4-Node Stabilised Shell Element Accounting for Large Displacements, Drilling and Draping in Structural Optimisation of Laminated Composites
Authors
Stagsted, Niklas Kristian Kronborg ; Bertelsen, Nikolaj Madum
Term
4. term
Education
Publication year
2023
Submitted on
2023-06-01
Pages
122
Abstract
Udformning af laminerede kompositdele er vanskelig, fordi tynde plielag ændrer fiberretning, når de lægges over krumme geometrier (drapering). Ingeniører har brug for modeller, der kan beskrive dette og samtidig finde gode fiberopbygninger. I afhandlingen udvikles et finitte element (FEM) skal‑element, der kan medtage drapering i både analyse og optimering. Elementet er et 4‑noded skal‑element med en stabiliseret formulering for pålidelighed. Det håndterer ikke‑lineær adfærd fra store deformationer og spændingsopstivning og introducerer en ny straffemetode til at medtage den såkaldte drilling‑frihedsgrad (rotation om tykkelsesaksen). Til optimering anvendes diskret materialeoptimering til at vælge fibervinkler fra et sæt kandidater. Draperede fibervinkler fra en adskilt draperingsanalyse indarbejdes ved at rotere den konstitutive stivhedsmatrix, så den følger de lokale fiberretninger. I tests gav metoden bedre nøjagtighed i smådeformations‑ (lineære) tilfælde og bedre konvergens i geometrisk ikke‑lineære tilfælde. Resultaterne var i stort omfang uafhængige af valg af drilling‑straffeparameter. Inklusion af drapering og brug af diskret materialeoptimering fungerede i praksis og gav forskellige optimale designs ved lineær eftergiveligheds‑ (compliance) optimering med drapering. Samlet set er 4‑noded‑skal‑elementet effektivt, robust og nøjagtigt til analyse og optimering af laminerede kompositter. Ved lineær eftergivelighedsoptimering gav drapering kun små gevinster, men der forventes større udbytte i mere komplekse problemer og for andre målsætninger, f.eks. styrke.
Designing laminated composite parts is challenging because thin fabric plies change fibre direction as they are laid over curved shapes (draping). Engineers need models that capture this and can also search for good fibre layouts. This thesis develops a finite element method (FEM) shell element that includes draping in both analysis and optimisation. The element is a 4‑node shell with a stabilised formulation for reliability. It handles non‑linear behaviour from large displacements and stress stiffening, and introduces a new penalty approach to include the drilling degree of freedom (rotation about the thickness). For optimisation, discrete material optimisation is used to choose fibre angles from a set of candidates. Draped fibre angles from a separate draping analysis are included by rotating the material stiffness matrix to match the local fibre direction. In tests, the method improved accuracy for small‑deformation (linear) cases and improved convergence for geometrically non‑linear cases. Results were largely insensitive to the drilling penalty. Including draping and using discrete material optimisation both worked in practice and produced different optimal designs in linear compliance (flexibility) optimisation with draping. Overall, the 4‑node shell element is efficient, robust and accurate for analysing and optimising laminated composites. In linear compliance optimisation, draping gave only small performance gains, but larger benefits are expected in more complex problems and for other objectives, such as strength.
[This summary has been rewritten with the help of AI based on the project's original abstract]
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