A meshless solution algorithm for the full potential equation has been developed by applying the principles of the Taylor Least Squares (TLS) method. This method allows for a PDE to be discretized on a local cloud of scattered nodes without the need of connectivity data. The process for discretizing the full potential equation within a meshless framework is outlined along with a novel Hermite T...

The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impac...

This paper presents the implementation of a three-dimensional dynamic code, for contact, impact, and penetration mechanics, based on the Meshless Local Petrov-Galerkin (MLPG) approach. In the current implementation, both velocities and velocity-gradients are interpolated independently, and their compatibility is enforced only at nodal points. As a result, the time consuming differentiations of ...

The stationary Fokker-Planck Equation (FPE) is solved for nonlinear dynamic systems using a local numerical technique based on the meshless Partition of Unity Finite Element Method (PUFEM). The method is applied to the FPE for two-dimensional dynamical systems, and argued to be an excellent candidate for higher dimensional systems and the transient problem. Variations of the conventional PUFEM ...

The regularized meshless method is a novel boundary-type meshless method but by now has largely been confined to homogeneous problems. In this paper, we apply the regularized meshless method to the nonhomogeneous problems in conjunction with the dual reciprocity technique in the evaluation of the particular solution. Numerical experiments of three benchmark nonhomogeneous problems demonstrate t...

The paper provides a computational technique that allows to compare all linear methods for PDE solving that use the same input data. This is done by writing them as linear recovery formulas for solution values as linear combinations of the input data, and these formulas are continuous linear functionals on Sobolev spaces. Calculating the norm of these functionals on a fixed Sobolev space will t...

Introduction Moving least squares approximation is one kind of meshless methods in which the approximation is built from nodes only. Comparing to mesh-based methods, meshless methods have advantages on (1) refining is simpler to incorporate, (2) moving discontinuities can be treated easily, (3) large deformation can be handled robustly, (4) higher-order continuous shape functions, (5) non-local...

It is widely acknowledged that 3-D mesh generation remains one of the most man-hours consuming techniques within computational mechanics. The problem of mesh generation is that the time remains unbounded, even using the most sophisticated mesh-generator. For a given distribution of points, it is possible to obtain a mesh very quickly, but it may require several iterations, including manual inte...

In this paper, a method based on a combination of an optimization of directions of orthotropy, along with topology optimization, is applied to continuum orthotropic solids with the objective of minimizing their compliance. The spatial discretization algorithm is the so called Meshless Local Petrov-Galerkin (MLPG) “mixed collocation” method for the design domain, and the material-orthotropy orie...