Two-dimensional Stress Analysis Research Articles

A photoelastic method for stress analysis of granular terrain beneath a wheel

This paper presents a photoelastic method for the stress analyses of granular terrains beneath a traveling wheel. Recently, wheel terramechanics have been studied using various advanced techniques such as particle velocimetry and machine learning. However, the dynamic profiles of the stress distributions in soil have not been directly observed. In this paper, we propose a photoelastic method to experimentally demonstrate the two-dimensional stress analysis of a granular terrain. This method uses photoelastic disks as terrain particles; thus, the internal stress and propagation of the granular terrain can be visualized using the interference fringe of light. This study aimed to observe the dynamic behavior of grains, typically simulating circular or spherical objects of the granular terrain. To demonstrate the photoelastic method for simulated ground, we developed a single-wheel testbed using photoelastic materials. Moreover, the effects of mixing with non-photoelastic materials were investigated to simulate steady states with small and large wheel-slip conditions. This paper presents a force chain analysis of the photoelastic particles beneath a single traveling wheel. The force chain structure was geometrically compared with the propagation angle and length. In addition, the orientational orders of the force chains were quantitatively evaluated under both small and large wheel slip conditions. The experimental results confirmed that the photoelastic method can reveal dynamic changes in the internal stress structures of granular terrain beneath the wheel under various slip conditions.

Numerical investigations on the damage tolerance of adhesively bonded pultruded GFRP joints with adhesion defects

Adhesive bonding has gained increasing acceptance in joining pultruded glass fiber reinforced polymer (GFRP) sections. However, one of the major issues hindering the widespread application of adhesive bonding in building and construction industries is the difficulty in predicting the mechanical behavior of the joints in the presence of adhesion defects. This paper investigates the damage tolerance of the adhesively bonded pultruded GFRP double-strap joints under quasi-static tensile loading using finite element analysis. Defects of various locations (along the bond length), sizes, and numbers were embedded within the bondline. A two-dimensional (2D) stress analysis was conducted to assess the effects of the bondline defects on the out-of-plane displacement, stress distribution, and peak stresses of the joints. Three-dimensional (3D) progressive damage models were further developed to predict residual joint capacity and provide insights into the effects of the adhesion defects on the damage mechanism of the joints. The progressive damage model uses the cohesive zone model (CZM) to simulate progressive interlaminar damage within the adherends as well as adhesive-FRP interface debonding. The proposed FE model was validated with published experimental data, and an excellent correlation was found between experimental and numerical results. The validated model was then used in a parametric study to assess the effects of design parameters such as adhesive types (from highly brittle to highly ductile) and joint geometry (adhesive chamfering, adherend chamfering, and recessing) on the damage tolerance of adhesively bonded joints. This paper also reports a comparative study on the damage tolerance between GFRP double-strap, single-strap, and single-step joints. The stress analysis results revealed that the presence of the bondline defects could increase the out-of-plane displacement of the adherends and the peak shear and peel stresses at the overlap ends. High-stress concentrations were also observed in regions adjacent to the defect extremities. The double-strap joints exhibited better damage tolerance than the single-strap and single-step lap joints. The damage tolerance of the joints can be improved by using stress-reduction methods such as adhesive chamfering, adherend chamfering, and recessing.

Two-Dimensional Stress Analysis of Thick Hollow Functionally Graded Sphere Under Non-Axisymmetric Mechanical Loading

In this paper, a functionally graded thick hollow sphere is considered for the analysis of two-dimensional steady state mechanical stress in the radial and circumferential directions under mechanical loading. Modulus of elasticity is varying with continuous nonlinear variation along the radial direction and Poisson’s ratio is kept as constant. The Legendre series and Euler differential equation are used to solve Navier equations. Geometry of the sphere is assumed in spherical coordinate system. Applying mechanical boundary conditions at inner and outer radii, we have carried out the analytical solutions for stresses, strains and displacements. In the numerical example, only internal pressure is varying along circumferential direction and external pressure is kept as zero. Displacements and mechanical stresses are presented graphically and the results are discussed numerically.

Finite Elements Using Neural Networks and a Posteriori Error

As the finite element method requires many nodes or elements to obtain accurate results, the adaptive finite element method has been developed to obtain better results with fewer nodes, where error information is used to refine the initial mesh adaptively. In contrast to this, we propose in this paper two new methods to directly derive accurate results by artificial neural networks using information about the errors of analysis results. One of the proposed methods employs error information obtained using a posteriori error estimator to predict accurate solutions from a single analysis with a coarse mesh. The other utilizes error information obtained from comparison between two analysis results: analysis results by using a coarse mesh and those by using the corresponding refined mesh. In both methods above, the artificial neural network is employed to predict accurate results at any target point in the analysis domain based on the error information around the point. These methods are successfully tested in two-dimensional stress analyses.

