Stress Analysis Problems Research Articles

Diaphragm stress analysis and fatigue strength evaluation of the flex-spline, a very thin-walled spur gear used in the strain wave gearing

This paper deals with diaphragm stress analysis and fatigue strength calculation problems of the flex-spline, a thin-walled spur gear used in the strain wave gearing (SWG). Firstly, a mechanics model and theoretical method used for contact analysis of SWG are presented in this paper. Then finite element method (FEM) software is self-developed through very long time efforts in order to realize the contact analysis and stress calculations of SWG. With the developed FEM software, bending and shear stresses of the diaphragm of the flex-spline are analyzed successfully. Secondly, in order to confirm the FEM software, an experimental method and device are presented in this paper. A three-directional, strain gauge is stuck on a straight surface of the tapered diaphragm of the flex-spline next to the corner of the diaphragm with the boss. Diaphragm strains are measured under the conditions of zero and 110Nm torques respectively and the measured stresses are compared with the calculated ones with the developed FEM software under the same conditions. It is found that the two results are in agreement with each other well. This means that the presented mechanics model and theoretical method are correct and effective. Finally, a method used to evaluate fatigue failure strength of the diaphragm is suggested based on the findings in this paper.

Concept of Finite Element Modelling for Trusses and Beams Using Abaqus

Abaqus is one of the powerful engineering software programs which are based on the finite element method. The Abaqus can solve wide range of problems from linear to nonlinear analyses. Abaqus is widely used in many sectors like automotive and mechanical industries for design and development of FEM products. The finite element method is a numerical technique for finding approximate solutions for differential and integral equations [1]. The finite element word was coined by Clough in 1960. In 1960s, engineers used the method for solving the problems in stress analysis, strain analysis, heat and fluid transfer, and other region. Abaqus CAE can provide a simple creating model, submitting the modal, monitoring, and evaluating result and then can also compare with theoretical calculation [2]. In this report all the steps will be explained in different areas such as sketch a modal, assigning material property, applying boundary condition and loads, submit and monitor the job and view the deformed models using the visualisation and create report for results. This report is to demonstrate to create and analyse a structure model in two dimensional with the aim of showing Abaqus software. The methods used to test the modal and analyse on different boundary conditions and also analyse the behaviour of modal with different elements such as truss and beam elements and assume frictionless pin joint in truss and rigid joints welded in beam elements. The results will be compared and explained with theoretical calculated statically determinate truss.

Locking‐free discontinuous finite elements for the upper bound yield design of thick plates

SummaryThis work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of Reissner–Mindlin thick plates in shear‐bending interaction. The main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields. In particular, it has been demonstrated for 2D plane stress, plane strain or 3D limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates. For this reason, discontinuous interpolations of the transverse velocity and the rotation fields for Reissner–Mindlin plates are proposed. The subsequent discrete minimization problem is formulated as a second‐order cone programming problem and is solved using the industrial software package MOSEK. A comprehensive study of the shear‐locking phenomenon is also conducted, and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment. This particular aspect is confirmed through numerical examples on classical benchmark problems and the so‐obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates. Copyright © 2015 John Wiley & Sons, Ltd.

A successive perturbation-based multiscale stochastic analysis method for composite materials

This paper introduces a successive perturbation-based method for multiscale stochastic analysis of heterogeneous materials such as composite materials. Microscopic random variations sometimes have a significant influence on homogenized material properties and microscopic stress fields. Therefore, multiscale stochastic problems should be analyzed to evaluate the reliability of composite structures. Further, in order to assess the result of numerical analysis of a composite structure, this type of uncertainty propagation should be taken into account. For this purpose, the successive perturbation based approach is proposed.As a numerical example, the stochastic homogenization and multiscale stochastic stress analysis problem of composite materials are solved considering microscopic random variations. From the numerical results, the proposed approach gives a more accurate estimation than the conventional perturbation approach. Also, our proposed method works well for both smooth nonlinear response functions and non-smooth response functions.

Explicit formulae for the internal stress in spherical particles of active material within lithium ion battery cathodes during charging and discharging

Abstract The fundamental process underlying the operation of lithium ion batteries is the diffusion of charge-carrying ions through the electrolyte that separates the anode from the cathode, and the reversible insertion of lithium ions into the host material’s crystal structure (intercalation and de-intercalation). Alongside the principal electrochemical consequences of this process, mechanical phenomena that accompany (de)intercalation are of fundamental significance for deformation and fragmentation of the active materials, since it is these phenomena that ultimately determine the battery structural integrity and durability. This article presents a sequentially coupled analytical treatment of the transient diffusion and stress analysis (eigenstrain) problem related to the lithiation and de-lithiation processes at the level of an individual spherical secondary particle of active material. Explicit closed form approximate solutions are derived for the stresses that arise within the particles during fast charging. They provide a firm basis for the assessment of the charging conditions influence on the internal stress states and the effects on battery damage, mechanical integrity and durability.

