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openaire: EC/H2020/745770/EU//SANDFECH The strength of laser-welded web-core sandwich plates is often limited by buckling. In design of complex thin-walled structures the combination of possible structural and material combinations is basically infinite. The feasibility of these combinations can be assessed by using analytical, numerical and experimental methods. At the early design stages such as concept design stage, the role of analytical methods is significant due to their capability for parametric description and extremely low computational efforts once the solutions have been established for prevailing differential equations. Over the recent years significant advances have been made on analytical strength prediction of web-core sandwich panels. Therefore, aim of the present paper is to show impact of this development to the design space of web-core sandwich panels in buckling. The paper reviews first, briefly the differential equations of a 2-D micropolar plate theory for web-core sandwich panels and the Navier buckling solution for biaxial compression recently derived by Karttunen et al. (Int J Solids Struct 170(1):82–94, 2019) by exploiting energy methods. By comparing the micropolar and widely-used classical first-order shear deformation plate theory (FSDT) solutions, it is shown that the different equivalent single layer (ESL) formulations and plate aspect ratios have a significant impact on the practical outcomes of the feasible design space and this way motivating further developments for micropolar formulations from practical structural engineering viewpoint.

This study investigates an analytical beam model to improve the analyses of welded thin plates with welding-induced curved distortions. The model addresses the rigidity of a butt-welded joint and its effect on plate bending and structural stress by including a rotational spring at the welded end. The spring rotational stiffness, k a , is replaced by the fixity factor, ρ a . The validity of the model is based on the assumption of small displacement and moderate rotation of the mid-plane of the welded plate. Using the Finite Element Analysis of a two-dimensional model, a semi-analytical method for the fixity factor computation is developed. Compared with the numerical analysis, the beam model showed a maximum error of 3% in deflection and hot-spot structural stress. Results suggest that the fixity factor is mainly dependent on the width of the weld bead and the far-end constraint. The introduction of ρ a can improve the analytical solution by 9% in the evaluation of the hot-spot structural stress. Neglecting the non-ideal joint rigidity may lead up to 54% underestimation in terms of fatigue life, when the S–N curve slope, m , equals 5. However, the relevance of ρ a decreases for increasing geometric slenderness of the welded plates.

This paper investigates experimentally the fatigue strength of high-strength steel, which has undergone the normal shipyard production process of plasma cutting, grinding, and sandblasting. The study includes steels with the yield strength of 355 and 690 MPa. The tested specimens are of dog-bone shape and represent the large-scale situation of a cruise ship balcony opening corner, loaded in shear or tension. The influence of surface roughness, internal inclusions, hardness, and residual stress on the fatigue strength are studied and discussed. Compared to the design curve as well as to the untreated surfaces, the results show significantly improved fatigue strength under constant amplitude loading at a load ratio of R = 0.1. However, very flat or even rising slope of the S-N curve indicates variations in the material and surface quality as well as in the residual stress. Surprisingly, internal defects even up to 100 μm in size did not decrease the fatigue strength.

Overload response of the stiffening frames in ship side structure due to ice loading is an important design consideration for ships operating in ice infested waters. By overload, we mean loads that are larger than assumed by the rules. Therefore, the response of ice strengthened grillage frames is investigated under a range of idealized rectangular pressure patches and by assuming different boundary conditions for the structural units. A flat, representative grillage of an ice-strengthened ship is considered and analysed using non-linear Finite Element Method. The response of the grillage frames is compared with the isolated frame response. Two frame types are considered: flatbars and L-frames. Finite element simulations revealed that patch length has strong effect on the frame deformation mode. The key characteristic that differentiates the response under shorter and longer patches is the longitudinal membrane stretching of the shell plating. Longer patches tend to suppress this deformation mode that leads to similar frame behaviour observed in isolated frame analysis. It is further shown that overload capacity of grillage frames reduces with increasing patch length to levels observed in isolated frame analysis. Analysis of plastic strain development in the frames and plating revealed that plastic strain localized faster in frames, but shell plating is more sensitive to patch height variations. This renders frames more susceptible to fracture than plating. Finally, the local failure mechanisms of the L-frames tend to diminish the load sharing capability and so negatively affects the overload behaviour.

Ductile fracture in large structures is often resolved with non-linear finite element (FE) simulations employing structural shell elements which are larger than localization zone. This makes solution element size dependent and calibration of material parameters complex. Therefore, the paper explores the ability of numerical simulations to capture the penetration resistance of stiffened panels after determining steel material fracture ductility at different stress states. The numerical simulations are compared with experiments performed with rigidly fixed 1.2 m square panels penetrated with half-sphere indenter until fracture took place. Response of the panels was measured in terms of indentation force versus indenter displacement. In parallel, tensile tests were performed with four different flat specimens extracted from the face sheet of panels to characterize the material fracture ductility at different stress states. Panel simulations were performed with two fracture criteria: one calibrated based on the test data from dog-bone specimen and other calibrated based on the data from all tensile tests. To evaluate the fracture criteria in terms of their capacity to handle mesh size variations, mesh size was varied from fine to coarse. Results suggest that fracture criterion calibrated based on the range of stress states can handle mesh size variations more effectively as displacement to fracture showed considerably weaker mesh size dependence.

