S.T. Lie

Modelling and mesh generation of weld profile in tubular Y-joint

Abstract This paper describes a systematic method of modelling the weld thickness of a tubular Y-joint. The intersection between the chord and the brace members is defined precisely. This intersection curve will then be used to evaluate the dihedral angle γ , which is the angle between the chord and the brace surfaces along the intersecting line. As the dihedral angle γ is an important parameter used to determine the weld thickness, its variation along the intersection curve and its relationship with the weld thickness is investigated first. It is shown that the smoothness of the weld path may not always be maintained if the minimum weld thickness, as specified in the American Welding Society (AWS) Codes D1.1-96, is to be followed strictly. Thus in some cases, modification of the intersection curve is necessary in order to model the weld path along the joint. Two scale factors F os outer and F os inner for the outer and inner intersection curves, and two constants m and n are introduced and proposed in this study. They are used to control the parameter k TW , which in turn controls the minimum weld thickness T W . Based on this model, an automatic mesh generator is developed to produce a well-graded finite element mesh. The stress concentration factors (SCFs) are shown to converge when the mesh is doubled and then tripled. Finally, some tubular welded specimens are fabricated, and the outer weld profiles are measured physically. It is shown that scale factors F os outer =0.3, F os inner =0.25 and constants m =2.0, n =0.4, are adequate to satisfy the required minimum outer weld profile. Therefore, the proposed method to model the weld size is both consistent and accurate for any tubular Y-joints.

Damage criterion and safety assessment approach to tubular joints

Abstract Based on the Continuum Damage Mechanics (CDM), a damage criterion is proposed to predict the macrocrack initiation for tubular joints. The guidance on prediction to ultimate load carrying capacity of flawed tubular joints is provided by means of the modified Central Electricity Generating Board (CEGB) Failure Assessment Diagram (FAD). Non-linear FE analyses were carried out on uncracked and cracked T, K and KK tubular joints. Triaxial stress distributions and equivalent plastic strains near weld toes in the chord around the brace were numerically obtained for uncracked tubular joints. The crack driving force, J -integral, and ultimate collapse loads of cracked tubular joints subjected to axial brace loading were evaluated by FE analyses. Load–displacement curves and ultimate strengths for uncracked and cracked T, K and KK-joints were numerically determined. A uni-planar KK tubular joint specimen was tested under anti-symmetrical axial loads. During the test, the load–displacement curve and the ultimate strength were measured. Meanwhile, crack initiation and growth were observed until complete failure. FE and test results show that the damage criterion gives good prediction for macrocrack initiation in tubular joints, and the modified CEGB approach is suitable for the safety assessment to flawed tubular joints.

Static Strength of Tubular T-Joints with Reinforced Chord under Axial Compression

A typical tubular T-joint is made up of a chord member and a brace member, and the brace member is connected to the chord surface with full penetration welds. As the stiffness of the chord in the radial direction is much weaker than that of the brace member in the axial direction, failure occurs easily at the weld toe on the chord surface when the chord is subjected to static axial load in the brace axial direction. To improve the static strength of a tubular T-joint, the chord near the weld toe can be reinforced locally by increasing its thickness. To study the effect of the chord reinforcement on the static strength of a tubular T-joint, 48 T-joint models with different reinforcements have been analyzed using the finite element method. The effects of the chord thickness and the length of the reinforced chord on improving the static strength of tubular joints have been investigated. It is found that the static strength can be greatly improved by increasing the chord thickness near the intersection. However, the increased chord thickness should not be much greater than the original chord thickness to avoid changing of the failure mode. On the other hand, it is not effective to improve the static strength by increasing the length of the reinforced chord. The effects of the geometrical parameters and the chord thickness on the static strength of the T-joints are also studied parametrically by analyzing another 240 T-joint models. Finally, a parametric equation is presented, and its accuracy in predicting the static strength of the tubular T-joint subjected to axial compression is verified through error analysis against the numerical results.

