Application Of Mesh-free Method Research Articles

A computational homogenization analysis of materials using the stabilized mesh-free method based on the radial basis functions

This study presents a novel application of mesh-free method using the smoothed-radial basis functions for the computational homogenization analysis of materials. The displacement field corresponding to the scattered nodes within the representative volume element (RVE) is split into two parts including mean term and fluctuation term, and then the fluctuation one is approximated using the integrated radial basis function (iRBF) method. Due to the use of the stabilized conforming nodal integration (SCNI) technique, the strain rate is smoothed at discreted nodes; therefore, all constrains in resulting problems are enforced at nodes directly. Taking advantage of the shape function satisfies Kronecker-delta property, the periodic boundary conditions well-known as the most appropriate procedure for RVE are similarly imposed as in the finite element method. Several numerical examples are investigated to observe the computational aspect of iRBF procedure. The good agreement of the results in comparison with those reported in other studies demonstrates the accuracy and reliability of proposed approach.
 Keywords:
 homogenization analysis; mesh-free method; radial point interpolation method; SCNI scheme.

Evaluation of soil-nail pullout resistance using mesh-free method

Soil nailing has been widely used in the world during the last two decades; because of its technical and economical advantages. The shear strength versus displacement behavior of soil-nail interface has significant effects on economic and safety design of a soil-nail system. In this paper, by application of mesh-free method, MFM, a new approach is presented to investigate the behavior of interface in soil-nail pullout process and also the interaction between nail and surrounding soil. Simulation of soil-nail interface in mesh dependent methods such as finite element method, FEM, has been associated with problems of heterogeneous deformations.In the presented method, the problem domain and its boundary are represented by using sets of nodes scattered in the problem domain and on its boundary. Interaction between nail and surrounding soil is simulated using interface layers with small thickness which is able to model slippage between nail and surrounding soil. The model is based on a Mohr-Coulomb failure criterion, including deviatoric hardening/softening during pre and post peak pullout point and ultimate state. A computer code has been developed to simulate elasto-plastic soil-nail pullout behavior. Simulation results show good performance of MFM in numerical simulation of soil-nail interaction and also soil-nail pullout resistance.

Meshfree Method in Geophysical Electromagnetic Prospecting: The 2D Magnetotelluric Example

As an important supplement and development of traditional methods, the meshfree method has received a great deal of attention in the field of engineering calculation, and has been successfully used to solve many problems which traditional methods have difficulty in solving. However, the application of meshfree method is relatively less in the area of geophysics. In this paper, we apply the meshfree method to the numerical simulation of geophysical electromagnetic prospecting, taking the 2D magnetotelluric as an example and deduce the corresponding meshfree radial point interpolation method (RPIM) equivalent linear equations in detail. The high-efficiency and accurate solutions of large-scale sparse linear equations are solved by the quasi-minimal residual method based on Krylov subspace. The optimal values of the shape parameters are given by numerical experiments. The correctness of the meshfree method is verified by a layered model. The root mean square error of the calculation results is no more than 0.35%, its accuracy is superior to the finite element method. We also compare the meshfree solution with FEM solution by calculating an inclined vein body model, and the calculation results are in good agreement. A continuously changing fault model and undulating terrain model which traditional methods have difficulty in simulating are respectively calculated, the sectional profiles of the apparent resistivity accurately reflect the trend of the anomalies. The meshfree method does not require the complicated mesh generation, and the physical parameters are loaded at a series of points, thus it is especially suitable for the calculation of the complex geological models. With the rapid development of computational science, the meshfree techniques will certainly become a new robust numerical simulation method in geophysical electromagnetic prospecting.

Application of Mesh-free Methods in Transient Dynamic Analysis of Orthotropic Plates

Application of Mesh-free Methods in Transient Dynamic Analysis of Orthotropic Plates

The Application of Mesh-Free Method in the Numerical Simulation of Beams with the Size Effect

The mesh-free method is employed to implement the numerical simulation of the bending behavior of beams with the size effect. On the basis of the classical Bernoulli-Euler beam theory, two higher-order strain components are involved in the beam model. The intrinsic bulk length and the directional surface length components are introduced into the constitutive relationship to describe the size effect, and the variation of the total potential is provided. The moving-least square approximation is used to construct the shape function and its second- and third-order derivatives, and the choice of the scaling factor is discussed in detail. A mesh-free scheme is built to implement numerical simulation, in which the higher-order strains are directly approximated with the nodal components due to the higher-order continuity of the shape function. The convergence of method is illustrated in virtue of an example of the simply supported beam, and the effect of the intrinsic bulk length and the directional surface length components are studied.

Application of Mesh Free Method to Evaluation of Woven Fabric Composite Elastic Moduli

A computational method for the micro-mechanical material model of woven fabric composite material was developed in this paper based on a repeated unit cell approach and two smooth fibre modes were presented. The stiffness matrix was evaluated with a domain integral by the use of radial basis function interpolations without element mesh. The applications of mesh free method to evaluate woven fabric composite elastic moduli have been presented and good accuracy has been achieved compared with the results by other approaches.

817 メッシュ生成・メッシュレス解析の障害とメッシュフリー法の応用例

817 メッシュ生成・メッシュレス解析の障害とメッシュフリー法の応用例