Stress Concentration Problem Research Articles

A pressure-loaded soft functionally gradient spherical capsule under finite deformation

Functionally gradient materials (FGMs) possess continuously varying properties, which avoid the problem of stress concentrations arising from abrupt material discontinuity in composite materials. Recent interests in soft FGMs for robotics and medical applications have motivated the present work, which develops analytical solutions for soft functionally gradient (FG) spherical capsules subjected to internal and external pressures. The work considers large deformation and second-order elasticity. Assuming power laws for the varying elastic constants, analytical solutions for the radial displacement and the first Piola-Kirchhoff and Cauchy stresses can be obtained in close and non-dimensional form. Considering gradient indices α and β for the second- and third-order elastic constants, the key results are: (1) the nonlinear elasticity contributes significantly to the elastic deformation, (2) different α and β values may result in displacement and stresses which are vastly different in magnitude and opposite in sign, (3) combined α and β values may be used to minimize the stress throughout the spherical capsule, thus aiding the theoretical design of FGMs, and (4) the thickness of the capsule influences the displacement and stress distributions significantly and the optimum thickness is dependent on the gradient indices.

Stress concentration at cruciform welded joints under axial and bending loading modes

The paper is concerned with the problem of stress concentration in cruciform fillet welded joints subjected to axial and bending load. Extended numerical analyses were carried out with the help of the finite element method. It made it possible to estimate stress concentration factors Kt for a variety of geometrical parameters defining the geometry of cruciform welded joints. It has been found that approximate Kt formulas, available in the literature, have two disadvantages, i.e. an unknown accuracy and small range of application with respect to geometrical parameters defining the weld shape. For these reasons, more general and accurate new formulas for stress concentration factors Kt have been derived. Even though the present approach is applicable to all types of welded joints, the analysis presented below has been conducted for a cruciform joint with the weld flank angle of θ = 45°. Final solutions have been given in the form of polynomial expressions, and they can be easily used in computer-aided design procedures.

Application of DIC Method in the Analysis of Stress Concentration and Plastic Zone Development Problems.

The paper presents the assessment of the possibility and reliability of the digital image correlation (DIC) system for engineering and scientific purposes. The studies were performed with the use of samples made of the three different materials—mild S235JR + N steel, microalloyed fine-grain S355MC steel, and high strength 41Cr4 steel subjected to different heat-treatment. The DIC studies were focused on determinations of dangerous zones with large stress concentrations, plastic deformation growth, and prediction of the failure zone. Experimental tests were carried out for samples with different notches (circular, square, and triangular openings). With the use of the DIC system and microstructure analyses, the influence of different factors (laser cutting, heat treatment, material type, notch shape, and manufacturing quality) on the material behavior were studied. For all studied cases, the stress concentration factors (SCF) were estimated with the use of the analytical formulation and the finite element analysis. It was observed that the theoretical models for calculations of the influence of the typical notches may result in not proper values of SCFs. Finally, the selected results of the total strain distributions were compared with FEM results, and good agreement was observed. All these allow the authors to conclude that the application of DIC with a common digital camera can be effectively applied for the analysis of the evolution of plastic zones and the damage detection for mild high-strength steels, as well as those normalized and quenched and tempered at higher temperatures.

Technical Note: The Anti-plane Scattering of SH Waves by the Non-circular Cavity in an Infinite Strip

ABSTRACT In this paper, the problem of dynamic stress concentration in the process of anti-plane motion caused by a single circular cavity in a strip medium and the non-circular cavity in a porous strip medium is studied. In the case of only a single circular cavity, a numerical calculating example is presented to solve scattering around a circular cavity with a given SH guided wave and describe dynamic stress distribution at the edge of a circular cavity. Then, the results of the finite element method and analytical method are used to verify each other. Firstly, a compatible guided wave is constructed in the elastic strip, which satisfies stress-free conditions in upper and lower boundaries. Secondly, the scattering of waves around a circular cavity is expressed as series form by the employed wave function expansion method, and compatible scattering guided waves resulting from the reflection of waves off the boundaries of the elastic strip is constructed by repeated image superposition. Lastly, the coefficients of the wave function expansion are determined based on the stress-free condition of circular boundaries with pre-given incident guided waves. In the case of the non-circular cavity in the medium, the scattering of guided waves from the cavity is solved by finite element analysis, the dynamic stress distribution factor around the edge of the cavity is given, and to discuss influences of wave frequency and cavity position. The conclusions of this paper are of great reference value to the selection and ultrasonic non-destructive testing of anti-seismic materials.

