Search results for "Quadrilateral"
showing 8 items of 8 documents
New Geometric Constraint Solving Formulation: Application to the 3D Pentahedron
2014
Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be …
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
A design algorithm for the optimization of laminated composite structures
1999
This paper is devoted to the optimal design of laminated composite structures. The goal of the study is to assess the quality and the performance of an algorithm based on the directional derivative method. Particular attention is paid to the one‐dimensional search, a critical step of the process, performed by cubic splines approximation. The optimization problem is formulated as weight minimization, under constraints on the mechanical behavior of the structure. The assumed design variables are the ply thicknesses, treated as continuous design variables, constrained by technological requirements. The structural analysis is performed making use of quadrilateral four‐node composite elements, b…
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
2018
We consider inequalities of the Poincare–Steklov type for subspaces of \(H^1\)-functions defined in a bounded domain \(\varOmega \in \mathbb {R}^d\) with Lipschitz boundary \(\partial \varOmega \). For scalar valued functions, the subspaces are defined by zero mean condition on \(\partial \varOmega \) or on a part of \(\partial \varOmega \) having positive \(d-1\) measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of \(\partial \varOmega \) (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincare type inequalities for domains typically used in finite …
Use of Language in Elementary Geometry by Students and Textbooks
1996
This chapter presents some results of a study on the definitions that appear in the Spanish textbooks for Primary School (Jaime, Chapa, and Gutierrez, 1992). Its aim is to point out the errors in the statements of definitions and inconsistent or inappropriate uses of definitions made in individual textbooks, or in series of textbooks. This study concerned geometry and, more specifically, triangles and quadrilaterals. Most of the problems that arose were strongly related to the understanding and use of language.
Mixed finite elements for nonlocal elastic multilayered composite plate refined theories
2020
Abstract A novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is presented. The finite elements are formulated starting from the weak form of a set of governing equations for the laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion order is considered as a free parameter. This way, finite elements for different refined higher order plate theories can …
The FLO Diffusive 1D-2D Model for Simulation of River Flooding
2016
An integrated 1D-2D model for the solution of the diffusive approximation of the shallow water equations, named FLO, is proposed in the present paper. Governing equations are solved using the MArching in Space and Time (MAST) approach. The 2D floodplain domain is discretized using a triangular mesh, and standard river sections are used for modeling 1D flow inside the section width occurring with low or standard discharges. 1D elements, inside the 1D domain, are quadrilaterals bounded by the trace of two consecutive sections and by the sides connecting their extreme points. The water level is assumed to vary linearly inside each quadrilateral along the flow direction, but to remain constant …
Previsione delle prestazioni del veicolo su strada: stato dell’arte
2016
Questo lavoro contiene una rassegna dei metodi che sono usati per la previsione delle prestazioni del veicolo su strada, in dipendenza del motore installato. La prima parte mostra il calcolo delle resistenze al moto, cioè le forze che il veicolo deve vincere per avanzare sulle strade piane e in salita. Particolarmente interessante appare la parte che riguarda la resistenza aerodinamica, della quale si tratta di metodi sperimentali (galleria del vento), metodi empirici e metodi CFD. Si propone inoltre l’applicazione della norma CUNA sulla velocità per la determinazione dei consumi anche al calcolo dei coefficienti aerodinamici. La rassegna esclude la resistenza accidentale in curva perché no…