Present paper investigates the factors contributing to the stress response of steel sandwich panel deck joints when applied into the hull girder of modern passenger vessel. The emphasis is put on the fatigue analysis, which is the critical design criterion in application of these structures to ships. Two types of joints are considered, i.e., a symmetrical and a nonsymmetrical prismatic joint with respect to the geometrical midplane of the sandwich panel. Stiffness properties are derived for the joints in order to enable the modeling of sandwich structures as part of the hull girder finite element model. The influence of sandwich joints to hull girder response is studied. Notch stress analysis is used for the fatigue strength estimation. The applicability of notch stress method for steel sandwich panels is validated with experiments. The investigation shows that the fatigue strength of steel sandwich panels does not depend only on local stress concentration factors at details, but also on the global stiffness of the structural hull girder system, the sandwich panels, and thus the joint response must be taken into account.

In this work, we create a framework for linear buckling and free vibration analyses of sandwich beams using a microstructure-dependent Timoshenko beam model founded on the modified couple-stress theory. The stiffness parameters of a structural web-core sandwich panel are determined by unit cell analysis. An extension to homogeneous cores is also carried out. By employing the exact general solution to the governing equations of the beam, an accurate approximate finite element stiffness matrix is formulated. Furthermore, the static shape functions are used to derive consistent linear geometric stiffness and mass matrices. A convergence study shows that the approximate finite element has good accuracy although the hyperbolic terms of the exact general solution have been expanded into only relatively low-order polynomial series. Results from examples show that the microstructure-dependent beam can predict critical buckling loads and natural frequencies with very good accuracy when compared to more sophisticated finite element models. Unlike the classical Timoshenko beam model, the microstructure-dependent model yields accurate results also when the sandwich assembly is transversely flexible and the bending stiffness of the faces non-negligible.

Laser stake-welded steel sandwich panels are widely used in engineering due to their high stiffness-to-weight ratios. The welds are thinner than the plates they join so that there are two crack-like notches on each side of a weld. As a consequence, the welded joints are susceptible to fatigue. In this study, as a remedy to the fatigue problem, low-density H80-grade Divinycell polyvinylchloride foam is bonded adhesively to the voids of stake-welded web-core sandwich beams. The foam reduces shear-induced stresses in the stake-welds. The choice of Divinycell H80 is founded on earlier J-integral-based finite element fatigue assessments of sandwich panels. Empty and the H80-filled sandwich beams are tested in three-point-bending for stiffness, ultimate strength and fatigue (load ratio R = 0.05). The failure modes in the weld joint region are studied using scanning electron microscopy. The experimental results show that the filling increases the stiffness of the sandwich beams by a factor of three while the weight is increased only by 6%. The ultimate strength is increased by 2.7 times. As for the fatigue behavior, the slope increases from m = 4.508 of empty panels to m = 7.321 of filled panels while the load level at 2 million cycles increases by a factor of 8.5. Keywords: Sandwich panels, Ultimate strength, fatigue strength, Hybrid structure, Scanning electron microscopy

In this paper, Reddy’s third-order shear deformable plate theory is employed for the analysis of centrosymmetric anisotropic plate structures within strain gradient elasticity. The general three-dimensional anisotropic gradient theory is reduced to a two-dimensional formulation for the analysis of thick plate structures. The third-order shear deformation theory (TSDT) takes into account quadratic variation of the transverse shear strains of the plate and does not require shear correction factors. In order to investigate the case of small strains but moderate rotations, the von Karman strains are considered. The TSDT is also simplified to anisotropic Kirchhoff plate theory within gradient elasticity. To study specific material properties in more detail, the (Kirchhoff and TSDT) gradient plate theory of general anisotropy is simplified to the more practical case of orthotropic plates. It is observed that the gradient theory provides the capability to capture the size effects in anisotropic plate structures. As case studies, the bending and buckling behaviors of the simply supported orthotropic (Kirchhoff and TSDT) plates are studied. Variationally consistent boundary conditions are also discussed. Finally, analytical solutions are presented for the bending and buckling of simply supported orthotropic Kirchhoff plates. The effects of internal length scales on deflections and buckling loads are presented.

Utilization of thin plates together with laser-based welding processes allows manufacturing of large weight efficient steel structures. However, the fatigue strength of welds in thin-plate structures with plate thicknesses below 5 mm is observed to have large variation, which brings challenges to fatigue strength assessment. One possible reason for this variation is the increased influence of actual weld geometry that is neglected in common fatigue strength assessment approaches utilizing geometry idealization. To reveal this influence the fatigue strength of 3 mm thick laser-hybrid welded butt joints were studied using the measured microscale weld geometry and the notch stress approach. Notch stresses were defined using Neuber’s stress averaging approach which allows the determination of the fatigue-effective stress without fictitious geometric modifications. For the studied specimens the large scatter of fatigue strength in the high-cycle region could be explained using this approach with high-resolution weld profile measurements combined with thorough finite-element analysis. It was observed that axial misalignment in narrow laser-hybrid welds causes a significant notch stress increase on the root side reducing the fatigue strength dramatically in terms of structural and nominal stress. In order to capture the increased notch stress it is crucial to use a significantly smaller stress averaging length than commonly assumed for welded joints.

