Elastic FEM Analysis Research Articles

Buckling Load Estimation of Two-way Grid Domes Stiffened by Diagonal Braces Under Vertical Load

The present study proposes an efficient scheme to estimate elastic-plastic buckling load of a shallow grid dome stiffened by diagonal braces. The dome is circular in plan. It is assumed to be subject to a uniform vertical load and to be supported by a substructure composed of columns and anti-earthquake braces. Based on FEM parametric studies considering various configurations and degrees of local imperfections, a set of formulations are presented to estimate the elastic-plastic buckling load. In the scheme, the linear buckling load, elastic buckling load, and imperfection sensitivity are first presented in terms of related parameters, and the elasticplastic buckling load is then estimated by a semi-empirical formula in terms of generalized slenderness ratio using a corresponding plastic load. For the plastic load, the present scheme adopts a procedure that it is calculated by a linear elastic FEM analysis, while an alternative formula for the plastic load is also proposed based on a shell membrane theory. The validity of the estimation scheme is finally confirmed through comparison with the results based on FEM nonlinear analysis. The formulations are so efficient and simple that the estimation may be conducted for preliminary design purposes almost with a calculator. .

Design With SADSF Method and Analyses of Elastic Properties of Torsion-Loaded Double-Tee Section With Torsional Box

The work presents the results of preliminary strength design of a thin-walled structure based on double-tee section loaded with a torsion moment. One of the solutions to this problem is considered, in which the torsional box is introduced in the central part. Then, one constructs a series of solution variants that differ in the torsional box length. In the design one uses the method of statically admissible discontinuous stress fields (SADSF) assuming the condition of equalized equivalent stress in the limit state. The work is complemented with elastic FEM analyses of one of the solution variants. Using this example, one shows good load-carrying properties of structures designed with the SADSF method, and proves that they could be several times better than the properties of structures designed with traditional or intuitive ways.

焼嵌めで構成された圧延用補強ロールに生じる残留曲がり生成メカニズムの解明

First, back-up rolls for rolling require toughness, particularly in the shaft portion, and high-hardness in the sleeve portion. The back-up rolls are classified into two types; one is a single-solid type, and the other is a shrink-fitted construction type consisting of a sleeve and an arbor. The shrink-fitted back up roll has several advantages, for example, different materials can be chosen and the arbor can be reused by replacing the damaged sleeve. Therefore, the shrinkfitted back-up rolls are economical. However, residual deflection becomes a major problem for the shrink-fitted back-up roll. Elucidating the mechanism of the occurrence of residual deflection and devising countermeasures are important issues. Unfortunately conducting a real experiment is difficult because of much time and huge cost. In this paper, we reproduce this phenomenon by elastic FEM analysis, establish a simulation method, and elucidate the mechanism behind underlying residual deflection.

Simple Springback Cause Analysis Using Measured Shapes of Dies and Pressed Part

A new springback cause analysis method was developed for sheet press forming with measured 3-dimentional shapes of dies and a formed part. In conventional springback cause analysis, a stress distribution is calculated by elasto-plastic FEM analysis of press forming. The newly developed method can be directly applied to a press formed part and its forming dies: an elastic FEM analysis of press forming is conducted using measured shapes of both a pressed part and forming dies, and a stress distribution which causes springback is obtained; and then a springback cause analysis is carried out based on the stress distribution. This calculation method is easier than that of conventional press forming simulation because plastic material properties and friction parameters are not required in its procedure. The philosophy of the new method and an example of application to an automotive part are described in this paper.

Study of Impact Behavior of Aluminum Thin Plate

The behavior of thin plate subjected to impact loading is still an interesting field to study. This paper studies about Aluminum thin plate perforation. It focused on the experimental result of thin plate perforation. The thin plates are tested using blunt and conical strikers on a instrumented impact testing machine. Two different thicknesses of was used to observed the maximum work done with four impact velocities. The result indicated that the maximum work done increased proportionally with impact velocities. In addition, an elastic FEM analysis is carried out to confirm the experimental result by using ANSYS software. Both experimental and numerical results showed a close agreement.

偏心荷重が作用するねじ込みボルト締結体の応力計算式に関する検討

Our objective is to analyze both tensional and bending stress of bolted joints under eccentric load. Especially, our analysis is under four combined conditions as described below, (1) embedded bolted joints, (2) thinner clamped plate, (3) large eccentric load, (4) permitting partial separation. Those combined conditions include some difference between ours and previous researches. The partial separation easily occurs at structural interfaces under those combined conditions, and both stresses sharply increase due to the propagation of the separation. That is the reason why it is very important to consider the effect of partial separation. There are many analytical methods based on numerical calculations or FEM analysis, however, there is no numerical calculation method, which is justly applicable under those combined conditions. We apply Faulhaber method proposed in VDI2230 and develop our original method considering the bolt axial loads, which are composed of both bolt's deflection and deflection angle as beam. Numerical calculations on the above-mentioned and experiments and elastic FEM analysis based on three dimensional contact theory were conducted. The results about our method's correlation against experiments and FEM analysis are shown in this report.

