Out-of-plane Bending Research Articles

Mooring Fatigue Assessment Evaluating Chain Twist and Out-of-Plane Bending for a Semi-submersible

Abstract A mooring fatigue assessment for mooring chain links of a semi-submersible in Offshore West Africa (OWA) is presented. Three cases that mooring chain links are subjected to pure tension, out-of-plane bending (OPB), and torque are considered in the assessment. For the case that mooring chain links are subjected to pure tension, a comparative study on S–N curves, T–N curves, and fracture mechanics (FM)-based mooring system fatigue analyses is made, and the results show that the fatigue lives predicted by these three approaches are generally comparable if the safety factors suggested by API and DNVGL are applied to T–N curves and S–N curves based approaches. For the cases that mooring chain links are subjected to the OPB and torque, the investigation shows that fatigue lives of mooring chain links are decreased significantly due to the OPB effects, while the decline of fatigue lives of mooring chain links happens when the twist angles are more than 10 deg.

Multi-scale approach for chain-mooring OPB-induced failure considering time-varying interlink bending stiffness and fairlead condition

In this study, a multi-scale approach concept is introduced to estimate OPB (out of plane bending)-induced failure considering time-varying interlink bending stiffness by using both high-fidelity nonlinear-FEM (finite element method)-based local structural analysis and low-fidelity global-system-simulation program so that they can mutually be interfaced during the time-stepping procedure. In addition, time-varying interlink-angle measurement and its use with respect to the global-system simulation are devised. For the fully-coupled hull-mooring-riser global dynamics simulation, in-house program CHARM3D is extended to accommodate the time-varying OPB interlink stiffness. The hot spots for OPB fatigue are selected from the high-fidelity local FE analysis including residual stress after proof-loading test. It is clearly shown that interlink angles are under-estimated if chain-hawse is not modeled in the global simulation. The OPB interlink angles, bending moments, and accumulated fatigue damages greatly increase when the fairlead connection is changed from hinged to fixed condition. Moreover, fatigue damage is underestimated if the residual stress effect is not considered.

Fracture mechanics analysis for mooring chain links subjected to out-of-plane bending (OPB)

A fracture mechanics (FM) based investigation on the mechanism of out-of-plane bending (OPB) between mooring chain links and its effects on fatigue lives of mooring chain links are conducted. Four types of OPB problems that mooring chain links laying on the chain wheel, chain links passing over the bending shoe, chain links constraint provided by the chain hawse, and chain links constraint provided by the chain stopper are considered. Tension ranges of mooring lines are calculated based on the combined loading process induced by the motions of wave frequency (WF) and low frequency (LF). Initial cracks are assumed to propagate from surfaces of chain links and stress intensity factors are calculated in terms of stress ranges determined by a finite element (FE) analysis. The results show that fatigue lives of mooring chain links are decreased significantly due to OPB effects. In addition, the increase of the number of pockets of chain wheel mitigates OPB effects on fatigue lives of mooring chain links laying on the chain wheel, and the increase of the track diameter would reduce OPB effects on fatigue lives of mooring chain links passing over the bending shoe as well. However, for chain links constraint provided by the chain hawse, the diameter of mooring chain hawse has no significant effect on fatigue lives of the mooring chain links subject to OPB if without the abrupt change of the contact conditions between chain links and chain hawse. For mooring links constraint provided by chain stoppers considering the effect of proof loading test, fatigue lives of mooring chain links would drop significantly with the increase of interlink angles and friction coefficient.

Stress concentration factors of multi-planar tubular XT-joints subjected to out-of-plane bending moments

The majority of tubular joints commonly found in offshore jacket structures are multi-planar. Investigating the effect of loaded out-of-plane braces on the values of the stress concentration factor (SCF) in offshore tubular joints has been the objective of numerous research works. However, due to the diversity of joint types and loading conditions, a number of quite important cases still exist that have not been studied thoroughly. Among them are multi-planar XT-joints subjected to out-of-plane bending (OPB) moment loading. In the present research, data extracted from the stress analysis of 81 finite element (FE) models, verified using experimental test results, was used to study the effects of geometrical parameters on the chord-side SCFs in multi-planar tubular XT-joints subjected to three types of OPB moment loading. Parametric FE study was followed by a set of the nonlinear regression analyses to develop three new SCF parametric equations for the fatigue analysis and design of OPB-loaded multi-planar XT-joints.

