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GEOMETRIC OPTIMIZATION BASED ON THE CONSTRUCTAL DESIGN OF PERFORATED THIN PLATES SUBJECT TO BUCKLING

Volume 4, Issue 2, 2012, pp. 119-129
DOI: 10.1615/ComputThermalScien.2012005125
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ABSTRACT

Elastic buckling is an instability phenomenon that can occur if a slender and thin-walled plate is subjected to axial compressive load. It is well known that the presence of holes in structural plate elements is almost inevitable in inspection, maintenance, and service purposes, or to reduce the structural weight. In this paper constructal design was employed to optimize the geometry of thin perforated plates submitted to elastic buckling. Simply supported rectangular perforated plates were analyzed with three different shapes of centered holes: elliptical, rectangular, and diamond. The purpose was to obtain the optimal geometry that maximizes the critical buckling load. The ratio between the height and length of the plate was kept constant, while the ratio between the characteristic dimensions of the holes was optimized for several hole volume fractions (φ). A finite-element model was used to assess the plate buckling load, and the Lanczos method was applied to the solution of the corresponding eigenvalue problem. When φ ≤ 0.20 the optimum geometry is the diamond hole, reaching maximum buckling loads around 80.0,21.5, and 17.4% higher than a plate without perforation and plates with elliptical and rectangular holes, respectively. For intermediate and higher values of φ, the elliptical and rectangular holes, respectively, led to the best performance. The optimal shapes were obtained according to the constructal principle of minimization of distribution of imperfections, showing that the constructal design also can be employed to define the optimized geometries in the mechanics of material problems.

CITED BY
  1. Rocha Luiz, Isoldi Liércio, Vasconcellos Real Mauro, Santos Elizaldo, Correia Anderson, Lorenzini Giulio, Biserni Cesare, Constructal design applied to the elastic buckling of thin plates with holes, Open Engineering, 3, 3, 2013. Crossref

  2. Lorenzini G., Helbig D., Real M. de V., dos Santos E. D., Isoldi L. A., Rocha L. A. O., Computational modeling and constructal design method applied to the mechanical behavior improvement of thin perforated steel plates subject to buckling, Journal of Engineering Thermophysics, 25, 2, 2016. Crossref

  3. Helbig Daniel, Silva Caio Cesar Cardoso da, Real Mauro de Vasconcellos, Santos Elizaldo Domingues dos, Isoldi Liércio André, Rocha Luiz Alberto Oliveira, Study About Buckling Phenomenon in Perforated Thin Steel Plates Employing Computational Modeling and Constructal Design Method, Latin American Journal of Solids and Structures, 13, 10, 2016. Crossref

  4. da Silva Caio César Cardoso, Helbig Daniel, Cunha Marcelo Langhinrichs, dos Santos Elizaldo Domingues, Rocha Luiz Alberto Oliveira, Real Mauro de Vasconcellos, Isoldi Liércio André, Numerical buckling analysis of thin steel plates with centered hexagonal perforation through constructal design method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 8, 2019. Crossref

  5. Martins Kauê L., Pinto Vinícius T., Fragassa Cristiano, Real Mauro V., Rocha Luiz A. O., Isoldi Liércio A., dos Santos Elizaldo D., A Simplified Numerical Method for the Design and Analysis of FPSO Platform Brackets Subjected to Operational Conditions, Journal of Marine Science and Engineering, 8, 11, 2020. Crossref

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