A homogenization method for geometric nonlinear analysis of structural core sandwich panels is proposed. The method provides high computational performance based on an efficient separation of scales. In the macroscale, the sandwich panel is discretized with an equivalent single layer of shell elements. The macroscale shell stiffness matrix is nonlinear, obtained from the analysis of a representative volume element. Prescribed displacement boundary conditions are applied to the representative unit based on the strain definitions of the first-order shear deformation theory. Changes in local wavelength in the post-buckling are considered in the analyses. Manufacturing-induced imperfections are introduced to local and global scales. The method allows for description of buckling in these two scales and is shown to hold good accuracy with respect to equivalent 3D FEM models. Examples include web-core and corrugated-core sandwich panels. The method can be extended to any periodic structure of complex local topology. It can be easily implemented to commercial FE packages.

A web–core steel sandwich panel is a lightweight structure where thin plates are welded together by laser-welding technique. The plates form a T-joint which has in the center a weld thinner than the plates themselves. Thus the rotational stiffness of the joint is not infinite. The paper investigates the influence of T-joint rotational stiffness on the lowest natural vibration frequency of the panel. The methods used in the study have different kinematic assumptions. Equivalent single-layer (ESL) theory is used to obtain the frequency of the global vibration. The local vibrations are predicted using an isolated part of the panel, the I-beam model. In addition, three-dimensional model of a sandwich panel is analyzed. Finite element method (FEM) and analytical solution are used to obtain the frequencies. First-order shear deformation theory (FSDT) is used. The joint is considered through its rotational stiffness whose quantitative values are presented in the literature. Four different cross-sections with industrial relevancy are considered. The rotational stiffness of the T-joint affects the transverse shear stiffness of the panels. The results show up to 22% reduction of the fundamental frequency when compared with the case of the rigid joint for the global vibration mode. The effect on local vibrations is up to 11% in the case of asymmetric rotation in the T-joint and is otherwise insignificant. The study furthermore outlined the limitations of the ESL approach for assessment of natural frequencies in web–core sandwich panels depending on the vibration mode shape. The results show that the rotational stiffness of the T-joint has to be considered in the conceptual design of these structures.

The paper investigates the fatigue strength of laser stake-welded T-joints subjected to reversed bending. The fatigue tests are carried out with the load ratio, R ≈ −0.8. The experimental data is firstly analysed using the nominal stress approach and then by the J-integral as the local fatigue strength parameter in the finite element (FE) assessment. The nominal stress approach demonstrated that the fatigue strength of the investigated T-joints is lower than encountered for any other steel joint under reversed tensile loading. The results also showed that the fatigue strength of this joint under the load ratio R ≈ −0.8 increases with respect to R = 0 bending by 22.6% in the case of the nominal stress approach and 13% in the case of the J-integral approach. However, the slopes of the fatigue resistance curves for different load ratios appear very similar, suggesting that the load ratio has an insignificant influence to the slope. In contrast to the similar slopes, the scatter indexes were different. The nominal stress approach shows that the scatter index is 3.4 times larger for R ≈ −0.8 than R = 0 bending. The J-integral approach showed that the scatter index for R ≈ −0.8 is only 67% larger than in the R = 0 case because the weld geometry is modelled in the FE analysis.

Groundings are among the most common and serious maritime accidents. The shape of the sea bottom is one of the important factors that determine the extent of grounding damage on ships, including loss of watertightness. This paper presents a four-step methodology for mathematically analyzing sea bottom shapes, where individual peaks are identified and isolated from larger datasets. To these individual peaks mathematical models are fitted and the goodness of the fit is evaluated. The aim is to develop mathematical rock models that can be used in grounding damage analysis. The method is applied to bottom topography data from the two busiest tanker harbors in Finland. As potential mathematical rock models common assumptions found in literature as well as new suggestions are used. It was observed that rocks vary in shape and size locally as well as between different geographical areas. This highlights the need to have rock models that are flexible enough to model a wide range of sizes and shapes so that the local conditions can be taken into account. This includes modeling asymmetrical shapes, which is not taken into account in the current models. The analysis results suggest using a binormal function to describe the bottom shape: This model gives overall better goodness-of-fit test results than the cone and polynomial models. In the data the binormal model can model well the also the bottom shapes where the polynomial and conical models had a good fit in statistical terms. Although the paper discusses data from the Gulf of Finland, the framework for analyzing bottom shapes is expected to be applicable to other sea areas as well. (C) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