Analysis of the Stress Distribution Pattern of Anatomic and Non-Anatomic Tooth Forms on Maxillary and Mandibular Edentulous Ridges—A Photoelastic Study

Aim: To compare the type of stress distribution pattern occurring with anatomic and non-anatomic tooth forms beneath a complete denture in both maxillary and mandibular arch. Methodology: A photoelastic model of the edentulous maxillary and mandibular ridge was prepared meticulously to simulate the human mandible and maxilla. Two sets of acrylic teeth with anatomic and non-anatomic occlusal forms were used to fabricate upper and lower dentures. A vertical static load of 100 N was applied through the mandibular model to the maxillary model. After load application on the dentures the photoelastic model as well as the upper and lower complete dentures were sectioned in the midline. The sectioned photoelastic model was viewed through a polariscope to observe the fringe pattern indicating varying amounts of stress distribution. In this study, a two-dimensional photoelastic stress analysis technique was utilized. Results: Force per unit area was observed more in anatomic teeth than the non-anatomic counterpart. Hence anatomic tooth forms may increase the possibility of bone resorption rate over a period of time. However, in non-anatomic lower teeth, a decrease in value was observed from posterior to anterior region. Conclusion: Stress of greater magnitude was observed with cuspal teeth whereas non-anatomic (0°) showed slightly less magnitude of stress. Depending upon the clinical situation the clinician needs to choose the type of occlusal tooth forms for edentulous patients.

Two-Dimensional Stress Analysis of an Infinite Plate with Anisotropic Inclusions by BFM

Based on the principle of a Body Force Method (BFM), any inclusion problem can besolved only by using a Kelvin solution which corresponds to a stress field caused by a point forceacting in a homogeneous infinite plate, regardless of the mechanical properties of the inclusion. Thischaracteristic is true even for an anisotropic inclusion in which the number of independent elasticconstants are larger than that of a homogeneous material. In the present study, some problems among anisotropic inclusions were analyzed numerically to demonstrate the validity.

Influence of three-dimensional weld undercut geometry on fatigue-effective stress

With modern automated welding processes, such as laser-hybrid welding, it is possible to produce high-quality welds with good resistance to fatigue. However, although the overall quality of the weld may be good, the joints can still contain significant geometrical variation and geometrical imperfections at the weld notches. In previous research for thin laser-hybrid welded butt joints, small undercut-type imperfections were observed in both toe and root side. These imperfections are usually short along the weld direction and may not be visible when the geometry of the weld is examined. However, such imperfections work as local stress risers and may influence the fatigue strength significantly based on the weakest link principle. Severity of the local notch geometry is commonly analysed by the two-dimensional analyses, which assumes constant geometry in weld direction. This approach is conservative for short undercuts due to macro-support of the surrounding material. In this study, the difference between two-dimensional and three-dimensional stress analyses for short semi-elliptic undercuts is examined using stress averaging approach. The study utilises parametric notch models, where geometric parameters, such as notch length, depth, radius and opening angle, are varied to examine the difference for different undercut shapes.

Boundary element analysis of laminated composite shear deformable shallow shells

In this work, a Boundary Element Method formulation for stress analysis of symmetrically laminated composite thick shallow shells is presented. The proposed formulation was obtained by coupling the boundary element formulation of shear deformable symmetrically laminated composite plates and the boundary element formulation for two-dimensional anisotropic plane stress analysis. Formulation uses the elastostatic anisotropic fundamental solutions proposed for these formulations. Domain integrals are transformed to the boundary by using the Radial Integration Method. Numerical examples are presented to demonstrate the efficiency and accuracy of the formulation. Obtained results concur with results available in the literature as well as with finite element results.

An adaptation of mixed-mode I + II continuum damage model for prediction of fracture characteristics in adhesively bonded joint

This work is focused on an adaptation of a continuum mixed mode I + II damage model which allows to simulate different paths of crack propagation as well as two-dimensional fracture process zone (FPZ) in adhesively bonded joints. A continuum mixed mode I + II damage model based on the exponential damage evolution with the B - K law is proposed in order to account for the nonlinear property of damage evolution in adhesively bonded joints and the elastic-plastic hardnening inherent to ductile adhesives. The current model is validated by comparison of simulation results of several types of single lap joint (SLJ) predicted using ABAQUS UMAT with the experimental and numerical results published in previous literature. Furthermore, the performance of the proposed model is examined by comparison with some previous models including the ABAQUS cohesive zone model, the virtual crack closure technique and the extended finite element method. Moreover, the effect of adhesive end fillet on the load carrying capacity and the fracture mode of the single lap joints are studied. It should be noted that two-dimensional plane stress and plane strain finite element analysis is preformed throughout this work. The application of the proposed model enables the simulation of a non-symmetric crack propagation path and the fracture process zone in adhesive bonded joints.

