This paper describes a new topology optimization (TO) technique based on meshless method to evolve two-dimensional truss structures. The meshless method has been considered as a very attractive computational technique since it does not need any mesh generation process during the analysis. It has been gradually and widely used in many engineering disciplines and a particular weak point such as t...

This article presents a summary of the key-note lecture delivered at Biomechanics 10 Conference held in August 2010 in Warsaw. We present selected topics in the area of mathematical and numerical modelling of the brain biomechanics for neurosurgical simulation and brain image registration. These processes can reasonably be described in purely mechanical terms, such as displacements, strains and...

Although, the finite element method numerically is efficient it exhibits difficulties whenever the remeshing of the analysis domain must be performed. For such problems, utilizing meshless computation methods is very promising. But, their large computational cost, which arises from following a time-consuming process to find shape functions, is one of the most important factors limiting the use ...

We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. The algorithm combines a meshless discretization of the deformation field with explicit surface tracking using a triangle mesh. We decompose the splitting operation into a first step where we synthesize crack surfaces, and a second step wh...

Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations. On one hand, high accuracy is always desired; on the other, ill-conditioning problems of the resultant matrices, that may lead to unstable algorithms, prevent some researchers from using meshless methods. For example, the optimal placements of source points in...

Point-based surface processing has developed into an attractive alternative to mesh-based processing techniques for a number of geometric modeling applications. By working with point cloud data directly, any processing is based on the given raw data and its underlying geometry rather than any arbitrary intermediate representations and generally artificial connectivity relations. In this paper, ...

Title of dissertation: OPTIMAL APPROXIMATION SPACES FOR SOLVING PROBLEMS WITH ROUGH COEFFICIENTS Qiaoluan Li, Doctor of Philosophy, 2009 Dissertation directed by: Professor John E. Osborn Department of Mathematics The finite element method has been widely used to solve partial differential equations by both engineers and mathematicians for the last several decades. This is due to its well-known...

We discuss a discretization approach for the p Laplacian equation and a variational inequality associated to fourth order elliptic operators, via a meshless approach based on duality theory. MSC: 35J20, 35J25, 65N99. keywords: nonlinear elliptic equations, Fenchel theorem, approximation, meshless method.