HIGH ORDER ELEMENTS FOR SLENDER BEAMS UNDER LARGE DEFORMATIONS. APPLICATION TO THE DYNAMICS OF OF FLEXIBLE BODIES.

• Grant number: 22/13172-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2022
• End date: November 30, 2023
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Marco Lucio Bittencourt
• Grantee: Henrique de Freitas Siqueira
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project aims to develop two and three dimensional thinand three-dimensional thin beam elements with large deformations for the analysis of flexible body dynamicsof flexible bodies using the Finite Element Method of High Order (FEM-AO).To this end, we will employ interpolation functions already developed that allowrepresent rigid translations and rotations. The equations of motion obtained must beintegrated in time using stable and efficient procedures. To this end, we propose thelocal procedures based on the method of least squares. An importantimportant aspect of such a class of methods is the use of a concentrated mass matrix. To this end,we intend to test the different diagonal mass matrices available in the literature andand select the one that best fits the mentioned integration procedures.The whole project will be developed using the software Matlab and the program(hp) 2 FEM program for solving mechanical problems using FEM-AO. The beambeam elements will be incorporated into the flexible dynamics module of (hp) 2 FEM and static and dynamicstatic and dynamic examples from the literature will be analyzed.