Degree of bending (DoB) in offshore tubular KT-joints under the axial, in-plane bending (IPB), and out-of-plane bending (OPB) loads

Through-the-thickness stress distribution characterized by the degree of bending (DoB) has a major effect on the fatigue behavior of tubular joints commonly found in steel offshore structures. The determination of DoB values is essential for improving the accuracy of fatigue life estimation using the stress-life (S–N) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. In the present research, data extracted from 648 finite element (FE) analyses carried out on 81 tubular KT-joint models was used to study the effects of geometrical parameters on the DoB values in KT-joints subjected to eight different types of loading including two types of axial loading, three types of in-plane bending (IPB) moment loading, and three types of out-of-plane bending (OPB) moment loading. Generated FE models were validated using experimental data, previous FE results, and available parametric equations. Geometrically parametric investigation was followed by a set of nonlinear regression analyses to develop 21 parametric design formulas for the calculation of the DoB in tubular KT-joints under the axial, IPB, and OPB loadings.

Extended Formulation of Stress Concentration Factors for CFST T-Joints

In previous research, the authors numerically investigated 212 finite-element (FE) models of concrete-filled steel tubular (CFST) T-joints under axial force in the brace to derive formulae for stress concentration factors (SCFs). The formulations involve four nondimensional parameters: diameter ratio β, diameter-to-thickness ratio of chord 2γ, thickness ratio τ, and relative chord length α. In the current study, the earlier formulation was extended to include four additional loading conditions: in-plane bending (IPB) in the brace, out-of-plane bending (OPB) in the brace, axial compression in the chord, and IPB in the chord. The validity of the new SCF formulae was demonstrated by comparing the SCFs obtained using the formulae with the results of numerical analysis.

Stress concentration factors in FRP-strengthened offshore steel tubular T-joints under various brace loadings

The stress concentration factors (SCF) in FRP strengthened tubular T-joints subjected to brace axial loading, in-plane and out-of-plane bending moments were investigated. The numerical analyses were performed using ABAQUS Finite Element software package. The benchmark joints were validated against the Lloyd's Register and API equations together with the experimental results. Six different types of FRP materials such as Glass/Vinyl ester, Glass/Epoxy (Scotch ply 1002), S-Glass/Epoxy, Aramid/Epoxy (Kevlar 49/Epoxy), Carbon/Epoxy (T300-5208) and Carbon/Epoxy (AS/3501) were used as strengthening material in order to investigate the SCF values on the chord member of the tubular T-joints. Results derived from analyses are promising and show that the FRP strengthening method could be considered as an effective method to reduce the SCFs and consequently extend the fatigue life cycle of tubular T-joints. Results of the analyses for a 6 mm CFRP layup show that under axial loading (AX), the FRP strengthening decreases SCFs up to 30% and 50% at Crown and Saddle points on the chord, respectively. Moreover, under the action of in-plane bending (IPB) and out-of-plane bending (OPB) moments, SCF reductions of about 45% and 50% were observed, respectively.

Optimizing pulsed fiber laser welding process parameters of thin Ti6Al4V sheet to control angular distortion

The present study deals with angular distortions generated in fiber laser welding of Ti6Al4V sheets performed utilizing pulsed mode of laser irradiations. Experiments were conducted considering laser power, scan speed, pulse frequency and duty cycle as input process parameters, and angular distortion measured in terms of out of plane bending was taken as the process output. A central composite design was employed for carrying out pulsed laser welding experiments. The angular distortion was modelled using the response surface methodology for correlating with the input process parameters. Angular distortion was observed to increase with the laser power and scan speed. Optimum values of laser pulse frequency and duty cycle were found for obtaining least angular distortion. The prediction accuracy of the developed model of angular distortion was found to be good. Then, the desirability function approach of optimization technique was used to determine the optimum process parameters for obtaining the minimum distortion. Optimal distortion value was verified by conducting experiments and results were found satisfactory.