Image decomposition and uncertainty quantification for the assessment of manufacturing tolerances in stress analysis

This article presents a methodology for the treatment of uncertainty in nonlinear, interference-fit, stress analysis problems arising from manufacturing tolerances. Image decomposition is applied to the uncertain stress field to produce a small number of shape descriptors that allow for variability in the location of high-stress points when geometric parameters (dimensions) are changed within tolerance ranges. A meta-model, in this case based on the polynomial chaos expansion, is trained using a full finite element model to provide a mapping from input geometric parameters to output shape descriptors. Global sensitivity analysis using Sobol’s indices provides a design tool that enables the influence of each input parameter on the observed variances of the outputs to be quantified. The methodology is illustrated by a simplified practical design problem in the manufacture of automotive wheels.

Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method

A multiscale spectral generalized nite element method (MS-GFEM) is presented for the solution of large two and three dimensional stress analysis problems inside heterogeneous media. It can be employed to solve problems too large to be solved directly with FE techniques and is designed for implementation on massively parallel machines. The method is multiscale in nature and uses an optimal family of spectrally dened local basis functions over a coarse grid. It is proved that the method has an exponential rate of convergence. To x ideas we describe its implementation for a two dimensional plane strain problem inside a ber reinforced composite. Here bers are separated by a minimum distance however no special assumption on the ber conguration such as periodicity or ergodicity is made. The implementation of MS-GFEM delivers the discrete solution operator using the same order of operations as the number of bers inside the computational domain. This implementation is optimal in that the number of operations for solution is of the same order as the input data for the problem. The size of the MS-GFEM matrix used to represent the discrete inverse operator is controlled by the scale of the coarse grid and the convergence rate of the spectral basis and can be of order far less than the number of bers. This strategy is general and can be applied to the solution of very large FE systems associated with the discrete solution of elliptic PDE.

Stress Analysis of Bolted Joints Part II. Contact and Slip Analysis of a Four Bolt Joint

For up-to-date bolted joints, first of all in vehicles, high strength bolts of 10.9 or even 12.9 are used, which are preloaded up to 90% or even 100% of the yield strength. The primary aim of this high degree utilization is the weight reduction. For the analytic dimensioning of bolted joints, the VDI 2230 Richtlinien German standard [1] provides support. However, the analytic model can mostly consider the true structural characteristics only in a limited way. The analytic modeling is especially uncertain in case of multiple bolted joints when the load distribution among the bolts depends reasonably upon the elastic deformation of the participating elements in the joints over the geometry of the bolted joint. The first part of this paper deals with the problems of numerical modeling and stress analysis, respectively specifying the analytic dimensioning procedure by applying elastic or rather elastic-plastic material law. The error magnitude in bolted joint calculation was examined in case of omitting the existing threaded connection—between the bolt and the nut—in order to simplify the model. The second part of the paper deals with the dimensioning of stands and cantilevers’ multi-bolt fixing problems, first of all, with the load distribution among the bolts keeping in view the analysis of the local slipping relations. For demonstrating the above technique, an elaborated numeric procedure is presented for a four-bolted cantilever, having bolted joints pre-tightened to the yield strength.

Stress Analysis of Bolted Joints Part I. Numerical Dimensioning Method

For up-to-date bolted joints, first of all in vehicles, high strength bolts of 10.9 or even 12.9 are used, which are pre-tightened up to 90% or even 100% of the yield strength. The primary aim of this high degree utilization is the weight reduction. For the analytic dimensioning of bolted joints, the VDI 2230 Richtlinien German standard provides support. However, the analytic model can mostly consider the true structural characteristics only in a limited way. The analytic modeling is especially uncertain in case of multiple bolted joints when the load distribution among the bolts depends reasonably upon the elastic deformation of the participating elements in the joints over the geometry of the bolted joint. The first part of this paper deals with the problems of numerical modeling and stress analysis, respectively specifying the analytic dimensioning procedure by applying elastic or rather elastic-plastic material law. The error magnitude in bolted joint calculation was examined in case of omitting the existing threaded connection—between the bolt and the nut—in order to simplify the model. The second part of the paper deals with the dimensioning of stands and cantilevers’ multi-bolt fixing problems, first of all, with the load distribution among the bolts keeping in view the analysis of the local slipping relations. For demonstrating the above technique, an elaborated numeric procedure is presented for a four-bolted cantilever, having bolted joints pre-tightened to the yield strength.