This paper presents the developments of the non-local sandwich beam theories that can be used to assess the micro- and macro-structural responses. The paper utilizes homogenization–localization, modified couple stress, and thick-faces beam theories. The homogenization derives prevailing differential equations from displacements through strains and stresses to external loading. This enables accurate localization process that recovers the microstructural effects from the homogenized solution and couples them to the global response. Some case studies are supported by computational experiments: the shortest beams have only four unit cell along their length. The present solution converges to the physically correct solution in the cases of infinite and zero shear stiffness. The limit of zero shear stiffness is important because there the traditional Timoshenko beam theory fails to predict the response correctly. Some difference in the solutions is observed on very short beams at intermediate rotation stiffness between the faces and the core, where the wavelengths of the global and local responses heavily interact. Present theory can be extended to different microstructures and to plates. The benefit of the present approach is that it is analytical which enables identification of the physical parameters.

The sandwich constructions are widely used in various industrial applications due to their ability to provide high bending stiffness coupled with light weight. In general, the sandwich structures are designed as panels that must carry bending loads. The three-point bending test is one of the most common material testing procedures for investigating the properties and behavior of materials with structural applications. In this sense, the bending deflection is one of the properties investigated by bending tests and is associated with the stiffness of the analyzed material. Considering this, within this paper is proposed a correction to first and Reddy’s third order shear deformation theory to determine the bending deflection of sandwich beams. The method is based on the Timoshenko’s theory for highlighting the local effect given by the applied load, adapted for sandwich structures. Also, this method approach the bending deflection maintaining compact the sandwich beam, is easy to apply and accurately estimate the vertical displacements along the cross-section. Two sandwich configurations were analyzed in the paper. The results showed on the one hand, the capability of the proposed relations to accurately estimate the vertical displacements of different points on the cross section and on the other hand the core flexibility effect on the bending behavior of the analyzed sandwich beams.

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.

In this investigation, ductile fracture in stiffened and unstiffened panels is simulated employing the fracture criterion, which depends on the mesh size, stress state and damage induced softening. The aim of the study is to show that employed fracture criterion removes mesh size effects more efficiently than traditional fracture criteria adjusted only on the basis of uniaxial tension. Fracture model is implemented into Finite Element software ABAQUS using user-defined material, VUMAT-subroutine, available for shell elements. Mesh size sensitivity analysis is carried out. Finite element simulation results are validated with experimental measurements available in literature. Comparison of numerical and experimental results shows that simulations effectively capture most of the experimentally observed features, especially when considering different mesh densities. In most cases, mesh size effects are considerably reduced compared with the fracture criteria adjusted on the basis of a uniaxial tension.

The paper presents investigation on periodic and homogenized bending response of the faceplates of filled web-core sandwich beams. The investigation is carried out using analytical, numerical and experimental methods. It is shown that the interaction between the web and faceplates and the filling material is complex phenomena. This affects the warping-induced deflection of the faceplates. The filling material stiffens the beams and reduces the shear-induced warping-deflection and resulting normal stress in the faceplates considerably. The homogenized solution is shown to agree with the periodic response well in terms of deflections. However, the normal stresses in the faceplates are considerably underestimated with the homogenized solution.

During the last period the interest on the sandwich structures has became more favorable due to the strength to weight ratio. In the same manner, in ship building field the lightweight structures became more and more attractive. With increasing the usage fields has increased the need to study the behavior of these structures. In general all the sandwich structures loaded in bending shows an effect of the secondary bending moment. In the case of web core sandwich panels used in ship structures has been observed a pronounced effect of the secondary bending moment on laser welded joints. Considering this, the paper presents an analysis of the fracture strength of laser welded joints of a web core sandwich structure, due to the effect of secondary bending moment. In the first part, the paper analytical formulation of the secondary bending moments and their effect on welded joints. This effect is explained on the basis of angle α defined in the paper and which depends on the thickness of the face plate, the thickness of the web plate and respectively the height. The paper continues with a numerical analysis of the stress and strain state from a web core sandwich beam and where also it is analyzed the effect of the secondary bending moment on the fracture strength of laser welded joints. Based on the carried out study it was observed that for high thickness of the web plate the effect of secondary bending moments is the overloading of the welded joints, instead for small thickness of the web plate the effect of the secondary bending moments can be of the unloading the welded joints. However, a small thickness of the web plate can affect the rigidity of the structure. Therefore, based on this study was proposed a solution to reduce the secondary bending moment without reducing the stiffness of the sandwich panel. The analysis conducted in this paper can be a design criterion for the web core sandwich structures.

Structural members made up of two stiff, strong skins separated by a lightweight core are known as sandwich panels. The separation of the skins by the core increases the moment of inertia of the panel with little increase in weight, producing an efficient structure against in-plane and out-of-plane loadings. In general, the mechanical behavior of cellular structures is given by the effective elastic modules, which are also dependent on the structure topology and different geometric parameters. This paper presents analytical equations for equivalent stiffness properties of a cylindrical cell honeycomb core. The cylindrical cells are obtained by connecting bended plate strips using adhesion or laser-welding. The stiffness properties and effective elastic modules for in-plane and out-of-plane compression and shear loadings are derived using an energy based approach. The analytical models are validated by 3D finite element method based on solid elements. The obtained mechanical properties are used to assess the stress and strain state of a sandwich beam in three-point bending. The present investigation shows that the analytical equations can predict the stiffness coefficients and respectively the effective elastic modules with very good accuracy.

