Moving least squares differential quadrature method and its application to the analysis of shear deformable plates

Liew, K.M.; Huang, Y. Q.; Reddy, J. N.

doi:10.1002/nme.646

Cited by 90 publications

(29 citation statements)

References 33 publications

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Section: Introductionmentioning

confidence: 99%

“…Belytschko et al (1994) discovered some noteworthy advantages by applying this method on analyzing elastic and heat conduction problems. Recently, the MLS shape functions have also been employed in the differential quadrature method (DQ) to further develop MLSDQ meshfree method for solving heat conduction problems (Liew et al 2002a) and plate problems (Liew et al 2002b).Intelligent structures are systems whose geometric and structural characteristics can be beneficially modified during their operational life to meet the host's requirement. They compose the main structure and a network of sensors and actuators.…”

mentioning

confidence: 99%

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Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

Liew

Lim

Tan

et al. 2002

Computational Mechanics

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An efficient meshfree formulation based on the first-order shear deformation theory (FSDT) is presented for the static analysis of laminated composite beams and plates with integrated piezoelectric layers. This meshfree model is constructed based on the element-free Galerkin (EFG) method. The formulation is derived from the variational principle and the piezoelectric stiffness is taken into account in the model. In numerical test problems, bending control of piezoelectric bimorph beams was shown to have the efficiency and accuracy of the present EFG formulation for this class of problems. It is demonstrated that the different boundary conditions and applied actuate voltages affects the shape control of piezolaminated composite beams. The meshfree model is further extended to study the shape control of piezolaminated composite plates. From the investigation, it is found that actuator patches bonded on high strain regions are significant in deflection control of laminated composite plates. IntroductionThe subject of numerical simulation has been dominated by the finite element method (FEM), finite difference method (FDM) and boundary element method (BEM) for the past few decades. Having been thoroughly developed and refined over many years, FEM has become a very popular, effective and versatile tool for the computer solution of complex problems in engineering disciplines. Since finite element solution is highly mesh dependent, its shortcomings such as prolonged time-consuming mesh refinements and elements of distorted shapes and sizes when handling different types of problems, such as crack propagation, high gradient (e.g., shock wave) and shear band strain localization are evident.A new family of methods has been developed to ameliorate the above-mentioned difficulties. In fact, these have drawn considerable attention as the methods employ an approximation of the unknown field based on a scattered set of nodes or particles. This class of methods is the socalled meshless or meshfree methods. In these methods, the domain of interest is discretized by a scattered set of particles instead of elements used in mesh-based methods such as FEM, and thus without having the need for characterization of the interrelationship of the nodes, be able to construct the discrete equations. It is developed by creating new shape functions using the interpolation of field variables at a global level. Owing to the above-mentioned advantages, increasing attention is placed on the development of meshfree methods as alternative to the finite element method.The element-free Galerkin method (EFG) is a truly meshfree one, as it does not need a 'finite element or boundary element mesh', i.e., there is no necessity for explicit meshes in the construction of moving least-square (MLS) shape functions. Although background cells are required for integration, the integration cells need not be compatible to the scattered nodes distributed on the structures, thus they can be generated more easily than the FEM meshes. The consistency of the MLS approxi...

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

Liew

Lim

Tan

et al. 2002

Computational Mechanics

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Section: Iûimentioning

confidence: 99%

“…The integrals in (42) and (43) can be evaluated in virtue of the background cells [27][28][29]. In this work, we use the background cells that coincide with the nodal arrangements [28,29], and the Gaussian quadrature is used in each cell. At each iteration step, we need to calculate the first-and second-order deformation gradients using (38)-(41) for each quadrature point and then to use the minimizing method in Section 3.1 to determine the stresses and tangent modulus.…”

Section: Iûimentioning

confidence: 99%

Application of the higher‐order Cauchy–Born rule in mesh‐free continuum and multiscale simulation of carbon nanotubes

Sun

Liew

2008

Numerical Meth Engineering

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SUMMARYThis paper investigates the application of a recently proposed higher-order Cauchy-Born rule in the continuum simulation and multiscale analysis of carbon nanotubes (CNTs). A mesh-free computational framework is developed to implement the numerical computation of the hyper-elastic constitutive model that is derived from the higher-order Cauchy-Born rule. The numerical computation reveals that the buckling pattern of a single-walled carbon nanotube (SWCNT) can be accurately displayed by taking into consideration the second-order deformation gradient, and fewer mesh-free nodes can provide a good simulation of homogeneous deformation. The bridging domain method is employed to couple the developed mesh-free method and the atomistic simulation. The coupling method is used to simulate the bending buckling of an SWCNT and the tensile failure of an SWCNT with a single-atom vacancy defect, and good computational results are obtained.

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“…The moving least-squares (MLS) approximation is one of the bases of the meshless method [4][5][6][7]. The trial function that is formed with the MLS approximation is simple, and can obtain a solution that has great precision.…”

Section: Introductionmentioning

confidence: 99%

A boundary element-free method (BEFM) for three-dimensional elasticity problems

2005

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This study combines the boundary integral equation (BIE) method and improved moving leastsquares (IMLS) approximation to present a direct meshless boundary integral equation method, the boundary element-free method (BEFM) for threedimensional elasticity. Based on the improved moving least-squares approximation and the boundary integral equation for three-dimensional elasticity, the formulae of the boundary element-free method are given, and the numerical procedure is also shown. Unlike other meshless boundary integral equation methods, the BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus giving it a greater computational precision. Three selected numerical examples are presented to demonstrate the method.

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Moving least squares differential quadrature method and its application to the analysis of shear deformable plates

Cited by 90 publications

References 33 publications

Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

Application of the higher‐order Cauchy–Born rule in mesh‐free continuum and multiscale simulation of carbon nanotubes

A boundary element-free method (BEFM) for three-dimensional elasticity problems

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