22 research outputs found
Analytical computation of moderate-degree fully-symmetric cubature rules on the triangle
A method is developed to compute analytically fully symmetric cubature rules
on the triangle by using symmetric polynomials to express the two kinds of
invariance inherent in these rules. Rules of degree up to 15, some of them new
and of good quality, are computed and presented.Comment: 13 pages, submitted to Journal of Computational and Applied
Mathematic
New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases
Cubature rules on the triangle have been extensively studied, as they are of
great practical interest in numerical analysis. In most cases, the process by
which new rules are obtained does not preclude the existence of similar rules
with better characteristics. There is therefore clear interest in searching for
better cubature rules. Here we present a number of new cubature rules on the
triangle, exhibiting full or rotational symmetry, that improve on those
available in the literature either in terms of number of points or in terms of
quality. These rules were obtained by determining and implementing minimal
orthonormal polynomial bases that can express the symmetries of the cubature
rules. As shown in specific benchmark examples, this results in significantly
better performance of the employed algorithm.Comment: 12 pages, 1 figur
Influence of various DEM shape representation methods on packing and shearing of granular assemblies
A novel efficient mixed formulation for strain-gradient models.
Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues, while being simpler and computationally cheaper. The behaviour of the new elements is further demonstrated through a numerical example