Failure analysis of a pinion of the jacking system of a jack-up platform

Component analysis, metallographic examination and hardness test were performed respectively for a failed pinion and a new rack of the jacking system of a jack-up platform. Experiment results showed that the superficial heat treatment of the pinion was not uniform and there was no hardened layer at the tooth root. At the same time, the hardened layer near the pitch circle had been worn out for long-term service, thus the surface hardness of the failed pinion was lower than that of the rack. Considering that each pinion bears different load during service, the exact load that each pinion bears under the action of self-weight, variable loads and wind loads, was deduced firstly. As per the deduced bearing load of the failed pinion, elastic FEM analysis was performed and the distribution of stresses on the rack and pinion was simulated when the platform was under preload condition. By comparing the Von mises stresses and contact stresses with those calculated according to the formula, the accuracy of FEM analysis was verified. Then elastic–plastic FEM analysis was performed for pinion models with hardened layer and without hardened layer respectively, the results were used to explain the failure of the pinion.

間隙水圧・変形連成問題への最近の取り組み 三軸圧縮破壊過程における岩石の透水性に封圧が及ぼす影響に関する研究

The permeability of Kimachi sandstone in triaxial compression failure process was investigated by laboratory experiments. Tests were carried out under a constant confining pressure of between 5.0 and 15.0 MPa with a constant pore pressure of 2.0 MPa until axial strain reached approximately 5.0%. The stress-strain relation was linear under low differential stress and gradually became nonlinear as peak differential stress approached. In the tests under confining pressure of 5.0 and 7.5 MPa, the permeability decreased in the elastic region and then increased as the peak strength approached. The permeability continued to increase at first in residual strength region, and then it decreased at axial strain of approximately 4.0%. In the tests conducted under higher confining pressure, the variation in the permeability was small until axial strain of 5.0%. It appeared that failure types were different depending on confining pressure from the observation of the thin sections made from the specimens after tests. In the tests under 5.0 MPa confining pressure, a macroscopic fault occurred in the test pieces. On the other hand it did not occur in the tests under higher confining pressures. It was suggested in the elastic FEM analyses that the failure types were influenced by the end constraint.

706 応力再配分軌跡(SRL)法による環状切欠き材(S20C)の低サイクル疲労き裂発生寿命推定(OS10-(2) 発電機器の材料・構造解析と評価,オーガナイズドセッション)

Stress redistribution locus (SRL) method has been proposed to provide an inelastic behavior reasonably employing both the elastic FEM analysis and a unique hyperbolic curve: ε={1/σ+(κ-1)σ}κ, where ε and σ show the dimensionless equivalent strain and stress normalized by the elastic FEM result. After low cycle fatigue tests are conducted using a smooth specimen and four kinds of circumferentially notched bars, the number of cycles to crack initiation got from the experiments is compared with the one estimated by the SRL method. When the adequate elastic region remais inside the notch root, the crack initiation life can be well predicted. However when the plastic region area occupies more than 30% in the notch root section, the equivalent strain range on the notch root surface calculated using the proposed SRL curve and the dynamic stress-strain curve become to be smaller than the one by FEM analyses, and then the crack initiation life will be estimated a bit critically.

Effect of stress relief groove on fretting fatigue strength and index for the selection of optimal groove shape

The applicability of small stress relief groove for the improvement of fretting fatigue strength was studied. Fretting fatigue tests were done using several kinds of grooved specimens. The shape of groove was systematically changed with parameters of groove radius R and tangential angle θ. The improvement of fatigue limit by a stress relief groove depended on both R and θ. The fretting fatigue limit with stress relief groove was increased with the increase of R and θ. The parameter θd ( d: groove depth) was selected for the unified evaluation of the improvement. FEM stress analyses were done to investigate the stress condition. In a simple elastic FEM analysis assuming that the contact edge is ideally shaped, a highly compressive stress field was generated near the contact edge, where small cracks could never propagate. This suggested that such a simple analysis was not enough to solve this problem. Thus, an assumption to relieve the highly compressive contact pressure near the contact edge was introduced to explain the experimental fact that a crack could propagate. The profile change was simulated by the local plastic deformation at the contact edge calculated by elasto-plastic FEM deformation analysis. This deformation reduced the highly compressive contact pressure and enabled the crack propagation. As a result, it was found that fretting fatigue limit of grooved specimen could be evaluated on the basis of the maximum axial stress near the contact edge. The estimation of fretting fatigue limit using a relationship between K t/ K t0 and θd provided a good estimation with the experimental results and it would be a useful method to select the optimal groove shape.