Scraper Conveyor Structure Improvement and Performance Comparative Analysis

The scraper is the core of the conveyor and its vulnerable part. The problem of bending fracture of common welding scrapers in actual production is under consideration. SolidWorks and ANSYS finite element analysis software were used to construct the three-dimensional model for simulation analysis, and the existing structure was improved and optimized. The comparison results showed: well-type stiffener contributes to improvement of the overall strength and rigidity of the scraper. Before optimization, the maximum equivalent stress on the press buckle part of the scraper was 310 MPa, and after optimization it dropped to 230 MPa, i.e., decreased by 26%, and the stress value of one side of stiffener was 170 MPa, with certain bending resistance. After optimization, the stress distribution of the scraper was uniform, with solving the problem of stress concentration. After optimization, the overall safety factor of the scraper increased by nearly 15%, improving its life. Integrity of the optimized scraper was nearly 100%, as compared to that before optimization under the same conditions, which confirmed the validity of scraper optimization.

Stressed deformed condition of orthotropic spherical shell, lowered by two circular hole

Methods of calculating the shell structures from composite materials and studying the concentration of strains near the holes are devoted to a rather large number of works. However, most of the research was carried out within the framework of the classical Kirchhoff-Love hypothesis, which does not take into account the interlayer and lateral shifts characteristic of composite materials. Application of finite elements method to solve the problems on orthotropic shells of composites, weakened by several holes is reported within the improved theory of Timoshenko type. A numerical algorithm has been developed using the finite element method and a software package has been implemented on a computer that makes it possible to solve problems of stress concentration near two apertures in shells of composite materials. Shearing parameter has been studied for its influence on stress concentration near two circular holes internal pressure for orthotropic spherical shells. Specific results are presented for the cases of large and small holes, taking into account the rigidity of the reinforcing elements. Thus, this software package can be applied to the calculation of the elements of shell structures from orthotropic composite materials weakened by several holes.

Structural Optimization and Finite Element Analysis of Swing Arm Plate Suction Device for Battery Packer

Aiming at the problem that the side mounting plate and the connecting plate of the swing arm type polar plate suction device in the upper plate mechanism of the battery pack machine are thick, Solidworks is used to optimize the structure of the upper plate mechanism, and Ansys finite element analysis software is used to carry out multi-objective optimization on the optimized side mounting plate and the connecting plate. The results show that adding two chamfers to the side mounting and adding a round corner to the corner of the connecting plate not only effectively reduces the weight and maximum equivalent stress of the plate suction device and solves the problem of stress concentration, but also obviously improves the working precision and production efficiency of the lead-acid battery pack machine.

Dynamic antiplane behavior of rare earth giant magnetostrictive medium with a circular hole defect in a right-angle domain

The dynamic stress concentration problem of circular hole defects near the boundary of the right-angle region of rare earth giant magnetostrictive medium under the SH-wave is studied. Firstly, the half space incident field is constructed by using the mirror image method. At the same time, the scattered displacement field and the scattered magnetic field satisfying two right-angled boundary stress free and magnetic insulation conditions are obtained by a complex function method. Then, based on the boundary conditions of the circular hole, the infinite linear algebraic equations are established to obtain the unknown coefficients of wave function and magnetic field function. Finally, the dynamic stress concentration factor and the magnetic field intensity concentration factor caused by the SH-wave scattering are obtained. Numerical examples show that the incident angle, the incident wave frequency, the distance between the circular hole and the two right-angled sides, the dimension-pressure magnetic coefficient, the magnetic permeability, and other factors have an effect on the dynamic stress concentration factor and the magnetic field strength concentration coefficient around the circular hole. Some valuable conclusions are given which are certain to be useful for the study of material properties of rare earth giant magnetostrictive materials with circular hole defects.

Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

Global-local deformation measurement of stress concentration structures using a multi-digital image correlation system

The digital image correlation (DIC) technique is a method of measuring the displacement and strain of the entire area of a structure by comparing surface images taken by digital cameras before and after deformation of the structure. The DIC technique is currently being spotlighted because it can overcome the weakness of conventional contact measurement methods. So far a single DIC system with one camera or two cameras has been used for most applications. However, many structures need two or more DIC systems in order to measure their deformation efficiently and precisely. For example, the stress concentration problem and the cylindrical shell buckling problem are typical applications for a multi-DIC system. This study focuses on the stress concentration problem. The paper presents a globallocal deformation measurement method with a multi-DIC system. First, a tensile test of an aluminum beam was performed and compared with the strain gage method to validate the accuracy of DIC method. Then the tensile test specimens with a hole or a notch were prepared, and one DIC system measured the local deformation near a hole or a notch and the other DIC system measured the global deformation of the specimen. The results confirmed the proposed multi-DIC technique can be applied to the stress concentration problem.

