Banca de DEFESA: Jailson França dos Santos

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Jailson França dos Santos
DATE: 19/05/2023
TIME: 14:00
LOCAL: Plataforma Microsoft TEAMS
TITLE:

Application of the boundary element method with multipole expansion and isogeometric approach in anisotropic elastic problems

KEY WORDS:

Boundary Element Method; Isogeometric analysis; Fast Multipole Method; Anisotropic Plane Elasticity

PAGES: 159
BIG AREA: Engenharias
AREA: Engenharia Mecânica
SUMMARY:

This thesis presents an Isogeometric Analysis of the Boundary Element Method (IGABEM) together with the fast multipole expansion method, applied to anisotropic elastic problems in a 2D plane. Lekhnitskii's anisotropic fundamental solution is used, and in it there are singularities, that of the weak type of the displacement kernel, which is treated with the Telles transform method, while the strong singularity of the surface force kernel is treated by the technique of the singularity subtraction (SST). The shape functions used in this work are NonUniform Rational B-Splines (NURBS). Thus, the same mathematical representation of Computer Aided Design (CAD) is used in the developed computational code, avoiding the generation of meshes and providing exact representation for most of the complex geometries used in engineering analysis. In addition to the FMM, in order to further improve the numerical efficiency of the code, reducing the computational cost, the NURBS are decomposed into Bézier curves without losing the continuity properties, using the Bézier decomposition. In this way, the isogeometric formulation becomes similar to the conventional boundary element method. As the matrices of the algebraic system are not explicitly assembled due to the FMM, it is necessary to use an iterative method to solve the system of linear equations. The generalized minimal residual method (GMRES) was chosen, according to its efficiency noted in previous works and according to the literature. To evaluate the accuracy of the formulation, different numerical examples applied to quasi-isotropic, anisotropic and orthotropic materials are analyzed. The numerical results of the IGABEM and its accelerated version by the FMM are compared with analytical solutions, and even with few degrees of freedom, they show that they have excellent numerical precision. In addition to these, the accelerated formulation was also applied to large-scale problems, models with thousands of degrees of freedom, proving that it is faster than the IGABEM, and therefore, it is a very suitable formulation for large-scale elastic problems, mainly for geometries that are best suited to the use of higher-order boundary elements.

BANKING MEMBERS:
Externo à Instituição - CARLOS FRIEDRICH LOEFFLER NETO - UEFS
Interno - 1722212 - EDER LIMA DE ALBUQUERQUE
Externo à Instituição - EDSON DENNER LEONEL - USP
Interno - 3375759 - TAYGOARA FELAMINGO DE OLIVEIRA
Interno - 2143651 - THIAGO DE CARVALHO RODRIGUES DOCA