Three-dimensional effect of stresses in open stope mine design

The stability graph method is widely used for open stope mine design. During the development of the method the effect of induced stresses were included by using two-dimensional or limited three-dimensional stress analysis. In this paper, three-dimensional numerical models are used to develop new induced stress curves, and to evaluate the effects on the stability graph method and open stope mine design. Significant differences are identified for the estimated stresses at the wall of the stopes, leading to an increase of the size of the stopes.

Modelling of stiffness degradation due to cracking in laminates subjected to multi-axial loading.

The paper presents an analytical approach to predicting the effect of intra- and interlaminar cracking on residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of multidirectional laminates under multi-axial loading is demonstrated on cross-ply glass/epoxy and carbon/epoxy laminates with transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delaminations. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

THE PROJECTED EFFECT FROM ACCEPTANCE OF CONSTRUCTIVE SOLUTIONS TO ENSURE THE RELIABILITY OF AN INDUSTRIAL FACILITY

In this paper a three-dimensional finite element analysis employed to predict thermal residual stresses field which arises during the cooling stage at the free edges of a thick walled filament wound cylinder with cross-ply lamination. The inner radius of composite is 50 mm and outer radius is 75 mm and the thickness of steel mandrel is 3 mm. The results showed that the radial stresses near the free ends of the cylinder increased two times compared to radial stresses in the middle of the cylinder and interlaminar shear stresses exceeded 6 MPa close to the free edges.Thus, a two-dimensional stress analysis does not fully reflect the complex state of stress of thick-walled cross-ply filament wound cylinders.

Bubbles breaking the wall: Two-dimensional stress and stability analysis.

Submerged granular material exhibits a wide range of behavior when the saturating fluid is slowly displaced by a gas phase. In confined systems, the moving interface between the invading gas and the fluid/grain mixture can cause beads to jam, and induce intermittency in the dynamics. Here, we study the stability of layers of saturated jammed beads around stuck air bubbles, and the deformation mechanism leading to air channel formations in these layers. We describe a two-dimensional extension of a previous model of the effective stress in the jammed packing. The effect of the tangential stress component on the yield stress is discussed, in particular how arching effects may impact the yield threshold. We further develop a linear stability analysis, to study undulations which develop under certain experimental conditions at the air-liquid interface. The linear analysis gives estimates for the most unstable wavelengths for the initial growth of the perturbations. The estimates correspond well with peak to peak length measurements of the experimentally observed undulations.

Seismic simulation of liquefaction-induced uplift behavior of a hollow cylinder structure buried in shallow ground

When designing buried structures using a performance-based framework, it is important to estimate their uplift displacement. A simplified method is proposed for predicting the uplift displacement of a hollow cylinder structure buried in shallow backfill based on the equilibrium of vertical forces acting on the structure during earthquakes. However, this method only provides the maximum value, which frequently is overestimated in practical applications. To offset this limitation, first, the uplift behavior of buried hollow cylinder structures subjected to strong earthquake motions was simulated. Then, two-dimensional effective stress analyses based on the multiple shear mechanism for soil were conducted, and the results were compared with the centrifuge test data. The soil parameters were evaluated based on laboratory test results. The seismic response data from 20g centrifuge tests were analyzed, and the results were generally consistent with the results of centrifuge model tests. In particular, the effective stress model showed a reasonable ability to reproduce the varying degrees of uplift displacement depending on the geotechnical conditions of trench soils adjacent to the hollow cylinder structures buried in shallow ground.

A general solution for the two-dimensional stress analysis of balanced and unbalanced adhesively bonded joints

This paper presents an efficient analytical solution strategy to determine the adhesive stresses in balanced and unbalanced adhesively bonded joints with mixed force loading and/or displacement boundary conditions. The adhesive stresses are expressed in terms of geometrical dimensions and material properties, combined with integration constants obtained numerically. The model is successfully applied for the analysis of various types of joints, including balanced and unbalanced stiffened plate/joint, single-strap joint, and single-lap joint. In all such cases, the linear equation sets are supplied to determine the integration constants in the final stress expressions. The analytical predictions agree well with the finite element results for adhesive stresses. This proposed model can be extended conveniently to predict the mechanical behavior of similar bonded structures such as composite laminates, electronics packaging, and flexible electronics structures.

