Robustness of isogeometric structural discretizations under severe mesh distortion

The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.

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An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

A new partition of unity finite element free from the linear dependence problem and possessing the delta property

In this article, two criteria are suggested to inspect whether a model of geospatial information diffusion is valid to fill in the missing observation in a gap unit. The first criterion serves for inspecting a gap unit in the study area, from which a sample is taken to train the model. The second criterion serves for a gap unit outside the area but nearby. The standard deviation of the trained model plays a key role in the former. The valid radiance determined by the maximum distance between the units of the sample point passed the test and the center of the study area plays an important role in the latter.

Risk Analysis Based on Data and Crisis Response Beyond Knowledge : Proceedings of the 7th International Conference on Risk Analysis and Crisis Response (RACR 2019), October 15-19, 2019, Athens, Greece

In the finite element method (FEM), a mesh is used for representing the geometry of the analysis and for representing the test and trial functions by piece-wise interpolation. Recently, analysis techniques that use structured grids have been developed to avoid the need for a conforming mesh. The boundaries of the analysis domain are represented using implicit equations while a structured grid is used to interpolate functions. Such a method for analysis using structured grids is presented here in which the analysis domain is constructed by Boolean combination of step functions. Implicit equations of the boundary are used in the construction of trial and test functions such that essential boundary conditions are guaranteed to be satisfied. Furthermore, these functions are constructed such that internal elements, through which no boundary passes, have the same stiffness matrix. This approach has been applied to solve linear elastostatic problems and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the FEM in quality but is less computationally expensive for dense mesh/grid and avoids the need for a conforming mesh. Copyright © 2007 John Wiley & Sons, Ltd.

Implicit boundary method for finite element analysis using non-conforming mesh or grid

An octree partition of unity method (OctPUM) with enrichments for multiscale modeling of heterogeneous media

Hierarchical tree-based discretization for the method of finite spheres

Towards an automatic discretization scheme for the method of finite spheres and its coupling with the finite element method

SUMMARY In this paper, we report the development of two new enrichment techniques for the method of finite spheres, a truly meshfree method developed for the solution of boundary value problems on geometrically complex domains. In the first method, the enrichment functions are multiplied by a weight function with compact support, while in the second one a floating ‘enrichment node’ is introduced. The scalability of the enrichment bubbles offers flexibility in localizing the spatial extent to which the enrichment field is applied. The bubbles are independent of the underlying geometric discretization and therefore provide a means of achieving convergence without excessive refinement. Several numerical examples involving problems with singular stress fields are provided demonstrating the effectiveness of the enrichment schemes and contrasting them to traditional ‘geometry-dependent’ enrichment strategies in which one or more nodes associated with the geometric discretization of the domain are enriched. An additional contribution of this paper is the use of a meshfree numerical integration technique for computing the J -integral using the domain integral method. Copyright 2006 John Wiley & Sons, Ltd.

Enrichment of the method of finite spheres using geometry‐independent localized scalable bubbles

In this paper we provide some examples where the method of finite spheres, a truly meshfree numerical technique, is enriched by functions derived from asymptotic solutions of the governing differential equations in the vicinity of singularities. Specifically, we demonstrate the effectiveness of this technique for the analysis of an elastic double edge notched tension specimen and an elastic domain indented with a right-sided rigid punch under slip and no slip conditions. The solutions are compared with those obtained using the method of finite spheres without enrichment and the traditional finite element method.

Michael Macri

Papers

An octree partition of unity method (OctPUM) with enrichments for multiscale modeling of heterogeneous media

Hierarchical tree-based discretization for the method of finite spheres

Towards an automatic discretization scheme for the method of finite spheres and its coupling with the finite element method

Enrichment of the method of finite spheres using geometry‐independent localized scalable bubbles

Some examples of the method of finite spheres with enrichment