Global buckling response of web-core steel sandwich plates influenced by general corrosion

A web-core steel sandwich plate is a lightweight, orthotropic structure. The constituent thin plates (2-4 mm) are joined by laser-welding. This thesis investigates the buckling and post-buckling behaviour of slender web-core sandwich plates loaded in the direction of the web plates. The influence of corrosion on the plate buckling is studied via finite element method (FEM). The corrosion scenario used is based on experimental observations from specimens submerged into the sea for 1 and 2 years. The plate strength analyses are performed with two methods: FEM having shell element mesh of the three-dimensional topology and the equivalent single-layer theory (ESL). In the later, the sandwich plate is represented with constant, homogenised stiffness coefficients, which are related to physical properties of the structure. The first buckling mode of slender web-core sandwich plates is characterised with global deformation between the edge supports. The buckling strength depends on the bending and transverse shear stiffnesses. This thesis revealed that the buckling strength is very sensitive to the variation in transverse shear stiffness opposite to the web plate direction, DQy, especially in sandwich plates with high bending stiffness. Furthermore, the stiffness of the sandwich plate as a whole in the post-buckling is controlled by that of the in-plane stiffness. The web plates impose high, shear-induced, secondary bending stresses on the face plates and these were found to be important for accurate estimation of the onset of yielding. The deformation resulting from the secondary bending of the face plates makes the unloaded edge stiffer. Although membrane stress can be higher there, local buckling during global post-buckling occurs further away where the secondary deformations are smaller, primarily in the centre of the face plate (x=a/2, y=b/2). Furthermore, the corrosion tests revealed that the cross-section is primarily affected by general corrosion. Under this circumstance, the reduction of the thickness of the face and web plates reduces the stiffness coefficients and also the buckling strength linearly. The buckling strength reduces rapidly, especially because of the reduction in the transverse shear stiffness DQy. The reduction of buckling strength doubles if, in addition to the outer faces, corrosion also occurs inside the sandwich plate. Beam bending tests also showed rapid reduction of the ultimate strength but, in addition, that it can be maintained using different protection methods. The results thus indicate that the protection against corrosion should be carefully performed. The future work will involve improving the accuracy of the ESL theory in the presence of local buckling

‘Healing’ and ‘repairing’ techniques for faster optimization with genetic algorithm

This paper presents two techniques, the ‘healing’ and ‘repairing’ that can reduce optimization time when using genetic algorithm for structural optimization. The techniques can be applied to: (a) quickly find feasible designs from completely infeasible set of alternatives, and (b) to make the best infeasible designs feasible. These procedures are implemented into a genetic algorithm ‘VOP’. The performance of the original and the modified version of the algorithm are compared with the widespread genetic algorithm ‘NSGA-II’ for the weight optimization of a 40 000 DWT chemical tanker midship section. The results show that these procedures can decrease the optimization time by approximately half.Peer reviewe

Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.Comment: 20 pages; 7 figure

Load-carrying behaviour of web-core sandwich plates in compression

This paper investigates theoretically the compressive load-carrying behaviour of geometrically imperfect web-core sandwich plates. Slender plates, which first buckle globally, are considered. The study is carried out using two approaches, both solved with the finite element method. The first is the equivalent single-layer theory approach. First-order shear deformation theory is used. The second approach is a three-dimensional shell model of a sandwich plate. Plates are loaded in the web plate direction. Simply supported and clamped boundary conditions are considered with a different level of in-plane restraint on the unloaded edge. The results show that the behaviour of the sandwich plate is qualitatively equal to the isotropic plate of the same bending stiffness for deflections lower than the plate thickness. As the deflections increase, the lower in-plane stiffness of the sandwich plate results in lower post-buckling stiffness. Local buckling of face plates in the post-buckling range of the sandwich plate further reduces the structural stiffness.Peer reviewe

Stress and frequency optimization of prismatic sandwich beams with joints: Performance improvements through topology optimization

Prismatic sandwich panels fabricated from metals offer a compelling alternative to more traditional panels across diverse industries, primarily due to their superior strength-to-weight ratio. Although several core types were proposed in the past, further improvements in performance could be achieved by devising the topology of the core through a topology optimization framework, which is explored in this article for the first time. Another novelty is the inclusion of joints between the sandwich beams and its surroundings in the analysis and optimization. Stress is minimized under uniform pressure loading on the beams and natural frequency maximized using the Method of Moving Asymptotes. The results are compared with X-core, Y-core, corrugated-core, and web-core sandwich beams, a few conventional prismatic sandwich types, which are optimized using a prominent global evolutionary algorithm. Manufacturing requirements are considered through practical limitations on the design variables. It is shown that structures produced by topology optimization outperform the conventional sandwich beams by up to 44% at intermediate to high mass levels, where volume fraction is between 0.2 and 0.4, but often through increased topological complexity. The new core topologies bear a certain resemblance with the conventional core types, underscoring engineering ingenuity that went into their development over the years. The topology of the optimized joints differs from the conventional joint. The results also show some limitations of the topology optimization framework, for example that it does not offer better-performing beams for volume fractions below 0.2.Comment: 17 pages, 3 tables, 19 figures, journal pape