Mohr space and its application to the activation prediction of pre-existing weakness

The activation coefficient equations in the “activation criterion of pre-existing weakness” are relatively complex and not easy to apply to specific applications. The relative activity of pre-existing weaknesses is often critical in geological analysis. The Mohr circle can be used only in two-dimensional stress analysis. By applying the “activation criterion of pre-existing weakness” and combining it with numerical analysis, we establish the correspondence between the pole (σn, τn) of a pre-existing weakness plane and its orientation in “Mohr space”. As a result, the normal stress (σn) and shear stress (τn) of a pre-existing weakness plane can be readily expressed in Mohr space. Furthermore, we introduce the method and procedures for predicting the activation and relative activation of pre-existing weaknesses in Mohr space. Finally, we apply the Mohr space method and compare the predictions to sandbox modeling results and 3D seismic data. The results show that Mohr space can be used in stress analysis to estimate the activation of a pre-existing weakness in any triaxial stress state.

Multiple Crack Propagation with Dual Boundary Element Method in Stiffened and Reinforced Full Scale Aeronautic Panels

In this work, the performance of a new methodology, based on the Dual Boundary Element Method (DBEM) and applied to reinforced cracked aeronautic panels, is assessed. Such procedure is mainly based on two-dimensional stress analyses, whereas the three-dimensional modelling, always implemented in conjunction with the sub-modelling approach, is limited to those situations in which the so-called secondary bending effects cannot be neglected. The connection between the different layers (patches and main panel) is realised by rivets: a peculiar original arrangement of the rivet configuration in the two-dimensional DBEM model allows to take into account the real in-plane panel stiffness and the transversal rivet stiffness, even with a two dimensional approach. Different in plane loading configurations are considered, depending on the presence of a biaxial or uniaxial remote load. The nonlinear hole/rivet contact, is simulated by gap elements when needed. The most stressed skin holes are highlighted, and the effect of through the thickness cracks, initiated from the aforementioned holes, is analysed in terms of stress redistribution, SIF evaluation and crack propagation. The two-dimensional approximation for such kind of problems is generally not detrimental to the accuracy level, due the low thickness of involved panels, and is particularly efficient for studying varying reinforcement configurations, where reduced run times and a lean pre-processing phase are prerequisites.The accuracy of the proposed approach is assessed by comparison with Finite Element Method (FEM) results and experimental tests available in literature.This approach aims at providing a general purpose prediction tool useful to improve the understanding of the fatigue resistance of aeronautic panels.KEYWORDSDBEM, full scale aeronautic panel, 2D/3D crack growth, MSD, doubler-skin assembly, damage tolerance

Two-Dimensional Stress-Wave Propagation in Finite-Length FG Cylinders with Two-Directional Nonlinear Grading Patterns Using the MLPG Method

AbstractThe application of meshless local integral equations based on the meshless local Petrov-Galerkin (MLPG) method for the two-dimensional (2D) dynamic stress analysis of a 2D functionally graded (FG) cylinder with two-directional grading patterns is developed. It is assumed that the inner bounding surface of the cylinder is excited by mechanical shock loading. The problem is studied in the frequency domain using the Laplace transformation, and then the stresses are transferred to the time domain using Talbot techniques. The mechanical properties of the FG materials (FGMs) are simulated using a nonlinear model with radial and axial volume fractions. The 2D propagation of stresses is tracked through the radial and axial directions in a 2D domain for various grading patterns at various time instants. By using the presented meshless technique, the maximum values of the stresses are calculated. The effects of various grading patterns on the maximum values of the stresses are studied in detail. The present...

Predicting residual stiffness of cracked composite laminates subjected to multi-axial inplane loading

This is a contribution to the exercise that aims to benchmark and validate the current continuum damage and fracture mechanics methodologies used for predicting the mechanical behaviour of fibre-reinforced plastic composites under complex loadings. The paper describes an analytical approach to predict the effect of intra- (matrix cracking and splitting) and inter-laminar (delamination) damage on the residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the damaged laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of a multidirectional laminate with multilayer intra- and inter-laminar damage is demonstrated for [Formula: see text] and [Formula: see text] cross-ply laminates made from a specific glass/epoxy system under in-plane uniaxial and biaxial loading damaged by transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delamination.

The impact of ellipsoidal particle shape on pebble breakage in gravel

We have studied the influence of particle shape and consequently loading configuration on the breakage load of fluvial pebbles. Unfortunately, physical strength tests on pebbles, i.e., point-load tests, can only be conducted under one specific stable loading configuration. Therefore, the physical uniaxial strength tests performed in this study were extended by a two-dimensional finite-element stress analysis, which is capable of investigating those scenarios that are not possible in physical tests. Breakage load, equivalent to that measured in unidirectional physical tests, was determined from the results of the stress analysis by a maximum tensile stress-based failure criterion. Using this assumption, allows the determination of breakage load for a range of different kind of synthetic loading configurations and its comparison with the natural breakage load distribution of the physical strength tests. The results of numerical modelling indicated that the configuration that required the least breakage load corresponded with the minor principal axis of the ellipsoidal pebbles. In addition, most of the simulated gravel-hosted loading configurations exceeded the natural breakage load distribution of fluvial pebbles obtained from the physical strength tests.