КОНЦЕНТРАЦІЯ НАПРУЖЕНЬ В ОКОЛІ ТРІЩИНИ В ДОРОЖНЬОМУ ПОКРИТТІ ПРИ ДІЇ ТРАНСПОРТНИХ НАВАНТАЖЕНЬ

The problem of stress concentration in the vicinity of a crack under the action of transport loads is posed. Its analysis takes place in an elastic (thermoelastic) formulation using the given modules that correspond to a given state of the system at a given load level. Cases where the coating has no cracks and has them in the upper and inner layers are considered. The effect of transverse cracks on the redistribution of stress fields under the action of transport loads is analyzed. In the case where the coating has no cracks, the greatest compressive stresses occur on the top plane of the coating. Tensile stresses predominate in the zone of the third layer. They increase as they approach the contact plane of the third and fourth layers. The maximum values of the tangent stresses are realized at the boundary of the second and third layers, thus being a potential cause of the coating delamination in this zone. If the crack penetrates the first two upper layers, then the greatest compression stress has moved to the fracture mouth, and the tensile stress remains almost unchanged. In the case where a vertical crack penetrates the inner layer, the maximum values of the normal and tangent values occur in the central and edge zones of the load distribution. A finite element analysis of the effect of the crack on the stress-strain state of the multilayer system is performed. The stress concentration in the crack zones depends largely on the geometry of the crack and its structure at its mouth. KEYWORDS: AUTOMOBILE ROAD, ROAD COATING STRUCTURE, TRANSPORT LOADS, NORMAL VOLTAGE, TENSION VOLTAGE, TENSION-DEFORMED CONDITION

Secondary Gob-side Entry Retaining Technology with Double Side Roof Cutting and Pressure Relief in Thin Coal Seam

In order to solve the problems of stress concentration and large deformation of surrounding rock of secondary gob-side entry retaining in thin coal seam caused by hard overhanging roof, the method of cutting off overhanging roof on both sides of roadway by manual pre-cutting seam is adopted. It can transfer high stress to goaf on both sides of roadway and reduce roadway deformation. The mechanism of roadway formation, the conditions of double side overhanging roof subsidence and the stress reduction of roadway side support of secondary gob-side entry retaining after double side roof cutting are given. This paper studies the pressure relief law of secondary gob side entry retaining after double side roof cutting in thin coal seam. After double side roof cutting, the stress of roadway side support is reduced by 76%, the maximum vertical displacement of roof is reduced by 84%, and high stress is transferred to goaf. The influence of different double side roof cutting thickness and angle on the pressure relief effect is analyzed. On the premise that the collapsed gangue can fill the goaf, the smaller the thickness of double side roof cutting is, the better the pressure relief effect is, and the greater the double side roof cutting angle is, the better the pressure relief effect is. It has been successfully applied in the left five roadway of No. 69 coal seam in Xinqiang coal mine, and the deformation of roof and floor is reduced by 47% and the deformation of two sides is reduced by 56% after double side roof cutting. It has important reference value for the future secondary gob-side entry retaining.

Estimation of the Strength of Plates with Cracks Based on the Maximum Stress Criterion in a Scale-Dependent Generalized Theory of Elasticity

The problem of the strength of a plate made of a brittle material with through mode I cracks is discussed. In contrast to the approach based on the singular solution of the classical theory of elasticity for a plane with a crack and on linear fracture mechanics, we propose to use nonsingular solutions obtained within the generalized elasticity theory and, as a result, to implement a method, conventional for the strength estimation of solids with stress concentration, based on the maximum stress criterion. The maximum stress is determined from a nonsingular solution of the generalized elasticity equations for a plane with a crack. The reported experimental results for plates with cracks under tension and bending confirm the solution obtained by the proposed method and allow it to be compared with a solution based on linear fracture mechanics. In fact, a new concept of fracture mechanics is put forward, which is free of singular solutions and allows the problems of fracture mechanics to be treated as problems of stress concentration. Comparison of the obtained analytical solutions with the experimental data has shown that the scale factor of generalized elasticity determines the critical state in fracture mechanics with no less accuracy than the critical stress intensity factor and therefore can be used as a fracture criterion. The resulting explicit nonsingular solutions allow the prediction of the stress concentration caused by a crack.

A New Approach to Non-Singular Plane Cracks Theory in Gradient Elasticity

A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the function on the right side of the Helmholtz equation is a singular classical solution. An assertion is proved that allows us to propose a new solution for displacements and stresses at the crack tip through the vector harmonic potential, which determines by the Papkovich–Neuber representation. One of the goals of this work is a definition of a new representation of the solution of the plane problem of the theory of elasticity through the complex-valued harmonic potentials included in the Papkovich–Neuber relations represented in a symmetric form, which is convenient for applications. It is shown here that this new representation of the solution for the mechanics of cracks can be written through one harmonic complex-valued potential. The explicit potential value is found by comparing the new solution with the classical representation of the singular solution at the crack tip constructed using the complex potentials of Kolosov–Muskhelishvili. A generalized solution of the singular problem of fracture mechanics is reduced to a non-singular stress concentration problem, which allows one to implement a new concept of non-singular fracture mechanics, where the scale parameter along with ultimate stresses determines the fracture criterion and is determined by experiments.

