Elastic Finite Element Analysis Research Articles

New parametric equations to estimate notch stress concentration factors at butt welded joints modeling the weld profile with splines

For fatigue life estimation as well as for fatigue testing analysis of welded structures by local stresses approaches, the stress concentration factor (SCF) at the weld must be known. Full penetration butt welded joints are extensively used in steel structures. Some empirical formulas to estimate SCFs are available in the literature, but their ranges of application are not always clearly defined, as well as the hypotheses on their local geometry. In this study, notch SCFs at steel butt welded joints under uniaxial tension are investigated by means of 2D plane strain linear elastic finite element analysis. The weld profile is modeled with splines. A detailed definition of the geometry is given. The influence of parameters such as the plate thickness, the weld reinforcement, the flank angle, the weld toe radius, the weld length and the presence of linear misalignment is assessed. Finally new parametric equations to estimate the SCFs at steel butt welded joints are proposed.

Creep-fatigue evaluation method for weld joint of Mod.9Cr-1Mo steel Part II: Plate bending test and proposal of a simplified evaluation method

In the present study, to develop an evaluation procedure and design rules for Mod.9Cr-1Mo steel weld joints, a method for evaluating the creep-fatigue life of Mod.9Cr-1Mo steel weld joints was proposed based on finite element analysis (FEA) and a series of cyclic plate bending tests of longitudinal and horizontal seamed plates. The strain concentration and redistribution behaviors were evaluated and the failure cycles were estimated using FEA by considering the test conditions and metallurgical discontinuities in the weld joints. Inelastic FEA models consisting of the base metal, heat-affected zone and weld metal were employed to estimate the elastic follow-up behavior caused by the metallurgical discontinuities. The elastic follow-up factors determined by comparing the elastic and inelastic FEA results were determined to be less than 1.5. Based on the estimated elastic follow-up factors obtained via inelastic FEA, a simplified technique using elastic FEA was proposed for evaluating the creep-fatigue life in Mod.9Cr-1Mo steel weld joints. The creep-fatigue life obtained using the plate bending test was compared to those estimated from the results of inelastic FEA and by a simplified evaluation method.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone.

The transport of fluid, nutrients, and signaling molecules in the bone lacunar–canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30–50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Asymmetric crack onset at open-holes under tensile and in-plane bending loading

Plates notched with open-holes that are subject to combined tensile and in-plane bending loading are studied in this analysis of crack onset. A finite fracture mechanics approach is employed to study the onset of asymmetric crack patterns in the notched structure. The stress field and the energy release rates required to solve the coupled stress and energy criterion are obtained from linear elastic finite element analyses. Closed-form expressions for the dependence of the solution on governing parameters as e.g. the structural size, the Young’s modulus or the ratio of bending to normal loading are given significantly reducing the computational effort required for the failure model. A comparison to experimental results and to numerical analyses using a cohesive zone model highlights the model’s ability to render brittle failure of the notched structure and to provide reliable failure load estimates. The results reveal that a certain threshold of the hole diameter exists, below which the hole does not affect the failure load. The threshold and the corresponding bearable loads are discussed using explicit solutions.

Development of a Simplified Procedure for the Determination of the Ultimate Load and Associated Spindle Torque of Propeller Blades

Blade deflection observed in experiments regarding the ultimate strength of controllable pitch propeller blades does not agree with the one that is assumed in the load case for the blade failure load currently defined in the Polar Class Rules. The reason is that a failure of the blade tip due to large plastic deformation is not taken into account, but can occur in reality if the load is applied relatively close to the trailing edge of skewed propellers. The plastic blade deformation can be computed by numerical simulations using an elastic-plastic material curve. These simulations, however, are time consuming and, hence, unpractical in the daily design process of propeller blades. Therefore, a simplified approach to determine the ultimate load and the associated spindle torque of the blade is presented. It requires elastic finite element (FE) analyses with varying point of load application, geometrical data, and a simplified material curve. The critical blade section is determined from highly stressed locations found in the elastic FE analysis. Afterward, the ultimate bending moment which the section can carry is determined by assuming a linear strain distribution over the thickness and a definite limit strain on the pressure surface. This allows the stress distribution to be transferred directly from the material curve. The ultimate load is determined by integrating the stress distribution over the section thickness and along the chord length, the latter in a simplified way. The approach is supported by various numerical simulations showing the fundamental elastic-plastic behavior of propeller blades and their response due to superimposed bending and torsional loads. In conclusion, the ultimate strength is mainly controlled by bending loads and the approach considers a failure of the blade tip, leading to more realistic spindle torques compared to the approach in the Polar Class Rules.