The paper presents experimental validation of the modified couple stress Timoshenko beam theory for web-core sandwich panels. The face and web-plates are assumed to be isotropic and to behave according to the kinematics of the Euler–Bernoulli beam theory. First, a modified couple stress theory for Timoshenko beams is reviewed. Then shear, bending and couple stress responses of homogenized web-core sandwich beams are examined. The developed theory is validated with experiments from open literature for beams in 3- and 4-point bending. The beams have 4, 9 and 15 unit cells along their length. It is seen that the developed theory is in excellent agreement with experiments. It is also seen that the theory converges to physically correct solutions in the cases of infinite and zero shear stiffness; while the first corresponds the case of Euler–Bernoulli sandwich beam, the second corresponds the case where the sandwich effect is lost and the bending is carried out purely by the bending of the faces. The paper also gives explicit expression for the couple stress stiffness in terms of unit cell dimensions and materials.

The fatigue assessment of welded ship structures includes high uncertainties. One source of uncertainty is the determination of relevant local stresses. To quantify the uncertainties and to improve the analysis guidelines, round robin studies were performed within the Network of Excellence on Marine Structures (MARSTRUCT) project. One recent study concerned load-carrying fillet welds, which are treated in different ways in structural stress approaches. In total, five partners participated in the work. Two structural configurations of 12 mm thick plates were analysed, that is, double-sided lap joints and doubler plates, each with two different weld throat thicknesses (2.5 mm and 7 mm). Differences in the results were identified and conclusions were drawn with respect to modelling guidelines and typical scatter of computed fatigue lives.

In this study, fracture propagation in large shell elements is modelled with the softening law. This law is given in a general form, enabling investigations of different softening behaviours to be conducted. The final fracture is simulated by removing elements. The softening parameters are derived using the energy-based representative volume element (RVE) approach. Tracing crack propagation through the RVE defines the physically justified softening parameters for the current model. The softening model is implemented into ABAQUS using VUMAT subroutines for the shell elements. A large-scale tearing experiment is simulated with the current model and RVE-based softening parameters. In addition, the softening laws from the literature have been used. The fracture propagation is assessed in terms of plastic energy dissipation in the RVE and the whole structure, load–displacement, and crack growth. The RVE-based model is shown to have better performance compared with other models from the literature.

This paper investigates the effect of initial distortion on the structural stress in 3 mm thick stiffened panels. The influence of initial distortion shape as well as magnitude is studied under axial tension and compression using geometrically non-linear finite element analysis. Different levels of structures are analyzed starting from the plate strips to an actual panel in order to understand how the structural response of thin initially distorted panel builds up. This way the difference between having initial distortion in one or two directions as well as the effect of boundary conditions becomes visible. The results reveal high non-linearity in the behavior of plate strip models and relatively linear behavior of actual plates and panel models in typical fatigue relevant ranges. This is due to support that the actual structures get from having initial distortion in two directions and from surrounding structures. In case of panels the most important effect on structural stresses near the transverse butt weld is the shape of the initial distortion. The second important is the magnitude of initial distortion and significantly less relevant is the straightening effect, i.e. decrease in structural to nominal stress ratio under loading.

The paper investigates the influence of highly localised stress distribution around the notch tips of the laser stake-welded T-joints to the slope of the fatigue resistance curve. The study considers experimental data of eight series involving joints under tension or bending loads. Various boundary conditions and plate thicknesses are considered. The stress distribution in the singularity-dominated zone ahead of the notch tips is investigated by means of the finite element analysis. The aim is to relatively distinguish the stress distribution from one case to another. The growth rate of the elastic singular stress with respect to the distance from the tip is described by the dimensionless gradient. This gradient is equal to the slope of the linear stress-distance function when presented in double-logarithmic scale. The slope of the fatigue resistance curve varies approximately from 4 to 8. It is observed that the change of the slope can be closely associated with the gradient of the maximum principal stress evaluated in the plane that is orthogonal to the crack path. The orthogonal plane corresponds to the maximum principal stress direction. In contrast, there is a large scatter in the relation between the slope and the gradient evaluated in the commonly assumed crack plane. The study shows that the dimensionless gradient exhibits sensitivity towards plate thicknesses, local weld geometry and the loading condition.

The corrosive marine environment is a threat to the ultimate strength of steel sandwich structures. Therefore, ultimate strength experiments were carried out in three-point bending for beams with different corrosion exposure times, i.e. one and two years. Standard laser-welded web-core sandwich beams are studied and different corrosion protection systems are considered. The beams experienced general corrosion. The thickness reduction in unprotected plates and laser welds is around the typical 0.1 mm/year. This led to an ultimate strength reduction of 10% and 17% for beams with exposure times of one and two years, respectively. The experimental ultimate strength is in agreement with finite element simulations. The ultimate strength was maintained for the beams protected with coating or closed-cell polyurethane (PU) foam.