Incremental recrystallization/grain growth driven by elastic strain energy release in a thermomechanically fatigued lead-free solder joint

A single shear lap solder joint specimen with lead-free eutectic Sn–Ag solder on copper substrates was exposed to 1500 thermomechanical fatigue (TMF) cycles between −15° (3.5 h) and 150 °C (20 min) to generate intrinsic thermal strains. The 0.15-mm-thick solder joint had a cross-sectional area of 1 mm 2. Orientation imaging microscopy was used to examine changes in the tin microstructure as a function of the number of TMF cycles. The tin phase consisted of embedded minority orientations within an initial dominant orientation, which varied by about 25° from one end of the joint to the other, by means of lattice curvature and low angle boundaries. Between about 150 and 750 cycles, an incremental recrystallization/grain growth process occurred where a minority solidification twin orientation grew and consumed the dominant initial orientation. An elastic FEM analysis incorporating anisotropic thermal expansion and elastic constants indicated that the final orientation had an internal stress state that was 20–100% smaller than the initial orientation, when subjected to a temperature change. The release of elastic strain energy provided the thermodynamic driving force for recrystallization/grain growth.

PLASTIC DEFORMATION ANALYSIS OF COARSE GRANULAR MATERIAL UNDER CYCLIC LOADING BY CUMULATIVE DAMAGE MODEL

This paper presents a simple method to estimate cyclic plastic deformation of ballasted track subjected to repeated train passages in terms of the strength and deformation characteristics of coarse granular materials. A new analytical procedure with linear elastic FEM analysis considering the cumulative strain derived from element test results of ballast was proposed, and it was revealed that the analytical procedure could roughly estimate the residual settlement of railroad ballast, which is an assemblage of poorly-graded crushed stone, by simulating small scale model tests of ballasted track.

Deformation Characteristics of Railway Roadbed and Subgrade Under Moving-Wheel Load

ABSTRACT To develop a relevant performance-based design method for railway asphalt roadbed, the resilient and residual deformation characteristics of railway roadbed and subgrade were investigated by means of scale model tests. In the scale model tests, the difference in the mechanism between moving-wheel loading and fixed-point loading were discussed. The deformation characteristics of roadbed and subgrade in the fixed-point loading which apply cyclic vertical load at a fixed point on rails above a certain sleeper was proved to be substantially different from the trend in behaviour when moving a wheel repeatedly on a model rail as in the full scale railway track. Therefore, it was con-cluded that the moving-wheel loading test is necessary to investigate the deformation characteristics of railway roadbed and subgrade. On the other hand, the result of moving-wheel loading test showed that the resilient deformation characteristics do not change even residual deformation caused by repeated loading. A resilient deformation characteristic of asphalt roadbed is an important factor because the fatigue criterion of asphalt concrete is specified in terms of resilient tensile strain. The resilient deformation characteristics of asphalt roadbed, including the maximum resilient tensile strains in the asphalt concrete layer, were simulated well by linear elastic FEM analysis using exact boundary condition and relevant material parameters described in this paper.

Nondestructive Evaluation Method of Welding Residual Stresses by Heating Method

In this paper, a new method of estimating welding residual stresses nondestructively is presented. From the strain changes on the surface due to the local change of Young modulus, distributions of eigenstrain are determined by the inverse analysis. Residual stresses are then evaluated by the elastic FEM analysis by using the eigenstrain as initial condition. Since the local change of Young modulus are due to temperature dependency by heating, we refered to the method as heating method. The method is used to estimate the residual stress distribution in a plate formed by joining two sections with a butt weld. The results show that the proposed method is robust, efficient and accurate. In this procedure, the simulated measured strains are generated by adding random error to the strain response form the solution of the direct solution, and the singular value decomposition method is used as a regularization method. The effects of number of sensors and their locations, the magnitude of measurement errors on the accuracy of estimations are investigated.

