Linear Elastic Finite Element Analysis Research Articles

The Minnesota inverted-tee system: Parametric studies for preliminary design

The precast concrete inverted-tee system was adopted by the Minnesota Department of Transportation after the 2004 FHWA/AASHTO International Scan Tour of bridge rapid construction techniques in Europe and Japan. As of 2005, two bridges were built in Minnesota adapting the Poutre-Dalle system developed in France. One of the two bridges, the Center City Bridge (MN bridge 13004), has been monitored for transverse load distribution and continuity over the pier since the deck was cast in September 2005. In addition, a two-span specimen was constructed to investigate different parameters, such as flange thickness, bursting rein- forcement, horizontal shear reinforcement, and flange surface treatment. One of the four precast concrete sec- tions of the laboratory specimen was identical to those used for MN bridge 13004. Part of the investigation was conducted to optimize section design through a parametric study. In addition, preliminary linear elastic finite element analyses were conducted to simulate the behavior of the system. The finite element models were calibrated using results obtained from static tests of MN bridge 13004 and the laboratory specimen. This paper presents a series of considerations obtained from a preliminary parametric study on different span lengths and bridge configurations. It also discusses some matters that had to be resolved to obtain ac- ceptable agreement between experimental results and analytical approach. For all of the cases investigated, the service stresses were found to control the design.

Fatigue design of welded bicycle frames using a multiaxial criterion

This paper describes the methodology developed by Decathlon, through its MKniX Engineering Center, to master the fatigue design of welded aluminium-alloy bicycle frame. The objective is to optimize the design prior to the standard testing by calculating the fatigue reliability of the bicycle frame. The fatigue assessment method is based on the Dang Van multiaxial fatigue criterion combined with a unique S-N design curve independent of the geometry of the welded structure and the loading mode. The design stress is defined through a linear elastic finite element analysis using a specific thin shell meshing method.

Influence of notch geometry on the estimation of the stress intensity factor threshold by considering the Theory of Critical Distances

Recently the Theory of Critical Distances was applied to estimate the threshold stress intensity factor, ΔKth, as an alternative to standard fracture mechanics tests. This strategy requires only a linear-elastic Finite Element Analysis (FEA) around the notch vicinity and fatigue limit data from notched and smooth specimens, usually available in the literature, or at least easier and cheaper to produce and test than fracture mechanics cracked specimens necessary in ΔKth experiments. The aim of this work is to revisit this numerical–experimental strategy and to assess the effect of notch geometry in the predictive methodology in order to evaluate its domain of validity mainly, but not only, in terms of notch root radius bluntness. A wide range of experimental data for different metallic alloys and types of notches were selected to validate the analysis. The results showed that only fatigue data from notch root radii, normalized with respect to the net cross section of the specimen, smaller or equal to 0.01 can provide estimates of ΔKth within an error interval about 20%.

Application of Two Methods for Notch Fatigue Life Prediction

The aim of this paper is the application of two methods for notch fatigue life assessment, methods which are based on finite element analysis: the theory of critical distances and the volumetric method. Firstly, un-notched and notched specimens (for three different geometries) were tested in tension under constant-amplitude loading. The use of theory of critical distances (TCD) to predict the notch fatigue life involves the determination of the material characteristic length L based on experimental results obtained for the un-notched and one type of notched specimens. For the others notched geometries, based on linear-elastic finite element analysis, the fatigue strength is predicted using the TCD. In order to apply the volumetric method, elastic-plastic stress field around notches are considered and notch strength reduction factor are determined. Finally, the predictions of the two methods were compared with experimental fatigue data for notched specimens.

Design, Optimization, and Evaluation of Integrally Stiffened Al-7050 Panel with Curved Stiffeners

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

In situ synchrotron X-ray imaging of high-cycle fatigue crack propagation in single-crystal nickel-base alloys

Fatigue crack propagation in single-crystal nickel-base superalloys was studied in situ with synchrotron X-ray imaging in a very high-cycle regime. Experiments were performed at ambient temperature with a newly developed portable ultrasonic fatigue instrument. The fatigue apparatus produced stable fatigue crack propagation with positive mean stresses for specimens as thin as 150 μm at a loading frequency of 20 kHz. Fatigue cracks propagated in a mixed-mode crystallographic manner along {1 1 1} slip planes. Phase-contrast imaging permitted analysis of the interaction of the crack front with microstructural features. Three-dimensional linear elastic finite-element analyses were performed to investigate the driving forces for crack propagation in the sheet specimen geometry. For the experimental conditions examined, fatigue crack growth is driven by the resolved shear and normal stresses on the active crack tip slip systems. An octahedral stress intensity is proposed as the relevant driving force for crack growth which determines the fatigue crack growth plane in nickel-base single crystals at room temperature.

