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K.m. Liew - One of the best experts on this subject based on the ideXlab platform.
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thermal buckling of functionally graded plates using a local kriging Meshless Method
Composite Structures, 2014Co-Authors: L W Zhang, Ping Zhu, K.m. LiewAbstract:The mechanical and thermal buckling behaviors of ceramic–metal functionally grade plates (FGPs) were studied by using a local Kriging Meshless Method. The local Meshless Method was developed based on the local Petrov–Galerkin weak-form formulation combined with shape functions having the Kronecker delta function property, constructed by the Kriging interpolation. The cubic spline function of high continuity was used as the weight function to simplify the local weak form of governing equations with the integration on the internal boundaries vanishing. The transverse shear strains of FGPs were incorporated by employing the first-order shear deformation plate theory and plate material properties were assumed to change exponentially along the thickness direction. Convergence and comparison studies examined the stability and accuracy of the presented Method. Two types of FGMs, Al/Al2O3 and Ti–6Al–4V/Aluminum oxide, were chosen for mechanical and thermal buckling analyses. The influences of volume fraction exponent, boundary condition, length-to-thickness ratio and loading type on the buckling behaviors of FGPs were discussed.
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Free vibration analysis of moderately thick functionally graded plates by local Kriging Meshless Method
Composite Structures, 2011Co-Authors: Ping Zhu, K.m. LiewAbstract:This paper mainly Presents free vibration analyses of metal and ceramic functionally graded plates with the local Kriging Meshless Method. The Kriging technique is employed to construct shape functions which possess Kronecker delta function property and thus make it easy to implement essential boundary conditions. The eigenvalue equations of free vibration problems are based on the first-order shear deformation theory and the local Petrov–Galerkin formulation. The cubic spline function is used as the weight function which vanishes on internal boundaries of local quadrature domains and hence simplifies the implementation. Convergence studies are conducted to examine the stability of the present Method. Three types of functionally graded plates – square, skew and quadrilateral plates – are considered as numerical examples to demonstrate the versatility of the present Method for free vibration analyses.
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complex variable moving least squares Method a Meshless approximation technique
International Journal for Numerical Methods in Engineering, 2007Co-Authors: K.m. Liew, Yumin Cheng, Cong Feng, S KitipornchaiAbstract:Based on the moving least-squares (MLS) approximation, we propose a new approximation Method-the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the Meshless Method that is formed from the CVMLS approximation than are required in the Meshless Method of the MLS approximation with no loss of precision. The Meshless Method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new Meshless Method for two-dimensional elasticity problems-the complex variable Meshless Method (CVMM)-and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional Meshless Method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM.
J R Xiao - One of the best experts on this subject based on the ideXlab platform.
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local heaviside weighted mlpg Meshless Method for two dimensional solids using compactly supported radial basis functions
Computer Methods in Applied Mechanics and Engineering, 2004Co-Authors: J R XiaoAbstract:Abstract Compactly supported radial basis functions (CSRBF) are employed for constructing trial functions in the local Heaviside weighted Meshless local Petrov–Galerkin Method for stress analysis of two-dimensional solids, where the Heaviside step function is used as the weighting function over a local sub-domain. The present Method is a truly Meshless Method based only on a number of randomly located nodes. No domain integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Effects of the sizes of local sub-domain and interpolation domain on the performance of the present Method are investigated. In this paper, the size of the support of the basis function has been treated as a shape parameter, and then, the behaviour of this shape parameter has been systematically studied for six different CSRBFs. Example problems in elastostatics are presented and compared with closed-form solutions. Results show that the proposed Method is highly accurate and possesses no numerical difficulties.
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a local heaviside weighted Meshless Method for two dimensional solids using radial basis functions
Computational Mechanics, 2003Co-Authors: J R Xiao, M A MccarthyAbstract:A Meshless Method is developed for the stress analysis of two-dimensional solids, based on a local weighted residual Method with the Heaviside step function as the weighting function over a local subdomain. Trial functions are constructed using radial basis functions (RBF). The present Method is a truly Meshless Method based only on a number of randomly located nodes. No domain integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Effects of the sizes of local subdomain and interpolation domain on the performance of the present Method are investigated. The behaviour of shape parameters of multiquadrics (MQ) has been systematically studied. Example problems in elastostatics are presented and compared with closed-form solutions and show that the proposed Method is highly accurate and possesses no numerical difficulties.
Yajie Deng - One of the best experts on this subject based on the ideXlab platform.
