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Nonlinear Finite Elements For Continua And Structures

This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced comp...

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A generalized gradient smoothing technique and the smoothed bilinear form for galerkin formulation of a wide class of computational methods

A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis

Quasi-static and dynamic compression tests are conducted on carbonate sand using a Material Testing System and a modified split Hopkinson pressure bar, respectively. The particle size distributions (PSDs) of carbonate sand before and after loading are measured via laser diffractometry. The stress–strain curves demonstrate that the carbonate sand investigated in this study exhibits strain rate effects. The stress–strain curves show slightly different features for quasi-static and dynamic loading conditions. The particle breakage extent, which is quantified from the PSDs of the samples before and after loading, is investigated at different stress levels and input energy values. The breakage efficiency under the quasi-static loading condition is higher than that under the dynamic loading condition. As a result, the particle breakage extent is higher under the quasi-static loading condition than under the dynamic loading condition at the same stress level. Furthermore, the particle breakage modes are highly dependent on stress. The breakage modes under the dynamic loading condition change from attrition and abrasion at low stress levels, resulting in the appearance of plateaus in the grading curves, to fracture at high stress levels, resulting in the disappearance of plateaus in the grading curves.

Particle breakage and energy dissipation of carbonate sands under quasi-static and dynamic compression

This paper explores the approximation power of Moving Least-Squares (MLS) approximations in the context of higher-order finite volume schemes on unstructured grids. The scope of the application of MLS is threefold: (1) computation of high-order derivatives of the field variables for a Godunov-type approach to hyperbolic problems or terms of hyperbolic character, (2) direct reconstruction of the fluxes at cell edges, for elliptic problems or terms of elliptic character, and (3) multiresolution shock detection and selective limiting. A major advantage of the proposed methodology over the most popular existing higher-order methods is related to the viscous discretization. The use of MLS approximations allows the direct reconstruction of high-order viscous fluxes using quite compact stencils, and without introducing new degrees of freedom, which results in a significant reduction in storage and workload. A selective limiting procedure is proposed, based on the multiresolution properties of the MLS approximants, which allows to switch off the limiters in smooth regions of the flow. Accuracy tests show that the proposed method achieves the expected convergence rates. Representative simulations show that the methodology is applicable to problems of engineering interest.

Finite volume solvers and movingleast-squares approximations for thecompressible Navier-Stokes equations onunstructured grids

At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.

An improved finite point method for tridimensional potential flows

The paper reports the results of suction-controlled triaxial tests performed on compacted samples of two well-graded granular materials in the range of coarse sand–medium gravel particle sizes: a quartzitic slate and a hard limestone. The evolution of grain size distributions is discussed. Dilatancy rules were investigated. Dilatancy could be described in terms of stress ratio, plastic work input and average confining stress. The shape of the yield locus in a triaxial plane was established by different experimental techniques. Yielding loci in both types of lithology is well represented by approximate elliptic shapes whose major axis follows approximately the K0 line. Relative humidity was found to affect in a significant way the evolution of grain size distribution, the deviatoric stress–strain response and the dilatancy rules.

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Yielding of rockfill in relative humidity-controlled triaxial experiments

Electronic version of an article published as "International journal for numerical methods in fluids", vol. 60, no 9, 2009, p. 937-971. DOI:10.1002/fld.1892

/pdf/a-finite-point-method-for-adaptive-three-dimensional-5aw3gvsemc.pdf

A finite point method for adaptive three-dimensional compressible flow calculations

A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind-biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual-time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h-adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi-core performance of the proposed technique is also discussed through the examples provided.

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Enrique Ortega

Papers

An improved finite point method for tridimensional potential flows

Yielding of rockfill in relative humidity-controlled triaxial experiments

A finite point method for adaptive three-dimensional compressible flow calculations

A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity

Comparative accuracy and performance assessment of the finite point method in compressible flow problems