# Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Fantuzzi, Nicholas (2013) Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Ingegneria strutturale ed idraulica, 25 Ciclo. DOI 10.6092/unibo/amsdottorato/5932.
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## Abstract

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Fantuzzi, Nicholas
Supervisore
Co-supervisore
Dottorato di ricerca
Scuola di dottorato
Ingegneria civile ed architettura
Ciclo
25
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Generalized Differential Quadrature Method, Generalized Differential Quadrature Finite Element Method, Composite Structures, Discontinuities, Crack
URN:NBN
DOI
10.6092/unibo/amsdottorato/5932
Data di discussione
31 Maggio 2013
URI