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an improved interpolating complex variable element free galerkin Method for the pattern transformation of hydrogel
Engineering Analysis With Boundary Elements, 2020Co-Authors: Yajie Deng, Ligang Sun, Ying DaiAbstract:Abstract In this paper, an effective interpolating complex variable element free Galerkin Method is proposed for the steady large deformation analysis of hydrogels. In this Meshless Method, the essential boundary conditions can be applied directly without using other special Methods, which leads to less unknown coefficients. Through computing the swelling large deformation of a square hydrogel with three constrained boundaries, the presented Meshless Method is validated with higher accuracy and efficiency than other non-interpolating Meshless Methods. Based on the developed Meshless Method, different samples with elliptical, circular and square holes in a square hydrogel are simulated for analyzing the pattern transformation. The numerical results indicate that the shapes and initial sizes of holes in hydrogels lead to different pattern transformation rules, actuating behaviors and area reductions of holes. Finally, according to the new findings, the potential applications of a square hydrogel are discussed by designing different shapes and initial sizes of holes.
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an improved interpolating complex variable Meshless Method for bending problem of kirchhoff plates
International Journal of Applied Mechanics, 2017Co-Authors: Yajie DengAbstract:An improved interpolating complex variable moving least squares (IICVMLS) Method is proposed for numerical simulations of structures, in which a complete basis function and singular weight function are used to form a new basis function through the orthogonalization process. In this Method, a new shape function which has the property of Kronecker δ function is derived to build the interpolating function. Based on the IICVMLS Method, an improved interpolating complex variable element free Galerkin (IICVEFG) Method is obtained for bending problem of Kirchhoff plates. In the IICVEFG Method, the essential boundary conditions can be satisfied directly, and thus the final discrete matrix equation is more concise than that in the non-interpolating complex variable element free Galerkin Methods. Hence, the proposed Meshless Method is more accurate and efficient than conventional complex variable Meshless Methods. Numerical examples of bending problem of Kirchhoff plates are presented to validate the advantages of ...
Ying Dai - One of the best experts on this subject based on the ideXlab platform.
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an improved interpolating complex variable element free galerkin Method for the pattern transformation of hydrogel
Engineering Analysis With Boundary Elements, 2020Co-Authors: Yajie Deng, Ligang Sun, Ying DaiAbstract:Abstract In this paper, an effective interpolating complex variable element free Galerkin Method is proposed for the steady large deformation analysis of hydrogels. In this Meshless Method, the essential boundary conditions can be applied directly without using other special Methods, which leads to less unknown coefficients. Through computing the swelling large deformation of a square hydrogel with three constrained boundaries, the presented Meshless Method is validated with higher accuracy and efficiency than other non-interpolating Meshless Methods. Based on the developed Meshless Method, different samples with elliptical, circular and square holes in a square hydrogel are simulated for analyzing the pattern transformation. The numerical results indicate that the shapes and initial sizes of holes in hydrogels lead to different pattern transformation rules, actuating behaviors and area reductions of holes. Finally, according to the new findings, the potential applications of a square hydrogel are discussed by designing different shapes and initial sizes of holes.
Yumin Cheng - One of the best experts on this subject based on the ideXlab platform.
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the complex variable element free galerkin cvefg Method for two dimensional elasticity problems
International Journal of Applied Mechanics, 2009Co-Authors: M J Peng, Pei Liu, Yumin ChengAbstract:Based on element-free Galerkin (EFG) Method and the complex variable moving least-squares (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) Method for two-dimensional elasticity problems is presented in this paper. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of moving least-squares (MLS) approximation, and we can thus select fewer nodes in the Meshless Method that is formed from the CVMLS approximation than are required in the Meshless Method of the MLS approximation with no loss of precision. The formulae of the CVEFG Method for two-dimensional elasticity problems is obtained. Compared with the conventional Meshless Method, the CVEFG Method has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG Method.
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complex variable moving least squares Method a Meshless approximation technique
International Journal for Numerical Methods in Engineering, 2007Co-Authors: K.m. Liew, Yumin Cheng, Cong Feng, S KitipornchaiAbstract:Based on the moving least-squares (MLS) approximation, we propose a new approximation Method-the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the Meshless Method that is formed from the CVMLS approximation than are required in the Meshless Method of the MLS approximation with no loss of precision. The Meshless Method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new Meshless Method for two-dimensional elasticity problems-the complex variable Meshless Method (CVMM)-and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional Meshless Method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM.
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a complex variable Meshless Method for fracture problems
Science China-physics Mechanics & Astronomy, 2006Co-Authors: Yumin ChengAbstract:Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable Meshless Method for fracture problems is presented, and the formulae of the complex variable Meshless Method are obtained. The complex variable Meshless Method in this paper has greater precision and computational efficiency than the conventional Meshless Method. Some examples are given.