Parametric Study of FRP Strengthening on Stress Concentration Factors in an Offshore Tubular T-Joint Subjected to In-Plane and Out-of-Plane Bending Moments

This paper describes numerical investigations conducted on a tubular T-joint strengthened by FRP composites under in-plane bending (IPB) and out-of-plane bending (OPB) moments. The FRP materials were applied as a protective layer on the T-joint, and the analyzed models were eventually validated against the results obtained from an experimental study. The effectiveness of using FRP materials on enhancing the fatigue life of a tubular T-joint was investigated through computing the relative SCFs of 150 finite element models using ABAQUS software package. Analyses have been performed to investigate different FRP parameters such as fiber orientation, FRP thickness, wrapping length and FRP material properties of the wrapped joint. Effectiveness of these FRP parameters on SCF reduction along with the most efficient lay-ups against both IPB and OPB moments were reported. According to the results of this study, further reduction in SCFs was observed when the joint was confined with stiffer FRPs. SCF reduction of around 15% was observed for only a 1 mm thick CFRP layup. Moreover, using a thicker FRP layup tends to increase its effectiveness significantly. However, it was observed that increasing the FRP wrapping length has negligible effect on SCF values, and has to be chosen so as to cover all the chord surface area influenced by the brace loading in order to balance the state of stresses and deformations.

Out-of-plane bending stiffness and hotspot stress based on advanced numerical analysis techniques

ABSTRACTThis paper aims to presents an integrated procedure to reach the out-of-plane bending (OPB) moment-induced hotspot stress distribution for the mooring chains of an 8MW class floating offshore wind turbine platform (FOWT). Three-link models of the mooring chains were used to obtain the OPB stiffness, mid-span stress distribution, hotspot stress, and stress concentration factor based on the prescribed rotation approach (PRA), direct tension approach (DTA), and empirical formula. Multi-link analyses were also conducted to build a tension angle-interlink angle relationship between two successive links at a given tension level. A combination of three-link and multi-link analyses produced the relation of the hotspot stress-tension angle. After a stress interpolation procedure for the hotspot stress history, the hotspot stress range distributions were presented using rainflow counting technique. The tension-induced stress range distribution well followed the Rayleigh distribution, while the OPB moment elevated the hotspot stress which will seriously affect the fatigue accumulation.

Strength Reduction Factors for Cracked Multi-planar Tubular DT-joints

This paper reports the strength reduction factors of cracked multi-planar tubular DT-joints subjected to three simple loadings. The three strength reduction factors are used to calculate the static strength of the cracked tubular DT-joints and they have never been reported in any reference. Mesh of the cracked tubular DT-joints is created using a set of mesh generation code, and then FE (Finite Element) analyses are carried out using commercial software. The strength reduction factor is defined as the ratio of the static strength of the cracked joint over the uncrack joint. The effect of the crack area on the static strength of tubular DT-joints is investigated prudently. It is found that when the crack area is 25% of the product of chord thickness and weld length, the static strength of the cracked tubular DT-joint can decrease more compared to the corresponding uni-planar tubular T-joint, and the decrease magnitude is up to 23.2%, 37.4% and 31.2% of the static strength of the uncracked tubular DT-joint for axial tensile, IPB (In-Plane Bending) and OPB (Out-of-Plane Bending) loading, respectively. Finally, based on the FE results, three linear equations are recommended for calculating the strength reduction factors of cracked tubular DT-joints.

Effects of geometrical parameters on the degree of bending (DoB) in two-planar tubular DT-joints of offshore jacket structures subjected to axial and bending loads

The fatigue life of tubular joints commonly found in offshore structures is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). In the present research, data extracted from the finite element (FE) analyses carried out on 81 two-planar tubular DT-joint models was used to study the effects of geometrical parameters on the DoB values in DT-joints subjected to six different types of loading including two types of axial loading, two types of in-plane bending (IPB) moment loading, and two types of out-of-plane bending (OPB) moment loading. Generated FE models were validated using available parametric equations. The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stress-life (SN) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. Geometrically parametric investigation was followed by a set of nonlinear regression analyses to develop three DoB parametric formulas for the fatigue analysis and design of two-planar DT-joints.

