SENSITIVITY ANALYSIS OF 3D FRICTIONAL CONTACT WITH BEM USING COMPLEXSTEP DIFFERENTIATION

  • CRISTIANO JOÃO BRIZZI UBESSI Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, - Porto Alegre, Rio Grande do Sul, Brasil
  • ROGÉRIO JOSÉ MARCZAK Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, - Porto Alegre, Rio Grande do Sul, Brasil

Abstract

THIS PAPER IS A STUDY ON THE APPLICATION OF THE COMPLEX STEP DIFFERENTIATION METHOD ON A PARAMETER SENSITIVITY ANALYSIS FOR A 3D ELASTIC CONTACT PROBLEM. THE ANALYSIS IS PERFORMED WITH BOUNDARY ELEMENT METHOD (BEM) WITH DISCONTINUOUS ELEMENTS, ALONG WITH THE GENERALIZED NEWTON METHOD WITH LINE SEARCH (GNMLS). A STANDARD BEM IMPLEMENTATION IS USED, AND THE CONTACT RESTRICTIONS ARE FULFILLED THROUGH THE AUGMENTED LAGRANGIAN.THIS METHOD IN CONJUNCTION WITH BEM ALLOWS TO SKIP THE CALCULATION OF THE NON-LINEAR DERIVATIVES DURING THE SOLUTION PROCESS, ALLOWING FOR A FAST AND RELIABLE SOLUTION PROCEDURE. THE PARAMETER SENSITIVITY IS EVALUATED USING COMPLEX-STEP DIFFERENTIATION. THIS WELL KNOWN METHOD APPROXIMATES THE DERIVATIVE OF A FUNCTION ANALOGICALLY TO THE STANDARD FINITE DIFFERENCES METHOD, WITH THE ADVANTAGES OF BEING NUMERICALLY EXACT, AND NEARLY INSENSITIVE TO THE STEP-SIZE. A HERTZ TYPE PROBLEM IS SOLVED, AND THE PARAMETER EVALUATED IS THE YOUNG MODULUS AND ITS INFLUENCE ON THE MAXIMUM CONTACT PRESSURE, AND COMPARED WITH ANALYTIC SOLUTIONS.

Author Biographies

CRISTIANO JOÃO BRIZZI UBESSI, Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, - Porto Alegre, Rio Grande do Sul, Brasil

Programa de Pós Graduação em Engenharia Mecânica

ROGÉRIO JOSÉ MARCZAK, Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul, - Porto Alegre, Rio Grande do Sul, Brasil

Departamento de Engenharia Mecânica

Published
2018-05-28
Section
MecSol 2017 Joinville