Exame de Qualificação: Topological Derivative-Based Optimization in the Synthesis of Pressure-Driven Compliant Mechanisms

Orientadores:
Antônio André Novotny - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC (presidente)
Marcio Rentes Borges - Laboratório Nacional de Computação Científica - LNCC
Marcel Duarte da Silva Xavier - Universidade Federal Fluminense - UFF

Suplentes:
Lucas dos Santos Fernandez - Laboratório Nacional de Computação Científica - LNCC

Resumo:

THE TOPOLOGICAL DERIVATIVE WAS RIGOROUSLY DEFINED BY SOKOŁOWSKI AND ŻOCHOWSKI IN 1999 AND, SINCE THEN, HAS PROVEN TO BE AN IMPORTANT TOOL FOR ADDRESSING VARIOUS PROBLEMS, INCLUDING TOPOLOGICAL OPTIMIZATION, INVERSE PROBLEMS, IMAGE PROCESSING, MULTISCALE CONSTITUTIVE MODELING, SENSITIVITY ANALYSIS TO MECHANICAL FRACTURE, DAMAGE EVOLUTION MODELING, AND SENSITIVITY ANALYSIS FOR CONTACT PROBLEMS. THE TOPOLOGICAL DERIVATIVE IS OBTAINED FROM THE ASYMPTOTIC ANALYSIS OF CLASSICAL SOLUTIONS TO BOUNDARY VALUE PROBLEMS IN SINGULARLY PERTURBED DOMAINS, COMBINED WITH THE ASYMPTOTIC ANALYSIS OF SHAPE FUNCTIONALS WITH RESPECT TO THE PARAMETER GOVERNING THE SIZE OF THE PERTURBATION. THIS WORK APPLIES THE TOPOLOGICAL DERIVATIVE METHOD COMBINED WITH A LEVEL-SET APPROACH TO THE SYNTHESIS OF PRESSURE-ACTUATED COMPLIANT MECHANISMS. BY MAPPING DESIGN-DEPENDENT PRESSURE LOADS AS AN EQUIVALENT DISTRIBUTED BODY FORCE VIA THE DIVERGENCE THEOREM, THE FORMULATION YIELDS AN EXPLICIT TOPOLOGICAL DERIVATIVE FORMULA EVALUATED AT ANY ARBITRARY POINT IN THE DOMAIN. IN THE SINGLE-MATERIAL OPTIMIZATION PROCESS, THIS DERIVATIVE IS COUPLED TO A LEVEL-SET FUNCTION USING AN OPTIMALITY CONDITION WRITTEN AS A FIXED-POINT CONDITION THAT ACTS AS A STEEPEST-DESCEN T DIRECTION BASED ON THE SIGN OF THE TOPOLOGICAL DERIVATIVE. PRELIMINARY NUMERICAL VALIDATION IMPLEMENTED IN FREEFEM++ CONFIRMS THAT TREATING THE PRESSURE CHAMBER VIA BODY FORCES MATCHES STANDARD BOUNDARY TRACTION METHODS, WITH RELATIVE DISPLACEMENT ERROR WHICH CORROBORATES THE EQUIVALENCY OF BOTH MODELS. BENCHMARK RESULTS FOR SINGLE-MATERIAL PRESSURE ACTUATED INVERTERS IN A FIXED CHAMBER SUCCESSFULLY MATCH EXISTING TOPOLOGIES IN THE LITERATURE. TO FILL THE REMAINING PROJECT REQUIREMENTS WITHIN THE DOCTORAL TIMELINE, FUTURE ACTIVITIES WILL EXPAND THIS FRAMEWORK INTO A MULTI-MATERIAL LEVEL-SET (MM-LS) ALGORITHM. UNDER THIS MULTI-MATERIAL FRAMEWORK, THE PRESSURIZED CHAMBERS ARE EXPLICITLY REPRESENTED AND TREATED AS A DISTINCT, LOW-STIFFNESS MATERIAL ALONGSIDE THE SOLID MATERIAL AND THE VOID REGIONS. THIS NOVEL MULTI-MATERIAL APPROACH ENSURES STRICT NON-OVERLAPPING BOUNDARIES, ENABLING AUTOMATED TOPOLOGICAL NUCLEATION OF PRESSURIZED CHANNELS AND STRUCTURAL LAYOUTS, FOR INSTANCE, FOR US E IN SOFT ROBOTICS APPLICATIONS.