Nodal integration of meshless methods

Meshless methods offer interesting properties for the simulation of bulk forming\ud processes. This research concerns the investigation of the stabilized conforming nodal integration scheme (SCNI) for use in metal-forming processes. Two tests are carried out. Firstly, the performance of SCNI is compared to a standard integration scheme. The performance seems problem specific. Secondly the footing of a piece of nearly incompressible material is used for testing the locking behavior of the method. No volumetric locking was found

Adaptive smoothed FEM for forming simulations

FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a\ud nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite\ud Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other.\ud A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear\ud assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselatio

On the use of local max-ent shape functions for the simulation of forming processes

In this work we review the opportunities given by the use of local maximum-\ud entropy approximants (LME) for the simulation of forming processes. This approximation can\ud be considered as a meshless approximation scheme, and thus presents some appealing features\ud for the numerical simulation of forming processes in a Galerkin framework.\ud Especially the behavior of these shape functions at the boundary is interesting. At nodes\ud on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the\ud prescription of boundary conditions. Shape functions at the boundary do not overlap internal\ud nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be\ud computed easily and efficiently compared to for instance moving least-squares approximations.\ud Furthermore, LME shapes also present a controllable degree of smoothness.\ud To test the performance of the LME shapes, an elastic and a elasto-plastic problem was\ud analyzed. The results were compared with a meshless method based on a moving least-squares\ud approximation

Comparison of ALE finite element method and adaptive smoothed finite element method for the numerical simulation of friction stir welding

In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane\ud strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of\ud the disc is clamped. Two numerical methods are used to solve this problem and an analytical solution is derived. The analytical\ud model is complementary to validate the two numerical methods, i.e. the arbitrary Lagrangian-Eulerian (ALE) method and the\ud adaptive smoothed finite elements method (ASFEM)

A comparative study on the performance of meshless approximations and their integration

The goal of this research is to study the performance of meshless approximations and their integration. Two diffuse shape functions, namely the moving least-squares and local maximum-entropy function, and a linear triangular interpolation are compared using Gaussian integration and the stabilized conforming nodal integration scheme. The shape functions and integration schemes are tested on two elastic problems, an elasto-plastic problem and the inf-sup test. The elastic computation shows a somewhat lower accuracy for the linear triangular interpolation than for the two diffuse functions with the same number of nodes. However, the computational effort for this interpolation is considerably lower. The accuracy of the calculations in elasto-plasticity depends to great extend on the used integration scheme. All shape functions, and even the linear triangular interpolation, perform very well with the nodal integration scheme and locking-free behavior is shown in the inf-sup test

Bezorgeconomie : de effecten op mobiliteit, milieu en leefomgeving.

De vaste kamercommissie EZK besprak de effecten van de bezorgeconomie. Experts hebben hierover een factsheet gemaakt: Wat zijn de effecten van onlinewinkelen voor de mobiliteit, het milieu en de leefomgeving en welke aanvullende maatregelen kan Nederland nemen voor een efficiëntere en duurzamere bezorgeconomie? Parlement en wetenschap

In vitro and in vivo study of commercial calcium phosphate cement HydroSet™.

The commercial calcium phosphate cement, HydroSet™, was investigated in vitro, studying phase formation, compressive strength and setting time, followed by an ovine in vivo study to measure osseointegration, bone apposition and bone-to-graft contact. The X-ray diffraction and P Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) results showed the initial formation of octacalcium phosphate and hydroxyapatite at one hour. Over 7 days the octacalcium phosphate transformed to apatite, which was the only crystalline phase of the cement at 28 days. This apatite phase is thought to be a calcium deficient apatite. In the scanning electron microscopy, histological images of 12-week ovine in vivo results showed a high degree of osseointegration, 92.5%. Compressive strength comparisons between in vitro and in vivo measurements showed a dramatic difference between the in vitro measurements (highest 25.4 MPa) and in vivo (95 MPa), attributed to bone ingrowth into the cement in vivo. To the best of our knowledge this is the first time phase evolution of HydroSet™ and the properties studied in vitro complement the in vivo evaluation of the cement in a publication. The significance of the new finding of initial formation of octacalcium phosphate in this cement is discussed