Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition. (C) 2013 Elsevier Masson SAS. All rights reserved.

Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfee method

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

Numerical Partition of Energy Absorption of Foam-filled Top-Hat and Double-Hat Sections

The interaction effect, i.e., the contribution of each component to the total energy absorption of an axially crushed foam-filled hat section was investigated quantitatively via numerical simulation. The FE results were first verified by experimental work of aluminum foam-filled top-hat and double-hat sections, then the contribution of foam-fillers and that of hat sections to the overall energy absorption were quantitatively obtained, respectively. When foam-filled, increase in energy absorption was found both in hat section component and foam-filler component, whereas the latter contributes predominantly to the interaction effect.

The effect of pH difference between two phases on the partition of lysozyme in aqueous two-phase system

In the investigation of effect of KSCN on the partitioning of lysozyme in PEG2000/ammonium sulfate aqueous two-phase system, it was found that the KSCN could alter the pH difference between the two phases. and thus affect the partition of lysozyme. The relationship between partition coefficients of lysozyme and pH differences between two phases was discussed.

The effect of KSCN on the partition of proteins in polyethylene glycol/(NH4)(2)SO4 aqueous two-phase system

The effect of potassium thiocyanate on the partitioning of lysozyme and BSA in polyethylene glycol 2000/ammonium sulfate aqueous two-phase system has been investigated. As a result of the addition of potassium thiocyanate to the PEG/ammonium sulfate system, the PEG/mixed salts aqueous two-phase system was formed. It was found that the potassium thiocyanate could alter the pH difference between the two phases, and, thus, influence the partition coefficients of the differently charged proteins. The relationship between partition coefficient of the proteins and pH difference between two phases has been discussed. It was proposed that the pH difference between two phases could be employed as the measurement of electrostatic driving force for the partitioning of charged proteins in polyethylene glycol 2000/ammonium sulfate aqueous two-phase system.