Industries nowadays demand lightweight and space-saving solutions such as sandwich panels that offer high strength-to-weight ratios. In general, sandwich panels consist of homogeneous core material that carries a shear force and face plates that carry a bending moment. The web-core sandwich panel has an inhomogeneous core as it consists of unidirectional web plates that are periodically distributed and connected to the face plates by laser stake-welded T-joints. The joint has two crack-like notches on each side of the weld. When the panel bends, the out-of-plane shear deformation opposite to the web direction causes local bending of the joined plates in the vicinity of the weld. This leads to tension at one notch tip and compression at the other. The fatigue crack initiates at the tensile tip and propagates through the weld under cyclic loading until the plates are separated and the sandwich effect is lost. The thesis investigates the fatigue resistance of laser stake-welded T-joints in the web-core panels under out-of-plane loading, i.e. lateral loading. The bending of the joined plates in panels can cause contact between the surfaces of the compressive notch. It is determined that the contact causes an increase of the stiffness of the T-joint in the case of significant face plate deflection since it results in a large rotation of the joint. The increase in the stiffness of the joint needs to be considered in the assessment of the global response of the panel, which defines the displacements that are imposed as the loads in the local strength assessment of the joint. If panel contains a low-stiffness filling material inside the voids, the contribution of the material increases the shear stiffness of the panel and reduces the deformation of the joint. Thus, under the same external loading, the filling prolongs the fatigue life of the panel. The evaluation of the J-integral at the tips of the notches, modelled using statistically mean notch depth values, gave agreement on the fatigue strengths between all the series that were investigated at five million load cycles. The agreement is obtained regardless of plate thicknesses, the type of loading or whether the filling material is present. Good agreement with other steel joints is also demonstrated at five million load cycles. However, the slope of the fatigue resistance curve varies, depending mainly on the load type, i.e. tension or bending. The research determined that the slope depends on the distribution of the maximum principal stress in the vicinity of the notch tip. When the stress is characterized by a dimensionless gradient, evaluated in the stress direction, the slope-gradient relation appears linear. The gradient shows sensitivity towards the loading type and the plate thickness effect.

The aim of this paper is to investigate the influence of the plate thickness on the fatigue strength of laser stake-welded T-joints under the tension loading condition. Fatigue tests were conducted on specimens with plate thicknesses below 5 mm subjected to tension loading with the load ratio R = 0. The statistical analysis of the weld geometry showed a normal distribution of the each parameter that was measured. In addition, the parameters had similar proportions in comparison to the specimens with plate thicknesses above 5 mm. FE analysis was performed with the aim of determining the stress state in the joint along with the J-integral. If the square root of the J-integral, √ΔJ, is used as the fatigue strength assessment parameter, the fatigue strength obtained at five million cycles is similar as in the case of other steel welded joint types. The investigation concluded that the stress state changes with the reduction of the plate thicknesses and the contribution of fracture mode II becomes significant. However, using √ΔJ as a fatigue strength assessment parameter ensures that the complex state of the mixed fracture mode loading is accurately accounted for. This fact further enables the fatigue strength of laser stake-welded T-joints of any plate thicknesses to be described by means of a narrower scatterband than the one obtained by the nominal stress approach.

The paper investigates the interaction between the hull and the superstructure in optimised passenger ships when exposed to bending loads. The coupled beam theory was applied to extend the basic beam theory to take into account the vertical and shear stiffness between various decks. Optimisation of passenger ships with respect to weight and vertical centre of gravity (VCG) is carried out to create a set of Pareto-optimal solutions. The responses of these designs are compared in detail. The investigation shows that vertical and shear coupling between different decks significantly affect the response of the passenger ships and changes load-carrying mechanism of the hull girder. In the weight optimal design, the vertical bending moment is shared equally by the hull and the superstructure, while in the VCG optimal design, the neutral axis approaches bottom plating of the ship, considerably increasing the share of load carried by the superstructure. This means that the global response evaluation needs to inclu...

This paper analyses the collision resistance of the X-core structure. The analysis includes a detailed investigation of the non-linear plate and laser weld material behaviour using optical, full-field strain measurements. The resulting material relationships are implemented into the finite element model. Furthermore, the finite element model includes the influence of the ship motions to accurately predict the collision resistance. The verification of the numerical results is done by a comparison of the experimental and numerical force versus penetration curves and by a comparison of the deformed geometries. The latter is achieved through a digitised three-dimensional model of the post-experimental X-core structure. As a result, the accuracy of the collision simulations is presented and discussed.