Use of the Eigenstrain Concept for Residual Stress Analysis

Problems of residual stress analysis can be formulated in terms of so-called eigenstrain or inelastic strain. Although the concept is almost 100 year old, the use of it by the residual stress community is quite limited, due to complexities of the associated mathematics. When mathematical difficulties are resolved and eigenstrain is reconstructed, the use of it can be beneficial in several ways. Firstly, the eigenstrain is essentially a generator function for residual elastic stress and elastic strain and it can be used, for generation of any stress field in FE models. Furthermore, eigenstrain distributions are frequently localized, even though the elastic stress or strain distributions are not. Both these properties can be used for effective data reduction. Another advantage of the use of the eigenstrain concept is that experimental data may be interpreted in a more meaningful way by using a narrower context, in terms of plastic deformation, thermal expansion/misfit and deformation caused by phase transformation, rather than just residual stress/strain field. The sample geometry and symmetry play an important role in resolving eigenstrain distributions from residual stress and elastic strain fields. Generally the equations are difficult to solve, however for a sample geometry of high symmetry, eigenstrain can be resolved and expressed as a solution of a relatively simple integral equation; which is the Fredholm of the second type with the kernel of the integral operator defined by the sample geometry/symmetry. Several such symmetries are investigated, yielding analytical solutions that are applied and contrasted to experimental data. An important issue for residual stress analysis is the uniqueness of the solution is also discussed.

Is notch sensitivity a stress analysis problem?

Semi–empirical notch sensitivity factors q have been widely used to properly account for notch effects in fatigue design for a long time. However, the intrinsically empirical nature of this old concept can be avoided by modeling it using sound mechanical concepts that properly consider the influence of notch tip stress gradients on the growth behavior of mechanically short cracks. Moreover, this model requires only wellestablished mechanical properties, as it has no need for data-fitting or similar ill-defined empirical parameters. In this way, the q value can now be calculated considering the characteristics of the notch geometry and of the loading, as well as the basic mechanical properties of the material, such as its fatigue limit and crack propagation threshold, if the problem is fatigue, or its equivalent resistances to crack initiation and to crack propagation under corrosion conditions, if the problem is environmentally assisted or stress corrosion cracking. Predictions based on this purely mechanical model have been validated by proper tests both in the fatigue and in the SCC cases, indicating that notch sensitivity can indeed be treated as a stress analysis problem.

Fuzzy Meshless Local Petrov-Galerkin Method for Analysis of Imprecisely Defined Systems

Many engineering systems contain uncertainties that cannot be described by either deterministic or probabilistic approaches. For example, the geometry, material properties, external actions (loads), and boundary conditions may be imprecise in a practical mechanical or structural system. The uncertainties present may be associated with parameters that are vague, imprecise, or linguistic. A fuzzy meshless local Petrov-Galerkin approach is developed in this work for the analysis of imprecisely defined systems. Starting from the basic concepts of fuzzy sets, fuzzy arithmetic, and fuzzy calculus (differentiation and integration) the various steps of the meshless local Petrov-Galerkin approach involved in the derivation of the equations are redefined using fuzzy concepts. The resulting fuzzy equations are derived using a fuzzy version of Gaussian elimination procedure coupled with truncation. A one-dimensional heat-transfer problem involving conduction, convection, and radiation with vaguely defined thermal properties of the material and boundary conditions and two stress-analysis problems (a beam and a plate with a hole) with vaguely defined material properties and external loads are considered to demonstrate the methodology. A truncation scheme is used to overcome the difficulty of overestimating the width of the response characteristics of the system due to repeated fuzzy arithmetic operations in the solution of the fuzzy equations. A simple sequential linearization scheme is used to handle the nonlinear boundary-value problem associated with the radiation boundary condition in the heat-transfer problem. The present approach represents a unique methodology that enables the handling of certain types of imprecisely known data more realistically compared to the existing procedures.

Inverse problem of non-homogeneous residual stress identification in thin plates

Vibration of solid bodies with residual stresses has been attracting attention of researchers from different countries for a long time. Problems of residual stress analysis have its applications in fields of building, mechanical engineering, aircraft construction, biomechanics, manufacturing of composite and functionally-gradient materials. The most common model of residual stresses (or prestresses) is the homogeneous prestress state model; however, in fact the prestress state is often non-homogeneous under natural conditions. One of the most powerful nondestructive methods of reconstruction of non-homogeneous prestress state is the acoustical method.In the present paper the direct problem formulations for 3D bodies and thin plates with non-homogeneous prestress fields are described. A formulation of the inverse problem on a reconstruction of non-homogeneous prestress state is given on the basis of acoustical method. The problem is reduced to the iterative process; at each step of the latter the direct problem and the integral Fredholm equation of the first kind are solved. Two ways of obtaining operator equations of the inverse problem are presented for two oscillation regimes – in-plane and out-of-plane plate vibration modes. Numerical results of solving the inverse problem on a reconstruction of the uniaxial prestress function in case of out-of-plane vibration for a thin rectangular plate are presented. Features and characteristics of the solutions obtained are revealed; the most auspicious conditions for a better quality of the identification procedure are pointed out.