Development of a probability distribution model for the LJF factors in offshore two-planar tubular DK-joints subjected to OPB moment loading

Probability distribution models are essential for the reliability-based analysis and design of offshore structures. The objective of the present research was developing a probability distribution model for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore wind turbines and oil/gas production platforms. A total of 324 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to four types of out-of-plane bending (OPB) moment loads. Generated FE models were validated using the available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical probability density functions (PDFs) were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the lognormal model was proposed as the governing probability distribution function for the fLJF. After substituting the values of estimated parameters, four fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to four types of OPB moment loads.

The post-breakage response of laminated heat-treated glass under in plane and out of plane loading

Abstract Any reliable use of glass for structural purposes cannot neglect that its breakage may be provoked by imponderable events, like impacts at critical spots or thermal shocks. Laminated glass, composed by glass plies sandwiching polymeric interlayer sheets, is used in architectural application thanks to its safe post-glass breakage response. When glass breaks, the interlayer retains the glass shards, and the cracked element maintain a certain residual load-bearing capacity, strongly influenced by the tension stiffening of the polymer due to the adhesion with the glass shards, which depends upon the size of the shards and of the debonded zones. Here, we review the most recent experimental results on the post-glass breakage response of laminated heat-treated glass elements, providing charts for the evaluation of such a stiffening effect. Based on this, simple formulas to analyze and interpret the experimental findings under both in-plane and out-of plane bending are proposed, providing analogies with the bending of bimodulus materials and the load-bearing mechanism of reinforced concrete, respectively.

Study on prediction of stresses by out-of-plane and in-plane bending moments in offshore mooring chain

ABSTRACTA fatigue evaluation due to an out-of-plane bending (OPB) and in-plane bending (IPB) moments has been a key engineering issue in the mooring design of a floating offshore unit. Choung and Han recently proposed a numerical approach to predict the fatigue damage which was dependent on the maximum principal stresses at final load step without using linearly superposed stresses at each load step for a hotspot. The proposed approach does not use the nominal OPB/IPB moments and the nominal OPB/IPB stresses therefrom, but it is important to compare them for verification of the proposed approach. Based on the mid-span elastic deflection, the nominal OPB/IPB moments are shown in this study. Since the elastic deflection-based nominal moment increased as the OPB tension angle develops, it was proven that the assumption of the elastic deflection was not suitable. By introducing BV guideline formulas, we show the OPB/IPB moments change along the OPB/IPB tension angles.

Fracture mechanics analysis for a mooring system subjected to tension and out-of-plane bending

A fracture mechanics analysis for the mooring system of a semi-submersible accounting for out-of-plane bending (OPB) is presented in this paper. Stress ranges acting on the mooring chain links are calculated based on tension and OPB of mooring chain links induced by motions of wave frequency (WF) and low frequency (LF). The narrow-banded method is used for predicting the combined mooring loading process. Initial cracks are assumed to propagate from surfaces of chain links and stress intensity factors are then calculated in terms of stress ranges determined by a finite element analysis. The influence of the OPB on the remaining service life of mooring chain links is investigated and the results show that the remaining service life of mooring chain links connecting to fairleads is significantly reduced due to the OPB effects.

Initial stiffness and strength characterization of minor axis T-stub under out-of-plane bending

No research has been performed yet that deals with the characterization of the minor axis of steel joints under out-of-plane bending. As a consequence, a complete description of all the components that become part of a 3D steel joint is not yet available either in scientific journals or current codes. Moreover, it is necessary to identify the behavior of each isolated component that is subjected to in and out of plane effects before studying the interaction among components and the interaction with the loads that act in both the major and minor axis of the joint.The aim of the research described in this paper is to define the behavior of the T-Stub under out of plane bending attached to the column minor axis. In the proposed kind of joint the minor beam is not attached to the column web but to additional plates welded to the column flanges.With the purpose of characterizing this component, two experimental tests have been performed that allow validating the finite element models. Then, a parametric study is performed by varying different characteristics of the joint to check their influence. Through the tests and models the additional plate in bending has appeared to be the most influential component, which is not characterized in the Eurocode 3.Finally, analytical expressions for the initial stiffness and strength of the additional plate of the T-Stub in minor axis under out of plane bending are presented.