Graph Neural Network for Stress Predictions in Stiffened Panels

Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product, such as ship structures, replacing computationally expensive finite element analysis (FEA) in optimization. In this study, we demonstrate how GNN can be used to predict stress distributions in stiffened panels with varying geometries under patch loading, for which we use Graph Sampling and Aggregation (GraphSAGE) network. Parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures

Vectorization in the Structural Optimization of a Fast Ferry

Vectorization assumes the conversion of constraints into objective functions. It turns a singleobjective, or scalar, optimization into a search for a Pareto optimal set, which will enhance the search for the optimum. Vectorization is studied here within a structural optimization of fast ferry’s midship section for the minimum of steel weight. Optimization applies a simple genetic algorithm (GA), whose performance is observed over both scalar and vectorized problem formulations. The obtained results show that the applied GA can improve the referenced design, and that the improvement can be signifi cantly better if vectorization is applied

Global buckling and post-buckling of web-core sandwich and stiffened panels: sensitivity to general corrosion

Corrosion can lead to reduction of structural stiffness and strength. This paper investigates the influence of a reduction in the thickness of the plates as a result of general corrosion on sandwich panel buckling load and onset of plasticity. The results are compared to the stiffened panel of the same in-plane and bending stiffness. Current guidelines for corrosion protection threat these two structures equally. Load-shortening curves are obtained with the finite element method, with the kinematics being represented using two approaches: (1) equivalent single-layer with first-order shear deformation theory, and (2) a three-dimensional model of the actual geometry of the structure, modeled using shell and connector elements. The former is also used to identify the influence of corrosion on the stiffness coefficients and, consequently, the buckling load, also via analytical equation. The decrease of the buckling load is found higher in sandwich panel than in stiffened panel. The reduction is especially high in the case of the diffusion of moisture (water) into the core. The reason for the higher sensitivity of sandwich panel is a larger reduction of transverse shear stiffness opposite to the stiffener direction due to corrosion.Peer reviewe

Influence of general corrosion on buckling strength of laser-welded web-core sandwich plates

The strength of a web-core steel sandwich plate is potentially reduced in a corrosive environment. This study is dedicated to the influence of a reduction in the thickness of the plates as a result of general corrosion on sandwich plate buckling strength and first-fibre failure. Two scenarios are investigated in which corrosion reduces the thickness of (a) the outer sides of the face plates and (b) all surfaces, including the core. The laser weld between the face sheets and the core is assumed to be intact. The assumptions are made on the basis of earlier experimental findings. Critical buckling and geometric non-linear analysis are carried out with the finite element method, with the kinematics being represented using two approaches: (1) equivalent single-layer with first-order shear deformation theory, and (2) a three-dimensional model of the actual geometry of the structure, modelled using shell and connector elements. The former is used to identify the effect of corrosion on the stiffness coefficients and, consequently, the buckling strength. The later is used for verification and for stress prediction during post-buckling. A rapid decrease in the buckling strength was found for corrosion affecting the outer sides of the sandwich plate. The decrease in the buckling strength doubled in the case of the diffusion of moisture (water) into the core. The shear-induced secondary bending of the faces was found to affect the first-fibre yield.Peer reviewe

MULTI-OBJECTIVE STRUCTURAL OPTIMIZATION – A REVIEW OF THE GENETIC ALGORITHM METHODS

Mnogo je načina za poboljšanje brodske strukture, s ciljem zadovoljenja zahtjeva brodogradilišta i brodovlasnika. Načini se odnose na karakteristike brodske strukture, koje su u osnovi sukobljene na način da se poboljšanje jedne karakteristike ne može postići a da se ne pogorša neka druga. Te su karakteristike uobičajeno: troškovi, masa, pouzdanost, sigurnost, stabilitet. Cilj je pronalaženje kompromisa s obzirom na važnost pojedine karakteristike. U tom su smislu evolucijski algoritmi, kao optimizacijski alati, kod većine inženjerskih problema dokazali svoju valjanost, budući da uspješno upravljaju velikim brojem varijabli i ograničenja, a u posljednje vrijeme i funkcija cilja. Proces usavršavanja tih alata ostvaruje se hibridnim rješenjima koja spajaju najbolje od nekoliko različitih pristupa. Stvaranje jednog algoritma koji bi bio primjenjiv na sve probleme je nemoguće. U ovom je radu prikazano nekoliko važnijih pristupa i metoda genetskog algoritma s više funkcija cilja s ciljem usmjeravanja stručnjaka koji ulaze u područje strukturne optimizacije na one metode koje su dokazale svoju valjanost u praktičnim primjenama.There are numerous means of enhancing ship structure in an attempt to satisfy both the shipyard and the ship owner requirements. These means are addressed as a ship’s attributes and they are regularly contrary in meaning, such that the improvement in one cannot be achieved without making some other worse. Typically these are e.g. cost, weight, reliability, safety and stability, which can be minimized or maximized to improve the final design. A compromise obviously has to be made between them, depending upon the importance of each attribute. Evolutionary algorithms have proven their worthiness in a great variety of practical engineering problems, handling many variables, constraints and objectives. However, the need to improve them is always present. This has recently been done by hybridization, combining different approaches in order to get the best of them. To devise an algorithm which will be applicable to all problems is impossible. In this review, for the purpose of directing the experts entering in the field of structural optimization, only a few of the most important approaches and multi-objective algorithms have been presented