This paper investigates the influence of weld rotation stiffness on the global bifurcation buckling strength of laser-welded web-core sandwich plates. The study is carried out using two methods, the first is the equivalent single-layer theory approach solved analytically for simply supported plates and numerically for clamped plates. First-order shear deformation theory is used. The second method is the three-dimensional model of a sandwich plate solved with finite element method. Both approaches consider the weld through its rotation stiffness. The weld rotation stiffness affects the transverse shear stiffness. Plates are loaded in the web plate direction. Four different cross-sections are considered. Weld stiffness is taken from experimental results presented in the literature. The results show a maximum of 24% decrease in buckling strength. The strength was affected more in plates with high reduction of transverse shear stiffness and high bending stiffness. Furthermore, clamped plates were influenced more than simply supported. The intersection between buckling modes shifted towards higher aspect ratios, in the maximum case by 24%. The results show the importance of considering the deforming weld in buckling analysis.

In this paper, a continuum-based discrete crack growth approach is introduced for the fatigue life analysis of welded steel joints. The proposed approach applies cumulative damage models utilising the material hardness and grain size statistics. The approach is validated with fatigue strength tests, and the predicted crack growth rates and fatigue lives have been observed to be in good agreement with the experiments.

Present paper investigates the interaction between laser-welded web-core sandwich deck plate and supporting girder under bending loads. The study is based on two linear-elastic Finite Element (FE) approaches, i.e. one using beam elements to model the girder and shell elements to model the homogenized web-core sandwich plate. With this approach the obtained FE model is considerably smaller than in the case of modeling the full, periodic, 3D geometry with shell elements. The FE solution results in stress resultants for beam and shell elements. These stress resultants do not describe accurately the periodic stress response of the sandwich plate or shear stress distribution at girder web. Therefore, the paper utilizes analytical methods to calculate these stress components from the obtained Finite Element solution. The second computational approach is based on modeling the actual 3D topology with shell elements. The two approaches are shown to be in very good agreement. The investigation shows that the effective flange width of the sandwich is different for the top and bottom face plates indicating that the interaction is different for these face plates. The present study also shows that this difference between the two faces depends strongly on the orientation of the web plates of the sandwich with respect to girder axis and the stiffness of the girder. The investigation also shows that the normal stress response in bending is dominated by the interaction between the sandwich plate and the girder, but also by the shear-induced normal stresses at the outer surface of the plate.

This paper aimed to investigate the geometrical variations of laser stake-welded T-joints and their influence on fatigue assessment. Another aim was to determine which of the rref = 1 mm, rref = 0.05 mm, and J-integral assessment approaches are applicable for this joint type. Because of the specimen geometry and the loading condition in this study, J-integral approach was equivalent to mode I notch stress intensity approach. Accurate measurements of geometry were taken. Statistical analysis of the weld geometry showed that all the geometrical properties are normally distributed. The results of the fatigue assessment showed that all the approaches applied have a relatively small scatterband and are valid for this joint type. The fatigue strength at 2 million cycles, estimated by all approaches, corresponded to the fatigue strength of other welded steel joints from the literature. However, in case of rref = 0.05 mm approach, fatigue strength at 2 million cycles proposed in literature, appeared to be slightly conservative for laser stake-welded T-joints. All the approaches, applied in this study, had the slope of the fatigue resistance curves different from the usual m = 3.

This paper presents a stress analysis method for web-core sandwich beams. The beam is a transverse cut from a sandwich plate. The analysis is carried out by transforming the initially periodic web-core sandwich beam, constructed from a set of unit cells, into an equivalent homogenous sandwich beam. Certain deformation components are set equal both in periodic and homogenous beams when a unit cell is considered. The structural analysis of the homogenized beam follows thick face plate kinematics giving the deflection, bending moment and shear force distributions. Then the normal stress components can be calculated accurately by reconsidering the periodic structure of the beam. The validation of the proposed method is carried out with FE-analyses.

The purpose of this paper is to describe experiments carried out on laser stake welded T-joints of web-core steel sandwich structures. A special test setup was developed to measure the shear-induced rotation at the T-joint. The ratio of the shear force to rotation angle gave the joint stiffness. This stiffness was measured for specimens with two different face-plate thicknesses. The influence of weld thickness, root gap and occurrence of contact were further investigated with finite element simulations. Finally, the shear stiffness of the sandwich structure transverse to the web plate direction was determined using the experimentally obtained average joint stiffness value. The validation of the shear stiffness was carried out by considering a beam in four-point bending. The agreement between calculated deflection and stress and experimental results was found to be good.

This paper presents an approach to the structural analysis of patch-loaded, laser-welded web-core sandwich plates. This approach is especially suitable for the concept design phase of ship structures. The method consists of two parts; the global bending response is evaluated using sandwich plate theory and the local response of the patch-loaded face plate is determined with the help of basic plate theory. Both analyses utilise analytical and numerical methods and include the effect of the rotation stiffness of the laser-welded T-joint between the face and web plate. Combining the results of these two analyses gives the total response of the web-core sandwich plate. The results of the proposed approach are compared to those given by 3D solid and shell element FE analyses and the agreement of deflections and normal stresses is found to be good. The sensitivity of the response to patch-load size, T-joint rotation stiffness, and plate aspect ratio is studied. The main benefits of the proposed approach are its short analysis time and the good accuracy of deflections and stresses. This considered advantageous when applied to the design of large ship structures such as hoistable car decks.