Analysis of reaction rates of single molecules on metal surfaces

The experimental results of the action spectra i.e., reaction rate R(V) as a function of a bias voltage V are analyzed for rotation of a single CCH (D) molecule on a Cu (100) surface [5] and hopping of a single H(D)2O molecule on Pd(111) surface [6]. In the former system it is identified that rotation occurs if enough energy stored in the C-H (D) in-plane bending (IPB) mode excited by tunneling electron is transferred to the C-H (D) out of plane bending (OPB) mode (reaction coordinate mode) via the anharmonic mode coupling in a single electron process. The calculated R(V) shows an excellent agreement with the experimental results except at the low bias voltages below V ≃ 60 mV where no experimental data is available for the nonlinear current I dependence of R(I). A reproduction of the experimental R(V) at the higher voltage region allows us to determine the vibrational density of states of the C-H IPB mode and its coupling rate to the C-H (D) OPB mode as well as the inelastic tunneling current to excite IPB mode. A change of a conductance upon excitation of the C-H IPB mode enables us to evaluate the electron-vibration coupling strength inducing the rotation motion of CCH molecule. In the latter system investigated at a high temperature of about 40K, the constant R(V) due to thermal hopping followed by the rapid increase is satisfactory explained by anharmonic inter-mode coupling between the scissor mode excited by tunneling electrons and the frustrated translation mode for H(D)2O molecule on Pd(111).

Geometrical effects on the local joint flexibility of two-planar tubular DK-joints in jacket substructure of offshore wind turbines under OPB loading

The local joint flexibility (LJF) of two-planar tubular DK-joints in offshore jacket structures under the out-of-plane bending (OPB) loads is studied in the present paper. Altogether, 81 finite element (FE) models were generated and analyzed by ANSYS in order to investigate the effects of DK-joint's geometrical parameters on the LJF factor (fLJF) under four types of OPB load cases. Generated FE models were validated against the existing experimental data, FE results, and parametric equations. After the parametric study of geometrical effects, the fLJF in two-planar DK- and uniplanar K-joints were compared. Results showed that the effect of multi-planarity on the fLJF values is considerable. Hence, the application of the equations already available for uniplanar K-joints to determine the fLJF in two-planar DK-joints might result in highly under-/over-predicting outputs. To suggest a solution for this issue, results of 324 analyses carried out on generated FE models were used to develop a new set of parametric formulas for the calculation of the fLJF in OPB-loaded two-planar DK-joints. Applicability of proposed formulas was assessed based on the UK DoE acceptance criteria.

Formability Evaluation of 3D Closed Section Parts from Sheet Metal Based on Geometrical Information

For successful sheet metal forming, a complex design and trial process are inevitably necessary. That complex process is geometrical design, forming process selection, tool / die face design and forming condition. It may take couple of months to carry out this process, and at the end of this process try out may result in unsuccessful. The cause of this unsuccessful try out is difficult to find out because of the complexity of the design and try out process. It is proposed that a new evaluation methodology can provide semi-quantitate evaluation for the forming difficulty of the sheet. The proposed method evaluates only geometry of sheet metal parts, starting with Riemann curvature, which is decomposed into Gaussian curvature and metric tensor. Because the nature of sheet metal forming failure (breakage and wrinkle) are mainly related to in-plane deformation and not so much related to out of plane bending. Gaussian curvature is an excellent index for in-plane deformation caused by geometry angulation. Metric tensor provide quantitative evaluation for in-plane deformation. Computational time for this proposed method is a couple of minutes and is suitable for the evaluation and modification of the upstream design.