Stress intensity factors for a surface crack in a tubular T-joint

Abstract This paper describes a systematic modelling of a general cracked tubular Y-joint commonly found in offshore structures. The Y-joint under consideration may contain either a through-thickness or surface crack which can be of any length and located at any position along the brace–chord intersection. This is particularly significant, as it has always been found in practice that the initiation site of a surface crack does not always start from the saddle or crown position when tubular joints are subjected to a complex loading condition. The geometrical model developed in the work described in this paper includes the weld detail which is compatible with the American Welding Society (AWS) standard [1] . Based on this geometry, well-graded finite element (FE) meshes were generated for a T-joint, which is a specific type of Y-Joint, to obtain the stress intensity factors (SIFs) for a surface semi-elliptical crack along the crack tip using quarter-point elements. The numerical analysis indicated that the FE models generated are appropriate to the geometry of the joints since converging values of SIF were obtained as the meshes used were refined. The accuracy of the Mode I, Mode II and Mode III SIFs demonstrates that the proposed model is reliable.

Analysis of mechanically fastened composite joints by boundary element methods

This article focuses on the boundary element formulation development for analyzing a mechanically bolted composite. Boundary equations are formulated for all the member panels of the composite joints. These equations are solved together with the fastener equations to get the resultant contact forces for all the fasteners involved. The fasteners are then modeled as 1D springs that are governed by linear relationship between the fastener forces and the displacements of member panels at the respective fastener centers. After obtaining all the fastener forces from the global analysis, detailed stress analysis is performed for region around an individual fastener. The stress distributions around fastener holes are then used to evaluate the margin of safety of the composite panels. The numerical predictions on the fastener forces, failure modes and failure loads of two typical bolted composite joints using the proposed method agree well with that of the experimental results.

Two-dimensional and three-dimensional magnification factors, Mk, for non-load-carrying fillet welds cruciform joints

Abstract Two-dimensional M k factors at the weld toe of non-load-carrying transverse welded attachments are derived indirectly using the principle of superposition and stresses obtained from boundary element analysis. The results are in good agreement with that obtained by Maddox and Andrews [1] for different ratios of l / T , where l is the weld toe to weld toe distance, and T is the main plate thickness. Further three-dimensional boundary element analysis using realistic crack shapes, confirm that l / T is the most important parameter. Two-dimensional edge cracks analyses overestimate and underestimate the deepest and surface points M k values by as much as 15% and 65% respectively. Parametric equations for three-dimensional M k are proposed for design purposes.

The θ scheme for time-domain BEM/FEM coupling applied to the 2-D scalar wave equation

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear 0 method which consists, basically, of computing the response at the time t n+1 from the response previously computed at the time t n+θ , θ ≥ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time t n+1 . Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation.

A boundary element analysis of misaligned load-carrying cruciform welded joints

Although it has been found that misalignment of the welded joints can reduce fatigue strength significantly, further studies are still required for comprehensive investigation, including varying geometry variables. In this study, boundary element technique and hypersingular boundary integral equation (HBIE) are employed to calculated the notch stress concentration factors and then predict the fatigue life as this method can lead to highly accurate and inexpensive results. The addressed variable is the root crack length, or partial penetration depth which can be more accurately modeled by the boundary element method. It is noted that the predicted fatigue life has a very good agreement with existing experimental results. The corresponding results, with different boundary conditions and root crack length, are presented. Finally, the effect of misalignment on the fatigue strength of load-carrying cruciform welded joints is discussed.

Fatigue crack shapes development of plate-to-plate welded joints

This paper presents crack shapes development of 3D surface semielliptical cracks which are always found at the weld toe of non-load-carrying cruciform welded joints. The alternating current potential drop technique has been used to measure the eight crack depths along the weld toe where probes are placed at 10-mm intervals. 3D crack shapes can be obtained at any particular cycle during the fatigue test. Subregion boundary element methods incorporating the transition and quarter-point elements along the crack front are used to validate the experimental stress intensity factors along the crack front. A method for evaluating the effective stress intensity factors is proposed. It is found that the numerical results generally agree with the experimental results.

Analysis of cracked tubular joints using coupled finite and boundary element methods

A coupling scheme of finite elements to boundary elements is suggested for solving any general cracked problems. The relationship between nodal displacements and tractions on the interface from finite element equations can be introduced into boundary integral equation as a natural boundary condition. The efficiency of the method is demonstrated by modellling and analyzing cracked T-tubular welded joints with an initial semi-elliptical surface crack at the saddle point. The boundary elements are used for stress intensity factor computations in the domain with crack and high stress gradient, and finite elements are used in other parts of the structure with low stress gradients. Numerical results are given to compare the accuracy and efficiency of the method.