A simple estimator for stress errors dedicated to large elastic finite element simulations

PurposeThis paper aims to deal with the verification of local quantities of interest obtained through linear elastic finite element analysis. A technique is presented for determining the most accurate error estimation. This technique enables one to address industrial‐size problems while keeping computing costs reasonable.Design/methodology/approachThe concept of error in constitutive relation is used to assess the quality of the finite element solution. The key issue is the construction of admissible fields. The objective is to show that it is possible to build admissible fields using a new method. These fields are obtained by using a high‐quality construction over a limited zone while the construction is less refined and less expensive elsewhere.FindingsNumerical tests are presented in order to illustrate a very satisfying presented methodology. It shows clearly how to take advantage of the method to treat large examples. They clearly show the interest of this new method to treat large examples.Originality/valueThe paper demonstrates clearly that verification of large finite element problem must have dedicated methods in order to be applicable.

Thrust Line Using Linear Elastic Finite Element Analysis for Masonry Structures

Failure of masonry structures are generally studied in terms of the formation of unstable mechanisms and the thrust line approach is considered to be the most useful tool for this. Thrust line analysis is a simple technique for studying the stability of masonry structures, although its applicability is limited to specific types of structures because of various implicit assumptions. Finite element analysis, on the other hand, is versatile but computationally more intensive. This paper presents a linear elastic finite element analysis based method of obtaining the thrust line of a masonry structure. The proposed method allows the application of the thrust line analysis to structures with any complicated geometry while retaining the simplicity of this approach for studying the stability of a masonry structure. The proposed method is applied to various case study structures and the sensitivity of the results to the adopted material property data in the finite element analysis is studied. The proposed method also allows a structural engineer, who is usually familiar with the finite element analysis, to easily migrate to the stability analysis of masonry systems.

Lower bound limit loads of ship structure components using the mα-tangent method based on single linear elastic analysis

Limit loads for ship structure components are determined in this paper based on a single linear elastic finite element analysis by invoking the concept of kinematically active reference volume in conjunction with the m α -tangent method. The method enables rapid determination of lower bound limit loads for ship structure components by taking their kinematically inactive volume into consideration. This method is applied to a number of ship structure components possessing different percentages of inactive volume. Results are compared with the corresponding inelastic finite element results, and available analytical solutions.

An approach for dealing with high local stresses in finite element analyses

Highly localised through-thickness stress concentrations, higher than the strength of the material, may occur when a linear elastic finite element analysis of a composite structure is performed. Such stresses may be caused by real geometrical or material discontinuities or by artefacts in the model. The objective of this paper is to present a validated approach to determine when these high stresses will not lead to failure by delamination or matrix cracking and can therefore be ignored. Named as the High Stress Concentration (HSC) method, the approach presented in this paper is found to provide good results when applied to several finite element analyses, and is also in agreement with experimental data.

Geometrical range of microscopic stress distribution change due to fibre array irregularities for thermally and transversely loaded CF/epoxy composites

A detailed numerical investigation has been carried out to investigate the effect of local fibre array irregularities on microscopic interfacial normal stress for transversely loaded unidirectional carbon fibre/epoxy composites with random fibre arrangement. Linear elastic finite element analyses were carried out for a two-dimensional image based model composed of 70 fibres. One fibre in this image based model is replaced with resin as the resin equivalent fibre, and the resulting change in microscopic interfacial normal stress distribution is investigated. Three fibres are selected for the resin equivalent fibres to clarify the individual local geometrical irregularity. Calculations were carried out for three loading conditions: case A, cooling of –155 K from the curing temperature; case B, transverse loading of 75 MPa chosen as an example of macroscopic transverse fracture strength and case C, both cooling from the curing temperature and transverse loading of 75 MPa. The effect of fibre array irregularities on the interfacial stress state is limited to the region between the resin equivalent fibre and its first neighbouring fibres. The contribution of the second neighbouring fibre is small and that of further fibres is negligible.

Investigation of the mixed-mode fatigue crack growth of a hot-rolled steel plate with a circular microdefect

The interaction between cracks and microdefects under mixed-mode loading conditions is important for precisely estimating the fatigue lifetime of a structure. In this study, the fatigue crack growth behavior of a crack with a circular microdefect is investigated under mixed-mode loading conditions experimentally using modified compact tension shear (CTS) specimens for various loading angles with/without a circular microdefect. The fatigue crack growth behavior observed through experiments is analyzed by linear elastic finite element (FE) analyses and the simulated crack path using the maximum tangential stress (MTS) criterion is compared and discussed with the crack path observed through experiments.

Study of loading rate effect on dynamic fracture toughness of high strength steel under impact loading

Dynamic fracture toughness (DFT) of a high strength steel, 30CrMnSiA, is determined using a hybrid experimental- numerical method, with a focus on improved understanding of the loading rate effect on DFT under impact loading. The experiments are conducted on the Hopkinson pressure bar (HPB) apparatus with striker velocities ranging from 9.2 to 24.1 m/s to obtain a series of loading rates. Linear-elastic transient finite element analyses are performed to calculate histories of dynamic stress intensity factor (DSIF). The results show that with the increase of striker velocity, the crack tip loading rate increases on the order of 10 6 MPa m 1/2 s −1 , while the fracture initiation time and the DFT both reduce. Fracture surface examination is

