Xiao-Wei Gao's research while affiliated with Dalian University of Technology and other places

Publications (137)

Article
A novel strong-form numerical algorithm, piezoelectric vibration element differential method (PVEDM), is proposed for simulating the static deflection and forced vibration of the structure integrated with piezoelectric layers, with the host structure being homogeneous or functionally graded materials. A unified manner for the steady-state and dynam...
Article
The transient quasi-static electromagnetic problems with nonlinear conductive effects are under consideration in this paper. The quasi-static electromagnetic problems include electro-quasistatic (EQS) and magneto-quasistatic (MQS) problems, which neglect the wave propagation effects, and are important in the electrical engineering. Numerical comput...
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In this paper, a new collocation type numerical method, Cross-Line Method (CLM), is proposed for solving general engineering problems governed by second order partial differential equations with proper boundary conditions. The method is based on the use of a finite number of lines crossing the collocation node under consideration and therefore it i...
Article
A new kind of dynamic seal with braided ceramic fibers has been designed to seal the movable panels in the scramjet engines, which are used for the propulsion of hypersonic vehicle. The braided ceramic fiber structure can provide buffer forces when the seals are subjected to the external dynamical preloads. However, it also makes the seals difficul...
Article
In the present work, a polygonal boundary element method (PBEM) for solving transient inhomogeneous heat conduction problems with spatially-varying heat generation is developed for the first time. A new general analytical method is proposed and employed in the present PBEM, by which the radial integrals associated with arbitrary spatially-varying d...
Article
In order to accurately identify the geometric boundary, the radial integration boundary element method (RIBEM) combined with the modified Levenberg-Marquardt (LM) algorithm is proposed for shape reconstruction in transient heat conduction problems. Compared with the finite element method (FEM), the boundary element method (BEM) only discretizes the...
Article
In this paper, a new robust numerical method, named element differential method (EDM), is developed to solve computational acoustic problems in time domain. The key aspect of the method is the direct differentiation of shape functions of the isoparametric elements used to characterize the geometry and physical variables, which can be utilized to ev...
Article
In this paper, a simple and efficient numerical method named time domain element differential method (TD-EDM) is proposed to solve electromagnetic wave scattering and radiation problems. In the method, the governing equations as well as boundary conditions are directly solved in a strong-form formulation. The computational domain is discretized usi...
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Full-text available
Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using. Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical p...
Article
In order to accurately identify the temperature-dependent thermal conductivity of solids, a novel method which combines the element differential method (EDM) with the modified Levenberg-Marquardt algorithm (LMA) is firstly proposed to solve the inverse heat conduction problems, where complex variable derivative method (CVDM) is introduced to obtain...
Article
The element differential method (EDM) is extended to solve the transient heat transfer problems with phase change. The governing equation of the phase change problem is established in the whole domain by using the effective heat capacity method. Based on the analytical expressions of spatial derivatives of the shape function with respect to the coo...
Article
With the rapid development of ultrashort-pulse laser heating and nanomaterials in science and engineering, the research on non-Fourier models to predict the anomalous heat conduction has attracted more and more attention. Among the existing non-Fourier models, the dual-phase-lag model can provide the best performance and it is more suitable for a s...
Article
Recently, the free element method(FREM), a novel strong-form method, is successfully used to solve thermal and mechanical problems. However, similar to some other strong-form methods, it is difficult to handle the geometric model with corner points. To overcome this weakness, the zonal free element method (ZFREM), which has strong adaptability to d...
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Our purpose is to establish a numerical method meeting the requirements of accuracy and easy-using for thermal-mechanical analysis of functionally graded structures. Faced with these demands, a new point collocation pseudo-spectral method named spectral element differential method (SEDM), is proposed in this paper. In this paper the Chebyshev polyn...
Article
A novel numerical method named element differential method (EDM) is first presented to solve linear and nonlinear static electromagnetic problems. The main idea of this method is to use the direct differentiation formulation of the shape functions of Lagrange isoparametric elements to evaluate geometry and physical variables. A new collocation meth...
Article
The cover image is based on the Research Article A free element scheme for simulating two‐ and three‐dimensional incompressible fluid flow by Hua‐Yu Liu et al., https://doi.org/10.1002/fld.4923.
Article
In this paper, a new and efficient Dual Boundary Element Method (DBEM) named Dual Boundary-Interface Integral Equation Method (DBIIEM) is presented to solve crack problems in objects composed of arbitrary number of different materials. The conventional DBEM has been widely used in crack analysis and proved to be one of the most effective BEM for so...