An efficient global/multi-local stress analysis of complicated engineering composite structures using multi-goal MapReduce

Detailed stress analyses of complicated engineering composite structures are computationally challenging due to the complexities of the microstructure. In this study, the primary objective is to close this gap by bringing high computational efficiency and scalability of MapReduce to the stress analysis problem. A new multi-goal MapReduce that extends the popular MapReduce programming model to multi-goal computations is proposed and combined with global/local analysis method to develop an efficient global/multi-local stress analysis strategy. The proposed approach is finally applied to the multi-phase and multi-layer plain weave composite laminate structure. The computational results are finally compared with the results of direct finite element computation and traditional global/local analysis in single node.

Commentary of research situation and innovation frontier in hydro-structure engineering science

In order to utilize water and hydropower resources in China, multitudes of water projects are established or to be constructed as an integral part of the national economy’s infrastructure. Under these circumstances, there are two outstanding problems: 1) a mass of existing dams are in danger and 2) in the southwest water-conservancy construction plan, dozens of existing or planned dams are high dams or even super high dams with heights between 200 and 300 m. In accordance with demands of “the National Program for Medium- and Long-Term Scientific and Technological Development” on the innovation frontier in hydro-structure engineering science, various key problems in science and technology such like stress analysis, ultimate bearing capacity, nonlinearity etc. for high dams, super high dams and sick dams have been investigated. This paper makes a commentary on the advances and results of the researches, then analyzes the advantages and disadvantages of current theoretics and methodologies, and finally presents corresponding research directions and the frontier of innovation.

Bringing out Fluids Experiments from Laboratory to In Silico – A Journey of Hundred Years

By making use of the developments in the fields of numerical methods, computational technology and fluid dynamics models, computational fluid dynamics (CFD) progress forward to play an active role today in various industrial, academic and research activities. In many cases, CFD simulations replace expensive and time consuming laboratory experiments successfully by allowing engineers and scientists to capture pressure, velocity and force distributions. Researchers are now able to test various theoretical conditions unavailable in the laboratory and CFD studies help them to get deeper insights on existing theories. The century-old history started just to solve some stress analysis problems numerically and today CFD methodology is being applied not only in fluid dynamics also in chemical engineering, mineral processing, fire engineering, sports, medical imaging and even in acoustics. This paper reviews the growth of CFD as a discipline and discusses its contemporary methodology.

Innovative use of Computer tools in Teaching Structural Engineering Applications

SummaryThis paper reports on using Microsoft Excel coupled with Visual Basic for Application (VBA) in teaching two courses for the students in the Civil & Environmental Engineering Department in United Arab Emirates University. The first course covers the use of the stiffness matrix method for the analysis of 2D trusses, beams and frames. The latter has a more advanced content by focusing on 2D solid elements, plates and shells. Throughout the offering of both courses, the authors, with the aid of hands-on sessions and multimedia, guide their students to develop different user-defined VBA functions in Excel, which are used to derive the solution of different structural and stress analysis problems. The paper also proposes a new method in Excel that may be used to eliminate possible cheating (e-cheating) when students exchange files using email, Bluetooth or any other means. The proposed method has been utilised by the authors to minimise potential e-cheating and copying among students.

Numerical solution of curved pipes submitted to in-plane loading conditions

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.

Improved thermal stress analysis for castings

Three algorithms are presented to address three problems in stress analysis of castings: difficulties for enmeshment of complicated casting into finite element meshes, coupling of thermal and stress analysis, and determination of inverse deformation, respectively. An algorithm of conversion of finite difference meshes into finite element meshes is achieved by reformatting the data of meshes. An algorithm of the heat transfer coefficient at the casting/mould interface is presented and the coupling of thermal and stress analysis is realised with the feedback of stress and deformation to heat transfer. Machining allowance is applied as a criterion for deformation evaluation of castings. And insufficient machining allowance is transformed to inverse deformation which is fed back to the original casting design for recalculation of stress and deformation. Therefore, the design of casting with appropriate inverse deformation is obtained. Case studies about a cylinder block and a hydro turbine blade casting are illustrated.

Thermo-elastic mismatch in nonhomogeneous beams

The problem of thermo-elastic stress analysis in multi-layered nonhomogeneous beams is considered. The proposed analytical approach based on the multi-layered beam theory permits to take into account an arbitrary distribution of the Young’s modulus, of the thermal-expansion coefficient, and of the temperature variation along the beam depth. The effect of shear deformability of the interfaces is also carefully analyzed. Useful closed-form solutions for the normal stresses in the layers and for the interface tangential stresses are provided in the case of nonhomogeneous bi- and tri-layered beams. The obtained results show the effectiveness of using functionally graded materials to relieve stress-concentrations due to the thermo-elastic mismatch typical of laminated beams with homogeneous layers.