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An approach for reliability assessment of a welded structure subjected to corrosion degradation and fatigue is developed. The objective of this work is to evaluate the fatigue reliability of a complicated ship welded structure subjected to random non-uniform corrosion and fatigue loading simultaneously. A three-dimensional finite element model accounting for randomly distributed non-uniform corrosion wastage based on non-linear time-dependent model is generated. Randomly corroded surface geometries are simulated by the use of the Monte Carlo simulation technique for different service times of corrosion wastage and linear elastic finite element analysis are performed. Hotspot stresses around welded details on a web frame joint are determined. Based on nonlinear regression analysis, the time-dependent functions for the hot-spot stresses affected by corrosion deterioration are fitted. The relationship between the structural fatigue damage and corrosion deterioration caused by corrosion thickness wastage at different times is quantified employing S–N approach. The statistical properties of fatigue damage and service life of critical hot-spots in the web frame welded joint are estimated taking into account random non-uniform time-dependent corrosion wastage. The fatigue reliability of the web frame welded joint during its service life is modelled as a series system of correlated components using the Ditlevsen bounds method.

Elastic modulus reduction method for limit load evaluation of frame structures

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio (EBR), and the elastic modulus reduction method (EMRM) is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion, and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility, accuracy and efficiency of the proposed method.

Numerical investigation of through crack behaviour under welding residual stresses

Numerous engineering structures operate under the presence of residual stresses resulting from welding or other manufacturing processes. In the present work, the effect of typical residual stress fields on stress intensity factors and crack propagation angle of cracks developing into the residual stress field under mixed mode loading conditions is studied. For the calculations a numerical methodology based on linear elastic finite element analysis is used. The presented results provide a useful tool for an efficient assessment of the influence of residual stress field on the crack evolution behaviour.

Static and dynamic loading of an ovaloid toroidal tank

In this study, two problems of static and dynamic loading for an ovaloid toroidal tank are considered. In the first problem, a linear elastic three-dimensional finite element analysis is carried out to determine the stress concentration in a pressurized ovaloid toroidal tank with a nozzle. For validation, comparison is made with previous results for a cylindrical shell with a nozzle. An analysis is carried out to indicate the influence of the nozzle location on the stress concentration. Results are provided for three ovaloid toroidal tanks, to indicate the variation of the stress concentration with nozzle geometry. In the second problem, a non-linear elastic–plastic shell-theory finite element analysis is carried out to determine the displacements arising in an ovaloid toroidal tank due to impact by a flat-nosed projectile. For validation, comparison is made with previous results for a spherical shell impacted by a projectile. Results are provided for three ovaloid toroidal tanks, impacted at the extrados or the crown, and these results are compared with results for equivalent shells of related geometry. Conclusions are drawn, noting characteristics of ovaloid toroidal tanks relevant to their design.

Simplified Limit Load Determination Using the mα-Tangent Method

Limit load determination of mechanical components and structures by the mα-tangent method is proposed herein. The proposed technique is a simplified method that enables rapid determination of limit loads for a general class of mechanical components and structures. The method makes use of statically admissible stress field based on a linear elastic finite element analysis to estimate the limit loads. The method is applied to a number of mechanical component configurations and the results compare well with those obtained by the corresponding elastic-plastic finite element analyses results.

Effects of Spot Diameter and Sheets Thickness on Fatigue Life of Spot Welded Structure based on FEA Approach

This study presents the effect of the spot weld and sheets thickness on the fatigue life of the of the spot-weld joints to predict the lifetime and location of the weakest spot-welds due to the variable amplitude loading conditions. A simple model was used to illustrate the technique of spot-weld fatigue analysis. Finite element model and analysis were carried out utilizing the finite element analysis commercial codes. Linear elastic finite element analysis was carried out to predict the stress state along the weld direction. It can be seen from the results that the predicted life greatly influence the sheet thickness, nugget diameter and loading conditions of the model. Acquired results were shown the predicted life for the nugget and the two sheets around the circumference of the spot-weld at which angle the worst damage occurs. The spot-welding fatigue analysis techniques are awfully essential for automotive structure design.

Finite Element Based Member Stiffness Evaluation of Axisymmetric Bolted Joints

For a reliable design of bolted joints, it is necessary to evaluate the actual fraction of the external load transmitted through the bolt. The stiffness of the bolt and the member of the joint decide the fractions of external load shared by the bolt and the member. Bolt stiffness can be evaluated simply by assuming the load flow to be uniform across the thickness and the deformation is homogeneous. Then, bolt may be modeled as a tension member and the stiffness can be easily evaluated. But, the evaluation of the member stiffness is difficult because of the heterogeneous deformation. In the present work, joint materials are assumed to be isotropic and homogeneous, and linear elastic axisymmetric finite element analysis was performed to evaluate the member stiffness. Uniform displacement and uniform pressure assumptions are employed in idealizing the boundary conditions. Wide ranges of bolt sizes, joint thicknesses, and material properties are considered in the analysis to evaluate characteristic behavior of member stiffness. Empirical formulas for the member stiffness evaluation are proposed using dimensionless parameters. The results obtained are compared with the results available in the literature.