Development of a Simplified Procedure for the Determination of the Ultimate Load and Associated Spindle Torque of Propeller Blades

Blade deflection observed in experiments regarding the ultimate strength of controllable pitch propeller blades does not agree with the one that is assumed in the load case for the blade failure load currently defined in the Polar Class Rules. The reason is that a failure of the blade tip due to large plastic deformation is not taken into account, but can occur in reality if the load is applied relatively close to the trailing edge of skewed propellers. The plastic blade deformation can be computed by numerical simulations using an elastic-plastic material curve. These simulations, however, are time consuming and, hence, unpractical in the daily design process of propeller blades. Therefore, a simplified approach to determine the ultimate load and the associated spindle torque of the blade is presented. It requires elastic finite element (FE) analyses with varying point of load application, geometrical data, and a simplified material curve. The critical blade section is determined from highly stressed locations found in the elastic FE analysis. Afterward, the ultimate bending moment which the section can carry is determined by assuming a linear strain distribution over the thickness and a definite limit strain on the pressure surface. This allows the stress distribution to be transferred directly from the material curve. The ultimate load is determined by integrating the stress distribution over the section thickness and along the chord length, the latter in a simplified way. The approach is supported by various numerical simulations showing the fundamental elastic-plastic behavior of propeller blades and their response due to superimposed bending and torsional loads. In conclusion, the ultimate strength is mainly controlled by bending loads and the approach considers a failure of the blade tip, leading to more realistic spindle torques compared to the approach in the Polar Class Rules.

Dynamic observations of welding phenomena and finite element analysis in high-frequency electric resistance welding

High-frequency electric resistance welding (hereinafter referred to as HFW) pipes and tubes are used for high-grade line pipes. To cope with the high need for weld seam reliability, the clarification of welding phenomena is important. To clarify the HFW phenomena, at first we developed a HFW simulation system by using electromagnetic, heat conductive and elastic plastic finite element analysis (FEA) methods. Continuous electromagnetic and heat conduction analysis was conducted by subdividing the cross section containing the electrode and the welding point into a large number of two-dimensional models. The temperature distribution in the HFW pipe welding procedure can be successfully simulated by this system. The deformation behaviour in which a portion of the weld rises to the inner and outer surfaces as the result of pressurization from welding rolls can be analysed with this system. Secondly, HFW phenomena have been visualized dynamically using a high-speed video camera technique. The high-intensity part visualized by high-speed images has good accordance with the temperature distribution of the FEA result. High-speed images have visualized the dynamic phenomena of molten metal flow and sputtering of molten steel. Very rapid movement of molten metal in the forming direction along the welding line was observed at the V-convergence point with a speed of 2–50 m s−1, which was far faster than the welding speed. This rapidly moved molten metal generated the peculiar sputtering which spread the molten metal particles as describing an arc perpendicular to the welding line. These phenomena were assumed to be caused by the electromagnetic force concerning the molten steel at the V-convergence point.

The use of the theory of critical distance and the stress-gradient approach in the fatigue life estimation of notched components

Fatigue life prediction for machine components is a fundamental factor in the industrial world, and therefore several methods can be traced in technical literature to estimate life of notched components. The present paper correlates the classical stress-gradient approach, or support factor method, proposed by Siebel, Neuber and Petersen with the more recent theory of critical distance approach by Tanaka and Taylor. On one hand, the main asset of the support factor method is the punctual information about the stresses needed to estimate the effective stress, namely the maximum stress and stress gradient at the hot spot. By contrast, the theory of the critical distance needs the calculation of the stress distribution for a finite depth inside the material. The main drawback of the support factor method is that the material parameter ρ* is available only for a limited series of materials. In order to overcome this limitation, the paper investigates the correlation between the material parameter ρ* and the critical distance L by relying on a parametric stress function. The proposed correlation aims at giving a simple method for the industrial engineers, which often needs straightforward methods to tackle practical problems. A comparison between the two methods is carried out by considering three different benchmark geometries: a typical V-notched specimen, a vessel under internal pressure and a complex industrial hydraulic control valve. In the first two benchmarks, the effective stresses are analytically retrieved and compared using both methods while an elastic finite element analysis is performed for the last one. The close match of the fatigue life prediction between the methods supports the possibility to exploit the data available in literature for the critical distance in order to estimate the effective stresses with the support factor method.