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In this paper, a new solution approach of using Free Element Method (FrEM) is proposed to solve thermal-mechanical problems consisting of composite materials and cracks. In this approach, the computational domain of the problem is discretized into multi-zones and in each zone a set of local nodes are generated. At the local nodes of each zone, the...
Article
In this paper, a meshless BEM based on the radial integration method is developed to solve transient non-homogeneous convection-diffusion problem with spatially variable velocity and time-dependent source term. The Green function served as the fundamental solution is adopted to derive the boundary domain integral equation about the normalized field...
Article
In this work, Free Element method (FECM) is extended to solve incompressible Navier‐Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoints are interpolated by improved Momentum Interpolation Method to avoid oscillation caused by decoupling of velocity and pressure. At l...
Article
In order to solve multi-medium nonlinear transient heat conduction problems, based on interface integration boundary element method, a new approach, which can convert the multi-domain integrals to the boundary integrals with high precision, is firstly proposed in this paper. The boundary element method with the internal and exterior source is used...
Article
In this paper, the application of Free Element Method (FREM) is extended to the transient nonlinear heat conduction problems, and the characteristics of anisotropic, heterogeneous, temperature-dependent thermophysical properties and heat generation are also involved. In order to improve the efficiency during the nonlinear iterations, an alternating...
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In this paper, a block-based Galerkin free element method is presented for the calculation of J-integral and mix-model stress intensity factors. Based on the free element collocation method, the Galerkin weak-form is constructed to achieve more accurate results. By absorbing the advantages of SFEM and FBM, the sub-domain mapping technique is used t...
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In this paper, a new single interface integral equation method is established for solving non-linear multi-medium heat transfer problems with temperature- dependent thermal conductivity. At first, the boundary-domain integral equation for nonlinear heat transfer in single medium is established based on the fundamental solution of Laplace equation....
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Full-text available
This work is focused on the detection of interlayer damages in multi-layer composite materials, which use the inverse analysis approach based on the reduced-order models (ROMs). Direct problems including heat conduction through the solid and heat radiation to the space are solved by finite element method (FEM), and the solutions of transient nonlin...
Article
Element differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher computational efficiency and it is more stable than other strong‐form methods. However, due to the utilization of strong‐form equations for all nodes, EDM become not so accurate when solving problems wit...
Article
In this article, a completely new numerical method called the Local Least-Squares Element Differential Method (LSEDM), is proposed for solving general engineering problems governed by second order partial differential equations. The method is a type of strong-form finite element method. In this method, a set of differential formulations of the isop...
Article
In this paper, the element differential method (EDM), a new numerical method proposed recently, is coupled with the multi-domain boundary element method (MDBEM), an improved Boundary Element Method (BEM), for solving general multi-scale heat conduction and elasticity problems. The basic algebraic equations in MDBEM are formulated in terms of displa...
Article
A novel strong form numerical method, Element Differential Method (EDM), is developed to solve geometrically complex mechanics problems based on triangular or tetrahedral meshes. The discretization of the structure under investigation has been based on Lagrange isoparametric quadrilateral or hexahedral elements while applying EDM. In this paper, a...
Article
In this paper, combination of radial integration boundary element method (RIBEM) with complex variable and Levenberg-Marquardt algorithm (LMA) is firstly proposed to identify temperature-dependent conductivity in the inverse heat conduction problem. To obtain the simulative temperature, radial integration boundary element method is used to solve th...
Article
In this paper, a family of global elements (GEs) are constructed for modeling geometries and representing physical variables, based on a set of complete basis functions formulated in terms of normalized global coordinates. The main benefits of using GEs are that the elemental nodes can be distributed and numbered in an arbitrary manner and the glob...
Article
The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. The computational results as presented in Part 1 have revealed some signatures of the basic algorithms, in which poor efficiency is its main shortcoming. In th...
Article
The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. Part 1 of this two-part articles presents the process and characteristics of basic algorithms, including POD explicit and implicit time-marching methods. The a...
Article
In this paper, a new type of finite elements, called as Cross-Line Elements (CLEs), are constructed, which have fewest nodes to interpolate physical variables in both two-dimensional (2D) and three-dimensional (3D) problems. These CLEs are then used in a new mesh free method, the Free Element Method (FREM), for solving general 2D and 3D boundary va...
Article
A novel general approach is proposed for solving three-dimensional transient nonlinear inverse heat conduction problems in irregular complex structures. The complex-variable-differentiation method (CVDM) is introduced into the commercial finite element method (FEM) software ABAQUS, for solving three-dimensional inverse heat conduction problems for...
