Maximum-entropy meshfree method for compressible and near-incompressible elasticity

Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a lockingfree small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum

/pdf/maximum-entropy-meshfree-method-for-compressible-and-near-16ichzmee2.pdf

Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity

The results on theoretical and numerical modeling of resonant piezoelectric devices in China are reviewed. Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW), surface acoustic waves (SAW), vibrations of finite bodies, and analyses of specific devices are discussed. Results from both the ultrasonics community and mechanics researchers are included. It is hoped that the paper will be useful for the understanding, communication and collaboration between Chinese and foreign scholars. The paper may also be helpful for bridging the gap between ultrasonics and mechanics researchers on piezoelectricity research. The paper contains 316 references.

https://rd.springer.com/content/pdf/10.1007%2Fs11433-008-0188-1.pdf

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

A global interpolating meshless shape function based on the generalized moving least-square (GMLS) is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS (IGMLS) shape function, an improved element-free Galerkin (EFG) method is proposed for the structural dynamic analysis. Compared with the conventional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasibility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

Free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method (LRPIM) into a Hamilton system. The governing equation is derived with a transfer matrix technique and a spring layer model based on a local weak-form equivalent to the modified Hellinger-Reissner variational principle. Main superiority of the present model is that the scale of the governing equation involves only the so-called state variables at the top and bottom surfaces, and is insensitive to the thickness and the layer number of the composite laminates. Several numerical examples for analyzing the vibration frequencies and mode shapes of delaminated composite beams and plates are given to validate the model. The results are in good agreement with the pre-existing results.

Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system

Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature (PUQ), for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods.

Zeng Qing-hong

Papers

Galerkin meshless methods based on partition of unity quadrature