Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

A Meshfree Weak-Strong-Form Method for Magnetohydrodynamic Flow in a Pipe

Abstract: In this paper, a meshfree weak-strong form method is presented to compute the fully developed magnetohydrodynmic flow in a pipe. The radial basis function point interpolation approximation is adopted to construct the shape functions. For the nodes whose local quadrature domain is intersect with the natural boundaries, a local weak form of radial point interpolation method is applied. Otherwise, a strong form of meshfree point collocation method is employed. Numerical simulations are carried out for fully developed magnetohydrodynmic flow in a rectangular pipe with arbitrary electrical conductivity.

Numerical simulation of the generalized Burger’s-Huxley equation via two meshless methods

Abstract: Numerical solution of the generalized Burger?s-Huxley equation is established utilizing two effective meshless methods namely: local differential quadrature method and global method of line. Both the proposed meshless methods used radial basis functions to discretize space derivatives which convert the given model equation system of ODE and then we have utilized the Euler method to get the required numerical solution. Numerical experiments are carried out to check the efficiency and accuracy of the suggested meshless methods.

Peridynamic Galerkin method: an attractive alternative to finite elements

Abstract: Abstract This work presents a meshfree particle scheme designed for arbitrary deformations that possess the accuracy and properties of the Finite-Element-Method. The accuracy is maintained even with arbitrary particle distributions. Mesh-based methods mostly fail if requirements on the location of evaluation points are not satisfied. Hence, with this new scheme not only the range of loadings can be increased but also the pre-processing step can be facilitated compared to the FEM. The key to this new meshfree method lies in the fulfillment of essential requirements for spatial discretization schemes. The new approach is based on the correspondence theory of Peridynamics. Some modifications of this framework allows for a consistent and stable formulation. By applying the peridynamic differentiation concept, it is also shown that the equations of the correspondence theory can be derived from the weak form. Likewise, it is demonstrated that special moving least square shape functions possess the Kronecker- $$\delta $$ δ property. Thus, Dirichlet boundary conditions can be directly applied. The positive performance of this new meshfree method, especially in comparison to the Finite-Element-Method, is shown in the calculation of several test cases. In order to guarantee a fair comparison enhanced finite element formulations are also used. The test cases include the patch test, an eigenmode analysis as well as the investigation of loadings in the context of large deformations.

Multiscale meshfree method for the analysis of carbon nanotube-based materials

Abstract: Publisher Summary Carbon nanotube (CNT) is a new generation of nanoscale material. This chapter presents a new multiscale meshfree approach for the mechanical analysis of carbon nanotubes and related nanostructures. By projecting the solution from direct molecular dynamics simulation onto its coarse-scale representation, a unique bridging scale decomposition of the displacement field is proposed. To approximate the curved surface at nanoscale, meshfree approximations are introduced to interpolate a single layer of atoms. Unlike the traditional shell or continuum element, the geometric constraint is only imposed in2D . The high order continuity property of the meshfree shape functions guarantees the accuracy in describing the geometry of the atomic bond. The chapter highlights the robustness of the method through a number of examples involving carbon nanotube-based structures.

Recent developments in particle-based method for simulation of explosive blast

Abstract: To support simulations of blast loading from explosives using the Material Point Method (MPM), preliminary studies of gas expansion in MPM using the recently developed Convected Particle Domain Interpolation (CPDI) integrator, as well as established integrators based on the Generalized Interpolation Material Point (GIMP) method, show that prevailing algorithms for updating the deformation gradient produce results that are often grossly inconsistent with the update of the particle positions. Mapping of velocity to boundary background nodes is analyzed and demonstrated to induce large errors in problems involving large velocities and rapidly changing velocity gradients (common in blast and penetration applications). The error in the velocity cascades to ultimately corrupt other variables, especially the velocity gradient and stress on which it depends. A well-respected code verification process (the method of manufactured solutions) is used to quantify the errors in the update of variables in the MPM using the CPDI interpolator. Different methods based on linear extrapolation were tested for their potential to improve the mapping of the large-deformation velocity fields in blast and penetration, but with only isolated successes in some cases that often worsened results in other cases. 1 Recent developments in particle-based method for simulation of explosive blast