Article
A novel implicit scheme based on free element method (FECM) is proposed to solve Navier–Stokes equations. The proposed method has the mesh-free features but elements are essential instead of point clouds. The isoparametric transformations, which are usually used in finite element method, are employed to obtain the coefficients in the spatial deriva...
Article
A new methodology is proposed for predicting the bank thickness covering and protecting the refractory brick walls of the smelting furnaces. The inverse method predicts the bank thickness changing with both time and coordinates, by using a two-dimensional physical model of the furnace that is more general and challenging than the previous studies....
Article
In this paper, a new weak-form method (Galerkin free element method – GFrEM) is developed and implemented for solving general mechanical and fracture problems. This method combines the advantages of the finite element method and meshfree method in the aspects of setting up shape functions and generating computational meshes through node by node. Th...
Article
Numerical solution of two-dimensional unsteady convection–diffusion problem is carried out by using the radial integration boundary element method in the paper. A boundary domain integral equation is established for the purpose by using the fundamental solution of Laplace equation. The convective and time-dependent terms of governing equation lead...
Article
In order to analyze the heat conduction problem of composite materials in aerospace engineering, a modified conjugate gradient method is proposed to identify the physical parameters of transient heat conduction problems in this paper. In the positive problem, the boundary element method based on radial integration method is used to obtain the measu...
Article
In this paper, a new numerical method, named as the Free Element Collocation Method (FECM), is proposed for solving general engineering problems governed by the second order partial differential equations (PDEs). The method belongs to the group of the collocation method, but the spatial partial derivatives of physical quantities are computed based...
Article
When solving structurally multi-scale problems with small or slender components using BEM, different sized boundary elements are inevitably required to simulate all kinds of related geometries. In this paper, a family of trans-accuracy boundary elements are constructed based on Lagrange interpolation formulation. These elements not only can fulfil...
Article
In this paper, a new numerical method, Element Differential Method (EDM), is developed for solving transient heat conduction problems with variable conductivity. The key point of this method is based on the direct differentiation of shape functions of isoparametric elements used to evaluate the geometry and physical variables. A new collocation met...
Article
s In this work a new strong-form numerical method, element differential method (EDM), is proposed to perform free and forced vibration analysis of elastodynamic problems. The present method establishes the global algebraic system equations directly based on the strong form of the equilibrium equations without using any variational principles or ene...
Article
In this paper, the element differential method is extended to solve a transient nonlinear heat conduction problem with a heat source and temperature-dependent thermophysical properties for the first time. The transient term is discretized by employing a finite difference scheme. An iterative methodology is developed to deal with the nonlinearity ca...
Article
In this paper, the radial integration boundary element method without internal cells is presented for solving steady convection-conduction problem with spatially variable velocity and thermal conductivity. The temperature boundary integral equation is derived by employing the fundamental solution for the potential problem (Green function) as well a...
Article
A new approach, radial integration polygonal boundary element method (RIPBEM), for solving heat conduction problems is presented in this paper. The proposed RIPBEM is a new concept in boundary element method (BEM), which would be of great flexibility in mesh generation of complex 3D geometries. Due to the characteristic of arbitrary shapes of polyg...
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Full-text available
In this article, two types of new quadrilateral and hexahedron quadratic isoparametric elements are proposed for the element differential method (EDM) for solving heat conduction problems. These elements, called as the Ultra elements, have the minimum numbers of nodes comparing with the existing elements and have the feature that a central node is...
Article
In this paper, a new and effective radial integration boundary element method (RIBEM) is presented to solve nonlinear heat conduction with temperature dependent thermal conductivity of materials. Boundary-domain integral equation is formulated for nonlinear heat conduction by utilizing the fundamental solutions for the corresponding linear heat con...
Article
A new radial integration boundary element method (RIBEM) for solving transient heat conduction problems with heat sources and variable thermal conductivity is presented in this article. The Green’s function for the Laplace equation is served as the fundamental solution to derive the boundary-domain integral equation. The transient terms are first d...
Article
In this paper, a new numerical method, Element Differential Method (EDM), is proposed for solving general heat conduction problems with variable conductivity and heat source subjected to various boundary conditions. The key aspect of this method is based on the direct differentiation of shape functions of isoparametric elements used to characterize...
Article
A new boundary domain integral equation with convective heat transfer boundary is presented to solve variable coefficient heat conduction problems. Green’s function for the Laplace equation is used to derive the basic integral equation with varying heat conductivities, and as a result, domain integrals are included in the derived integral equations...