Fatigue strength assessment of ship structures accounting for a coating life and corrosion degradation

PurposeFatigue strength and reliability assessment of complex double hull oil tanker structures, based on different local structural finite element approaches, is performed accounting for the uncertainties originating from load, nominal stresses, hot spot stress calculations, weld quality estimations and misalignments and fatigue S-N parameters including the correlation between load cases and the coating life and corrosion degradation.Design/methodology/approachShip hull wave-induced vertical and horizontal bending moments and pressure are considered in the analysis. Stress analyses are performed based on the nominal, local hot spot and notch stress approaches. A linear elastic finite element analysis is used to determine the stress distribution around the welded details and to estimate structural stresses of all critical locations. Fatigue damage is estimated by employing the Palmgren-Miner approach. The importance of the contribution of each random variable to the uncertainty of the fatigue limit state function is also estimated. The probability of fatigue damage of hot spots is evaluated taking into account random coating life and corrosion wastage. Fatigue reliability, during the service life, is modelled as a system of correlated events.FindingsThe fatigue analysis showed that the fatigue damage at the hotspot, located at the flange of the stiffener close to the cut-out, is always highest in the cases of the structural hot spot stress and effective notch stress approaches, except for the one of the nominal stress approach. The sensitivities of the fatigue limit state function with respect to changes in the random variables were demonstrated showing that the uncertainty in the fatigue stress estimation and fatigue damage are the most important. Fatigue reliability, modelled as a parallel system of structural hot spots and as a serial system of correlated events (load cases) was evaluated based on the Ditlevsen bounds. As a result of the performed analysis, reliability and Beta reliability indexes of lower and upper bounds were estimated, which are very similar to the ones adopted for ultimate strength collapse as reported in literature.Originality/valueThis paper develops a very complex fatigue strength and reliability assessment model for analysing a double hull oil tanker structure using different local structural finite element approaches accounting for the associated uncertainties and the correlation between load cases and the coating life and corrosion degradation. The developed model is flexible enough to be applied for analysing different structural failure modes.

GLOBAL SENSITIVITY ANALYSIS IN STABILITY PROBLEMS OF STEEL FRAME STRUCTURES

Slender steel frame structures are characterised by a number of imperfections which may reduce their load carrying capacity drastically. This article studies the effects of these imperfections on the load carrying capacity of a single storey steel plane frame using global sensitivity analysis and geometrically nonlinear (second-order) elastic finite element analysis. Imperfections are considered as random variables. Statistical load carrying capacities needed for the evaluation of sensitivity analysis are processed using classical statistical methods upon the emulation of Latin Hyper­cube Sampling simulation methods. The main interaction effects of random imperfections on the load carrying capac­ity are identified using global sensitivity analysis. It is illustrated that the effects of imperfections on the load carrying capacity varies dramatically depending on the height of the columns and the boundary conditions of the end conditions of the columns.

Assessment of root failures in tube-to-flange steel welded joints under torsional loading according to the Peak Stress Method

In the context of the local approaches to fatigue design of welded joints, the notch stress intensity factor (NSIF) approach assumes the weld toe as well as the weld root profile as sharp V-shaped notches, the V-notch opening angle being greater than zero at the toe side and equal to zero at the root side. The Peak Stress Method (PSM) is an engineering, finite element (FE)-oriented method to rapidly estimate the NSIF local stress parameters by means of linear elastic FE analyses with coarse meshes. By using the averaged Strain Energy Density (SED, which can be expressed as a function of the relevant NSIFs) as a fatigue strength criterion, a so-called equivalent peak stress can be defined and adopted to assess either weld toe and weld root fatigue failures in conjunction with an existing design fatigue curve, that was originally calibrated on experimental results relevant only to weld toe failures. In the present paper new fatigue test results relevant to weld root failures have been generated by testing tube-to-flange fillet-welded steel joints under torsional loading. Good agreement has been obtained between theoretical estimations according to the PSM and experimental fatigue test results.

鋼管ブレース式球形貯槽タンクの耐震性能

A significant fire and explosion accident on spherical storage tanks for Liquefied Petroleum Gas (LPG) at Chiba prefecture in Japan were occurred due to the strong ground motion of the 2011 Great East Japan Earthquake. The braces made of steel pipe for supporting columns of a spherical tank, which was filled with water for purging air at that time, were broken by the strong seismic inertia force. Then, buckling of columns was occurred by the aftershock. To clarify the failure mechanism of the pipe braces of its supporting frame of a spherical tank, the elastic and elastic-plastic finite element analysis (FEA) was performed. From FEA results, the failure mechanism of the pipe brace was revealed as follows; (1) high stress was generated in the intersection of long and short braces due to the structural discontinuities, (2) the generated high stress was a trigger of the failure initiation of the damage of the supporting frame, (3) the breakage of the intersection of the long and short braces of the supporting frame was caused overturn of the spherical tank at the aftershock of predominant earthquake. In this paper, the fracture mechanism of the spherical storage tank was clarified for prevention of the same type accidents, and the effective reinforcement method of pipe braces of spherical tanks was proposed for securing safety.Copyright © 2015 by ASME

