A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method

With a wide applicability in several types of engineering problems, topology optimization is one of the most interesting fields of structural optimization. Many meshless methods have been developed, however, they were less explored in topology optimization compared to other methods, as the Finite El...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 67; no. 7; p. 110
Main Authors: Sousa, Laise, Oliveira, Suzana, Vidal, Creto, Cavalcante-Neto, Joaquim
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2024
Springer Nature B.V
Subjects:
Boundary value problems
Computational Mathematics and Numerical Analysis
Engineering
Engineering Design
Finite element method
Galerkin method
Mathematical analysis
Meshless methods
Optimization
Polynomials
Shape functions
Theoretical and Applied Mechanics
Topology optimization
Topology optimization
Direct meshless local Petrov–Galerkin method
Bi-directional evolutionary structural optimization method
Meshless method
ISSN:1615-147X, 1615-1488
Online Access:Get full text
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Summary:With a wide applicability in several types of engineering problems, topology optimization is one of the most interesting fields of structural optimization. Many meshless methods have been developed, however, they were less explored in topology optimization compared to other methods, as the Finite Element Method (FEM). The Direct Meshless Local Petrov–Galerkin (DMLPG) is characterized as a truly meshless method since it does not use a mesh at any stage of its development. It has been applied to solve many boundary value problems, achieving results with good precision and computational efficiency. Instead of performing the numerical integral of complicated shape functions, the DMLPG considers low-degree polynomials. The new topology optimization approach proposed in this work couples the DMLPG method with a Bi-Directional Evolutionary Structural Optimization (BESO) method. DMLPG is used to obtain smooth nodal displacements, strains, and stresses, and BESO updates the structural geometry based on design sensitivity values. Numerical examples performed were compared with the results obtained with FEM and with other works in the literature, showing the applicability and validity of the technique.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-024-03813-y