A theory for the bending response of web-core sandwich plates is presented in this paper. Response is evaluated by transforming an originally discrete core into an equivalent homogenous continuum giving a sandwich plate, which follows, thick-face-plate kinematics. The approach exploits analytical formulations for the determination of the equivalent stiffness properties of the plate. The finite element method is used to determine the internal forces and displacements of the plate for given load and boundary conditions. Thereafter, the periodic structure is reconsidered and the internal forces are used in the stress predictions based on analytical formulations. The validation of the present approach is carried out with 3D FE analyses. The case studies consider various combinations of load and boundary conditions. A good agreement is obtained between the proposed theory and 3D FE analyses.

This paper studies the frequency of ice loads of varying lengths and the occurrence probability of their magnitudes in full-scale. In these measurements, the four frames were instrumented with shear strain gauges on the Polar Supply and Research Vessel S.A. Agulhas II. The experiments were carried out on first-year ice in the Baltic Sea. An influence coefficient matrix based on analytical and numerical analyses was used to determine the load length in the horizontal direction. Rayleigh separation was used to define the load amplitudes. The measurements show that the ice loading has to be long in order for the shear-load maximum on a single frame to occur. Furthermore, the statistical study showed that the Weibull distribution gives the best fit to the measured loads on a frame. The probability distribution of the ice loads on a frame is exponential-like for short loads and lognormal-like for long loads.

The 4th International Conference on Marine Structures, MARSTRUCT 2013, was held in Espoo, Finland, between 25 and 27 March 2013, and it follows on from previous events held in Glasgow, Scotland; Li...

Previously, it has been shown that the grain size distribution plays an important role in the mechanical properties of welded steel. In the previous investigation, the volume-weighted average grain size has been shown to capture the influence of grain size distribution, resulting in a better fitting Hall–Petch relationship between grain size and hardness. However, the previous studies exclude the effects arising from local variation in grain size. In this paper, the grain size measurement methods are extended for the characterisation of the local grain size variation, which is significant for welded joints and can have an adverse effect on mechanical properties. The local gradient of grain size variation and its dependency on measurement direction are considered. In addition, examples of grain size and hardness variation are shown for S355 base metal and two weld metals, and characteristic differences are highlighted and discussed. The coarse-grained areas of a heterogeneous microstructure are found to have lower hardness than fine-grained areas. However, the surrounding microstructure, i.e. local grain size gradient, has an influence on the measured hardness values.

A geometricallynonlinear modelfor periodic sandwich structures based on the modified couple stress Timoshenko beam theory withvon Kármánkinematics is proposed. Constitutive relations for the couple stress beam are derived assuming an antiplane core and then extended for a generic periodic cell. A micromechanical approach based on the structural analysis of a unit cell is proposed and utilized to obtain thestiffness propertiesof selected periodic sandwich beams. Then, alocalizationscheme to predict the stress distribution over the faces of the selected beams is defined. The present model is shown to be equivalent to the thick-face sandwich theory for a linear elastic antiplane core cell. Numerical studies validate the present model against three-dimensionalfinite element modelsand the thick-face sandwich theory, and compare it with the conventional Timoshenko and couple stress Euler–Bernoulli beam theories. The present model is shown to predict deflections, stresses and buckling loads with good accuracy for different periodic cell setups. The model is able to describe elastic size effects in shear-flexible sandwich beams and the core stiffness influence onmembrane and bending stressresultants.

Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler-Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results., This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Action grant agreement No 745770 - SANDFECH - Micromechanics-based finite element modeling of sandwich structures. The preprint has been replaced by the accepted manuscript

A 2-D micropolar equivalent single-layer (ESL), first-order shear deformation (FSDT) plate model for 3-D web-core sandwich panels is developed. First, a 3-D web-core unit cell is modeled by classical shell finite elements. A discrete-to-continuum transformation is applied to the microscale unit cell and its strain and kinetic energy densities are expressed in terms of the macroscale 2-D plate kinematics. The hyperelastic constitutive relations and the equations of motion (via Hamilton's principle) for the plate are derived by assuming energy equivalence between the 3-D unit cell and the 2-D plate. The Navier solution is developed for the 2-D micropolar ESL-FSDT plate model to study the bending, buckling, and free vibration of simply-supported web-core sandwich panels. In a line load bending problem, a 2-D classical ESL-FSDT plate model yields displacement errors of 34-175% for face sheet thicknesses of 2-10 mm compared to a 3-D FE solution, whereas the 2-D micropolar model gives only small errors of 2.7-3.4% as it can emulate the 3-D deformations better through non-classical antisymmetric shear behavior and local bending and twisting., This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Action grant agreement No 745770 - SANDFECH - Micromechanics-based finite element modeling of sandwich structures. The preprint has been replaced by the accepted manuscript