Simplified limit load estimation using mα-tangent method for branch pipe junctions under internal pressure and in-plane bending

The mα-tangent method is a simple way to estimate limit load for mechanical components. The method is based on a linear elastic finite element analysis to estimate the limit loads. Present work reports limit loads for branch pipe junctions under internal pressure and in-plane bending which is determined by ma-tangent method. All results are compared with published closed-form solutions and also FE results. The FE results can be found by small-strain three-dimensional finite element (FE) limit load analyses using elastic–perfectly plastic materials. Various branch pipe geometries are considered to verify the accuracy of the ma-tangent method.

A numerical finite fracture mechanics approach on asymmetric cracks in open-hole plates

Using an efficient numerical approach, a model rendering the initiation of asymmetric crack patterns in open-hole plates subject to combined tensile and in-plane bending loading is presented. In the framework of finite fracture mechanics a stress and an energy criterion are enforced simultaneously and used as a coupled condition for the formation of cracks of finite size. Using closed-form expressions for the dependence of the stress and energy quantities needed to solve the coupled criterion on the structural and material parameters, only a limited number of linear elastic finite element analyses is required for a comprehensive analysis of the notched plate. The failure load predictions of the presented model are shown to agree well with experimental results and predictions of a cohesive zone model. The finite fracture mechanics approach allows for a study of crack patterns associated to failure.

Buckling failures in insect exoskeletons

Thin walled tubes are often used for load-bearing structures, in nature and in engineering, because they offer good resistance to bending and torsion at relatively low weight. However, when loaded in bending they are prone to failure by buckling. It is difficult to predict the loading conditions which cause buckling, especially for tubes whose cross sections are not simple shapes. Insights into buckling prevention might be gained by studying this phenomenon in the exoskeletons of insects and other arthropods. We investigated the leg segments (tibiae) of five different insects: the locust (Schistocerca gergaria), American cockroach (Periplaneta americana), death’s head cockroach (Blaberus discoidalis), stick insect (Parapachymorpha zomproi) and bumblebee (Bombus terrestris audax). These were tested to failure in cantilever bending and modelled using finite element analysis (FEA). The tibiae of the locust and the cockroaches were found to be approximately circular in shape. Their buckling loads were well predicted by linear elastic FEA, and also by one of the analytical solutions available in the literature for elastic buckling. The legs of the stick insect are also circular in cross section but have several prominent longitudinal ridges. We hypothesised that these ridges might protect the legs against buckling but we found that this was not the case: the loads necessary for elastic buckling were not reached in practice because yield occurred in the material, causing plastic buckling. The legs of bees have a non-circular cross section due to a pollen-carrying feature (the corbicula). We found that this did not significantly affect their resistance to buckling. Our results imply that buckling is the dominant failure mode in the tibia of insects; it likely to be a significant consideration for other arthropods and any organisms with stiff exoskeletons. The interactions displayed here between material properties and cross sectional geometry may provide insights for the biomimetic design of engineering structures using thin walled tubes.

Local-distortional buckling interaction on cold-formed steel lipped channel beams

This paper deals with the ultimate strength, post-buckling behaviour and design of cold-formed steel lipped channel beams affected by local-distortional buckling mode interaction, subjected to uniform bending of the major axis. The cross-sectional dimensions and length of the beams were chosen to have almost equal local and distortional critical buckling stresses by using the GBTUL-2.0β and CUFSM software. The beams are analysed under pinned with warping free end conditions. 12 sections were selected for this study. The selected sections satisfy the geometric limitations for pre-qualified sections in AISI-S100:2007. Elastic buckling and non-linear finite element analyses were carried out using ABAQUS. The results were compared with corresponding results from experiments available in the literature. The numerical parametric study of 60 analyses of different geometries and yield stress values was undertaken. Based on the comparison of ultimate strengths obtained from the finite element analysis and Direct Strength Method (DSM), a design equation is proposed for lipped channel sections which have their elastic local and distortional buckling moments nearly equal.

