upper bound solution in strain energy efficiently for force driven problems

2D general solution and fundamental solution for orthotropic thermoelastic materials

Abstract: The 2D general solution for the plane problem of thermoelastic materials is derived in terms of three harmonic functions using strict differential operator theory for the case of distinct eigenvalues. Based on the obtained general solution, the 2D fundamental solution for a steady line heat source in an infinite and a semi-infinite thermoelastic plane is obtained by three newly introduced harmonic functions. All components of coupled fields are expressed in terms of elementary functions and they are convenient to be used.

Group preserving scheme for the Cauchy problem of the Laplace equation

Abstract: In this paper, we consider the Cauchy problem for the Laplace equation by group preserving scheme (GPS) which is an ill-posed problem, because the solution does not depend continuously on the data. For this, the Laplace equation, by using a semi-discretization method namely method of line, is converted to an ODEs system and then obtained ODEs system is considered by GPS. Stability of GPS for ill-posed Laplace equation is shown. The problem numerical results show the efficiency and power of this method.

Boundary element analysis of 2D thin walled structures with high-order geometry elements using transformation

Abstract: Thin structures have been widely designed and utilized in many industries. However, the analysis of the mechanical behavior of such structures represents a very challenging and attractive task to scientists and engineers because of their special geometrical shapes. The major difficulty in applying the boundary element method (BEM) to thin structures is the coinstantaneous existence of the singular and nearly singular integrals in conventional boundary integral equation (BIE). In this paper, a non-linear transformation over curved surface elements is introduced and applied to the indirect regularized boundary element method for 2-D thin structural problems. The developed transformation can remove or damp out the nearly singular properties of the integral kernels, based on the idea of diminishing the difference of the orders of magnitude or the scale of change of operational factors. For the test problems studied, very promising results are obtained when the thickness to length ratio is in the orders of 1E−01 to 1E−06, which is sufficient for modeling most thin structures in industrial applications.

Internal stress analysis for single and multilayered coating systems using the boundary element method

Abstract: Various thin-coating films are designed and utilized for industrial applications to improve machining performance due to better temperature and wear resistant properties than their substrate counterparts. However, the widespread experimental research on thin coatings underlies a general lack of modeling efforts, which can accurately and efficiently predict the coating and thin film performance. In this paper, the boundary element method (BEM) for 2D elastostatic problems is studied for the analysis of single and multilayered coating systems. The nearly singular integrals, which is the primary obstacle associated with the BEM formulations, are dealt efficiently by using a general nonlinear transformation technique. For the test problems studied, very promising results are obtained when the thickness of coated layers is in the orders of 1.0E−6 to 1.0E−9, which is sufficient for modeling most coated systems in the micro- or nano-scales.