Discrete Material Optimisation of Laminated Composite Structures using EAS and MITC Stabilised 4-Node Shell Element
Author
Schøn, Rasmus Kaalund
Term
4. term
Education
Publication year
2024
Abstract
Simulation and optimization are key to developing products in industries such as wind energy and aerospace. For laminated composite structures (layered materials), fast and reliable methods help avoid costly prototypes, reduce expenses, and shorten time to market. This thesis applies gradient-based optimization together with Discrete Material Optimisation (DMO), which represents material choices in the design, to enhance structural integrity. To improve computational efficiency, the work derives and implements analytical sensitivities (exact derivatives that show how results change with design changes) for a 4-node shell finite element with Enhanced Assumed Strain (EAS) and Mixed Interpolation of Tensorial Components (MITC) in the MUltidisciplinary Synthesis Tool (MUST). Analytical sensitivities for buckling load factors are also developed and implemented to better address buckling (sudden loss of stability). Benchmark examples maximize buckling load factors using a bound formulation and show a significant reduction in computation time compared with a 9-node isoparametric shell formulation. Because there is no universally accepted failure criterion for laminated composites, analytical sensitivity analyses are implemented for the maximum stress, maximum strain, and Tsai–Wu criteria. A benchmark example minimizes an aggregate function for each of these criteria. Overall, the work makes gradient-based optimization of laminated composite structures in MUST faster and more directly targeted at both buckling and failure.
Simulation og optimering er centrale i udviklingen af produkter i bl.a. vind- og luftfartsindustrien. Når man designer laminerede kompositstrukturer (lagdelte materialer), er hurtige og præcise metoder vigtige for at undgå dyre prototyper, sænke omkostninger og forkorte udviklingstiden. Denne afhandling bruger gradientbaseret optimering sammen med Discrete Material Optimisation (DMO), der beskriver valg af materialer i designet, for at forbedre strukturel integritet. For at øge beregningseffektiviteten udvikles og implementeres analytiske følsomheder (præcise afledte, der fortæller, hvordan resultatet ændrer sig, når designet ændres) for et 4-node skal-element med Enhanced Assumed Strain (EAS) og Mixed Interpolation of Tensorial Components (MITC) i MUltidisciplinary Synthesis Tool (MUST). Derudover udledes og implementeres analytiske følsomheder for knæklastfaktorer for bedre at håndtere knæk (pludseligt stabilitetstab). Benchmark-eksempler maksimerer knæklastfaktorer ved hjælp af en grænseformulering og viser en markant reduktion i beregningstiden sammenlignet med en 9-node isoparametrisk skalformulering. Da der ikke findes ét universelt accepteret brudkriterium for laminerede kompositter, implementeres analytiske følsomhedsanalyser også for maksimal spænding, maksimal tøjning og Tsai–Wu-kriteriet. Et benchmark-eksempel minimerer en samlet målfunktion for hvert af disse brudkriterier. Samlet set gør arbejdet gradientbaseret optimering af laminerede kompositstrukturer i MUST hurtigere og mere målrettet mod både knæk og brud.
[This apstract has been rewritten with the help of AI based on the project's original abstract]
Keywords