내압이 작용하는 직관과 엘보우의 경계면에 존재하는 원주방향 관통균열의 응력확대계수 및 탄성 균열열림변위 예측식

Article history: Fracture mechanics analysis for cracked pipes is essential for applying the leak-before-break (LBB) concept to nuclear piping design. For LBB assessment, crack instability and leak rate should be predicted accurately for through-wall cracked pipes. In a nuclear piping system, elbows are connected with straight pipes by circumferential welding; this weld region is often considered a critical location. Hence, accurate crack assessment is necessary for cracks in the interface between elbows and straight pipes. In this study, the stress intensity factor (SIF) and elastic crack opening displacement (COD) were estimated through detailed 3D elastic finite element (FE) analyses. Based on the results, closed-form solutions of shape factors for calculating the SIFs and elastic CODs were proposed for circumferential through-wall cracks in the abovementioned interfaces under internal pressure. In addition, the effect of the elbow on shape factors was investigated by comparing the results with the existing solutions for a straight pipe.

Out-of-plane welding distortion prediction and mitigation in stiffened welded structures

A holistic investigation on out-of-plane welding distortion in fabrication of several stiffened welded structures with considering prediction and mitigation is presented. Experiments of typical fillet welded joints and its assembled stiffened welded structures are conducted first, and out-of-plane welding distortion is systematically measured. Different welding distortion patterns, so-called bending distortion and welding buckling, are obviously obtained from the measurements of the examined parallel and cross stiffened welded structures, respectively. A combined computational approach, which involves thermal elastic plastic (TEP) finite element (FE) analysis, eigenvalue analysis, and elastic FE analysis, is then employed to predict the out-of-plane welding distortion and clarify the generation mechanism for different welding distortion patterns. In particular, eigenvalue analysis can support the critical condition for welding buckling occurrence. Since the bending and welding buckling are caused by different reasons, the mitigation processes with flame heating are carried out individually. In detail, line heating is implemented in the opposite side of welded joint to produce inverse bending, and spot heating is employed to heat the region far away from welding line to eliminate effect of inherent deformation on welding buckling generation.

Stress Intensity Factor and Elastic Crack Opening Displacement Solutions of Complex Cracks in Pipe Using Elastic Finite-Element Analyses

In the present paper, the closed-form expressions for the stress intensity factors (SIFs) and the elastic crack opening displacements (CODs) of complex-cracked pipes are derived based on the systematic three-dimensional (3D) elastic finite-element (FE) analyses. The loading conditions that are evaluated include global bending moment, axial tension, and internal pressure. In terms of geometries, the geometric variables affecting the SIFs and the elastic CODs of complex-cracked pipes, i.e., the crack angle of through-wall cracks (TWCs), the crack depth of fully circumferential, internal surface cracks in the inner surface of pipe, and the ratio of pipe mean radius to thickness, are systematically considered in the present FE analyses. The FE analysis procedure employed in the present study has been validated against the existing solutions for the circumferential TWC pipes. Using the present FE results, the shape factors of SIF and elastic COD for complex-cracked pipes are tabulated as a function of geometric variables. The results are applied for closed-form expressions of SIF and elastic COD when the pipe is subjected to simple loading conditions of bending, axial tension, or internal pressure. The proposed closed-form expressions can estimate SIF and elastic COD of complex-cracked pipes within maximum differences of 2.4% and 5.9% with FE results, respectively.

Nonidealized Surface to Through-Wall Crack Transition Model for Axial Cracks in Cylinders

Recent studies have shown that a subcritical surface crack, due to primary water stress corrosion cracking (PWSCC), can transition to a through-wall crack (TWC) with significant differences between the inner diameter (ID) and outer diameter (OD) crack lengths. This behavior has been observed for both circumferential and axial cracks. Recently, a surface to TWC transition model has been developed for circumferential cracks using existing K and COD (crack opening displacement) solutions for nonidealized circumferential TWCs. In this paper, a similar crack transition model (CTM) was developed for axial cracks. As a first step, a study was conducted to define the appropriate crack front shape for nonidealized axial TWCs. Then, elastic finite element analyses were carried out to develop K and COD solutions using these crack front shapes. The newly developed solutions were utilized for the CTM. The present CTM includes a criterion for transitioning the final surface crack to the initial nonidealized TWC. This criterion determines when the transition should occur (based on surface crack depth) and determines the two crack lengths (at ID and OD surfaces) of the initial nonidealized TWC. Furthermore, nonidealized TWC growth calculation can be conducted using the proposed model. Example results (crack length and COD) obtained from the proposed model were compared to those obtained from the natural crack growth simulations. Results presented in this paper demonstrated the applicability of the proposed model for simulating axial crack transition.