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Full-text available
Aim: To explore the possibility of human umbilical cord mesenchymal stem cells (hUCMSCs), human umbilical vein endothelial cells (hUVECs), human dental pulp stem cells (hDPSCs) and human periodontal ligament stem cells (hPDLSCs) serving as feeder cells in co-culture systems for the cultivation of limbal stem cells. Methods: Different feeder laye...
Article
In this paper, a new numerical method, Element Differential Method (EDM), is proposed for solving general thermal-mechanical problems. The key point of the method is the direct differentiation of the shape functions of Lagrange isoparametric elements used to characterize the geometry and physical variables. A set of analytical expressions for compu...
Article
Metallic materials such as an Inconel and an alloy steel play very important roles for bearing in the reusable metallic thermal protection system (TPS) for a hypersonic aircraft. Accurate determination of temperature-dependent thermal conductivities of these metallic materials is a key issue for both design and optimization of the TPS, which determ...
Article
In this paper, a new and simple boundary-domain integral equation is presented for solving transient nonlinear heat conduction problems with temperature-dependent conductivity of materials. The boundary-domain integral equation is formulated for transient nonlinear heat conduction problems by using the fundamental solution for the corresponding ste...
Article
Damping factor is a key parameter in Levenberg-Marquardt algorithm for solving inverse problems, which significantly affects the efficiency and the convergence stability of Levenberg-Marquardt algorithm and needs to be updated with the iterative number. A new approach is presented for determining damping factors in Levenberg-Marquardt algorithm in...
Article
In this paper, a new and simple boundary-domain integral equation is presented to solve nonlinear heat conduction problems with temperature-dependent conductivity of materials. The boundary-domain integral equation is formulated for nonlinear heat conduction problems by using the fundamental solutions for the corresponding linear heat conduction pr...
Article
Despite numerous studies of Levenberg–Marquardt (LM) algorithms for solving inverse heat conduction problems, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if multi-dimensions, transient states and n...
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In this paper, based on the numerical investigation of singular integrals over narrow strip boundary elements stemming from BEM analysis of thin and slender structures with different numbers of Gauss points, an efficient method is proposed for evaluating the narrow strip singular boundary integrals using an adaptive unequal interval element-subdivi...
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An innovative method is proposed for constructing isoparametric boundary elements to simulate closed surfaces. These elements are named “isoparametric closure elements” and can not only accurately simulate spherical, elliptical, and other closed surface geometries, but also interpolate physical quantities defined over these surfaces. As a result of...
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Full-text available
Aim: To demonstrate the changes in ultrastructure and histopathology of the cornea in acute corneal alkaline burns after femtosecond laser-assisted deep lamellar keratoplasty. Methods: The New Zealand white rabbits treated with alkaline corneal burn were randomized into two groups, Group A (16 eyes) with femtosecond laser-assisted deep lamellar...
Article
In this paper, a new iterative method, for solving sparse nonsymmetrical systems of linear equations is proposed based on the Simultaneous Elimination and Back-Substitution Method (SEBSM), and the method is applied to solve systems resulted in engineering problems solved using Finite Element Method (FEM). First, SEBSM is introduced for solving gene...
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Full-text available
Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expa...
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In this paper, based on the general stress-strain relationship, displacement and stress boundary-domain integral equations are established for single medium with varying material properties. From the established integral equations, single interface integral equations are derived for solving general multi-medium mechanics problems by making use of t...
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An efficient numerical method for evaluating all kinds of singular boundary integrals presented in Ref. Gao, 2002 [16] is improved by using a newly derived formulation for computing the spatial derivative of the global distance, which is inevitably used in the finite part of radial integrals. Based on this improvement, more accurate and stable resu...
Article
A new approach is presented to calculate boundary stresses in thermal stress analysis of structures consisting of functionally grades materials (FGMs) based on the traction-recovery method. In this approach, the in-plane strains are calculated first using the computed nodal displacements by simply differentiating shape functions at the point of int...
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The relaxation factor is a key parameter in gradient-based inversion and optimization methods, as well as in solving nonlinear equations using iterative techniques. In gradient-based inversion methods, the relaxation factor directly affects the inversion efficiency and the convergence stability. In general, the bigger the relaxation factor is, the...
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This paper presents a set of new analytical expressions for evaluating radial integrals appearing in the stress computation of several kinds of variable coefficient elastic problems using the radial integration boundary element method (RIBEM). The strong singularity involved in the stress integral equation is explicitly removed from the derivation...
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In this paper, a single stress integral equation is presented for solving multi-medium elasticity problems, and by using a newly proposed method for treating arbitrarily high order of singular boundary integrals, a new method is developed for computing the stresses on the interfaces of multi-media. Comparing to conventional multi-domain boundary el...