Hierarchical theories of structures based on Legendre polynomial expansions with finite element applications

the role of task-based techniques on the acquisition of english language structures by the intermediate efl students

this study examines the effetivenss of task-based activities in helping students learn english language structures for a better communication. initially, a michigan test was administered to the two groups of 52 students majoring in english at the allameh ghotb -e- ravandi university to ensure their homogeneity. the students scores on the grammar part of this test were also regarded as their pre...

Appropriate Loading Techniques in Finite Element Analysis of Underground Structures

Stability of underground structures is assessed by comparing rock strength with induced stresses resulted from ground stresses. Rock mass surrounding the opening may fail either by fracture or excessive deformation caused. Accurate calculation of induced stresses is therefore fundamental in the stability analysis of an opening. Although numerical methods, particularly finite element method, are...

Finite Element Approximation with Hierarchical B-Splines

Finite Element Methods with Hierarchical WEB-splines

Piecewise polynomial approximations are fundamental to geometric modeling, computer graphics, and finite element methods. The classical finite element method uses low order piecewise polynomials defined on polygonal domains. The domains are discretized into simple polygons called the mesh. These polygons might be triangles, quadrilaterals, etc., for two-dimensional domains, and tetrahedra, hexa...

Representation of sparse Legendre expansions

We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M N nonzero terms from only 2M function resp. derivative values f (1), j = 0, . . . , 2M − 1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evalu...