Residual stress measurement by Piezospectroscopy of cross sections through thermal barrier coatings

Piezo-spectroscopic measurements of the residual stress in the TGO have been demonstrated on cross sections through thermally cycled TBC systems with high spatial resolution (approximately 2 × 2 × 5 µm). The residual stress is perturbed by relaxation at the free surface, but this can be taken into account in an approximate way. This relaxation has a range approximately equal to the YSZ thickness indicating that the YSZ imposes significant mechanical constraint on the TGO despite its low modulus.The measurements have shown that the non-planar morphology of the TGO induces large deviations from the thermo-elastic equi-biaxial stress expected for a planar TGO. The mean level of compressive residual stress is reduced by relaxation due to bending of the non-planar TGO, in agreement with elastic FEM analysis of sinusoidal TGO morphology. However, the real morphology is not sinusoidal and in some locations the local curvature is extremely high. In these regions the residual stress is observed to become tensile and as high as 1 GPa. The failure mechanism is by nucleation and growth of local damaged regions caused by these tensile stresses (which are evident as low stress regions on analysis through the YSZ) into larger regions that eventually become unstable to large-scale buckling and spalling.

８．メインテナンスの力学問題 有道床軌道の最適まくらぎ形状に関する検討

In this paper, the effects of sleeper size on the cyclic deformation properties of railway ballast under the cyclic loading are discussed. The two-dimensional linear elastic FEM analyses were performed in order to investigate the effects ofsleeper size on the stress distribution in the ballasted track. Based on the results of FEM analyses, a series of full-scale cyclic loading tests using the various sleepers changed the length and height were performed. It is found that the track settlement in the state where a clearance gap is between the sleeper and the railway ballast can be explained the displacement amplitude and the maximum sleeper displacement speed up to the touching.

Local load stresses in cylindrical shells at plate clips

Site personnel have to ascend columns, tanks, etc., and to stand on platforms; insulation has to be kept in position to preserve energy; equipment has to be lifted on occasions. Quite a number of such loads are small and often simple plate clips are used to fasten ladders, platform and hoisting cables. But sometimes it is desirable to assess quickly the stresses at such clips. Here we provide some simple but accurate formulae for a wide range of clip/cylinder geometries. These non-dimensional parameter expressions were developed from a large number of linear elastic FEM analyses. In addition a generally applicable stress limit is proposed for the local stresses in cylindrical shells at clip points.

Prediction of Welding Deformation and Residual Stress by Elastic FEM Based on Inherent Strain

The welding residual stress and the distortion are considered to be produced by the inherent strain. The plastic strain in a bead welding computed through the thermal-elastic-plastic analysis is an ideal example of the inherent strain, since there is no glove which may introduce additional mismatch. Such inherent strain produced in the welding process is primarily determined by the highest temperature reached and the constraint at each point. Thus, the mechanical phenomena in the bead welding process are closely analyzed by the thermal-elastic-plastic FEM and the mechanism in which the inherent strain is produced is clarified from the aspect of the highest temperature reached and the constraint. Further, based on the knowledge obtained through the study, a simple formula to calculate the inherent strain distribution is proposed. Using the inherent strain given by the formula, the welding residual stress and the distortion can be predicted by elastic FEM analysis.

Fracture mechanics investigations on a pipe with a circumferential flaw supported by FEM

The transferability of crack resistance properties obtained from fracture mechanics specimens to analyse stable crack growth of a 120°C surface flaw in a pipe of large diameter under pure bending is discussed supported by results of an elastic-plastic FEM calculation. The ratio of triaxiality, hydrostatic stress and the von Mises effective stress, is about 2.6 and does neither depend on the location Φ at the crackfront ( if Φ < +-45°C) nor on the bending stress ( if σ b > 100 MPa). Thus, stable crack growth of a circumferential surface flaw in a pipe under bending may conservatively be estimated using the J R -curve of a large or side-grooved CT specimen. An elastic FEM analysis of the pipe under four-point bending according to a test shows that the distribution of the bending stress across the cross-section is getting asymmetrical due to the ovalization of the pipe. The evaluation of the J- integral was performed using the bending moment versus crack mouth opening displacement curves measured at various locations along a 120° circumferential notch under four-point bending (notch radius 0.25 mm). The result reveals a much higher J- integral level caused by the same bending moment when the ovalization of the pipe is not taken into account. Thus, the question may be raised whether the four-point bending test on large diameter pipes with flaws will meet the worst case because in the vicinity of the connection between pipe and pressure vessel the high local stiffness of the system will prevent ovalization of the pipe. An estimate of the crack resistance under four-point bending with ovalization indicates that the J R - curve for the circumferential notch corresponds better to that of a CT-25 specimen with a fatigue precrack than to the J R - curve of a CT-25 specimen with a notch of 0.1 mm resp. 0.25 mm notch radius.