Multiobjective Intelligent Cooperative Design for the Multilayer Interference Fit

Interference fit has extensively been applied in different mechanical fields due to its advantages such as compactness and high rigidity. With the actual needs of engineering, the multilayer interference fit has also been widely used. It is significant for the design and manufacture of multilayer interference fit to consider stress concentration problem and achieve multiobjective and multivariable collaborative optimization in the optimization algorithm. To achieve this goal, the mechanical model and reliability mathematical model of the multilayer interference fit are established. Giving an evaluation method of reliability, the recommended range of interference amount is obtained. Considering the lightweight design and stress concentration problems, a multiobjective intelligent cooperative design (MOICD) method for the multilayer interference fit is proposed, and multiparameter analysis is done. Taking the typical wind turbine’s shrink disk of three-layer interference fit structure as an application example, the key design parameters of the shrink disk are determined, and its sample data are obtained using the orthogonal experimental method. Considering yield strength, torque, and mass, the approximate mathematical model of response surface using the Kriging algorithm is given. Nondominated sorting genetic algorithm-II (NSGA-II) is selected as the optimal algorithm to realize MOICD of the shrink disk. Numerical analysis and analytical calculation proved that the optimization index of the MOICD method is improved compared with the traditional method. The sample is tested on a specific test bench, and the test results meet the design requirements, which verifies the feasibility of MOICD.

Stressed State of a Quasiorthotropic Half Plane with Curvilinear Edge

By the method of singular integral equations, we consider a plane periodic problem of the theory of elasticity for a quasiorthotropic half plane containing an infinite row of edge angular rounded notches. By using the unified approach to the solution of the problems of stress concentration near notches with sharp and rounded vertices, we determine the stress intensity factors at the sharp tips of the corresponding edge notches. The same method is used for the solution of the problem of stress distribution in a quasiorthotropic half plane with sinusoidal edge.

Design and application of integrated parabolic soft actuator

PurposeThe purpose of this paper is to solve the common problems of outer phenomenon and stress concentration among pneumatic networks soft actuators.Design/methodology/approachOn the basis of imitating the caterpillar structure, the new soft actuator adopts the integral circular ladder structure instead of the traditional independent distributed structure as the air chamber. Through the comparison of several different structures, the parabolic in-wall curve is found to be fit for designing the optimal integrated chamber structure of the soft actuator. The curve function of each ladder chamber is computed based on the torque distribution model, aiming to decrease the terminal deformation. Meanwhile, the FEM analysis method is applied to establish the motion model of the integrated parabolic ladder soft actuator. The model’s accuracy, as well as structure’s deformation and stress, are verified.FindingsCompared with the FEM data, the experimental data indicate that the new soft actuator has no obvious outer phenomenon, the maximum stress decreases and the stiffness increases. The new actuator is applied for designing a flexible gripper to grasp objects of different shapes and sizes. The gripper can grasp objects of 52.6 times its own mass.Practical implicationsThe designed gripper is available for flexible production in various fields, such as capturing fruits of different sizes, soft foods or parts with complex shapes.Originality/valueThis paper proposes a new type soft actuator, which provides a solution for exploring the field of the soft robot. The problems of outer phenomenon and stress concentration are suppressed with pneumatic networks soft actuators.

Adaptive finite element analysis with local mesh refinement based on a posteriori error estimate of element energy projection technique

PurposeThis study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.Design/methodology/approachIn view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.FindingsRepresentative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.Originality/valueThe proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.

Geotechnical localization analysis based on Cosserat continuum theory and second-order cone programming optimized finite element method

Based on the Hellinger-Reissner mixed variational principle, a second-order cone programming optimized finite element method for elastic and elastoplastic analyses of Cosserat continuum (named CosFEM-SOCP) is proposed. To examine the correctness and effectiveness of CosFEM-SOCP, three well-known numerical examples are revisited. In the plane-strain elastic problem of stress concentration around a circular hole, the stress concentration factors calculated by CosFEM-SOCP are in good agreement with the existing solutions, and the correctness of CosFEM-SOCP can be verified. In the analysis of load-displacement response of a flexible strip footing resting on the soil ground, it is found that load-displacement response may be affected by the internal characteristic length lc, and generally a larger lc may result in a wider and deeper slip surface as well as more elements being included in the shear bands. From the plane-strain soil strip with the Drucker-Prager (DP) failure criterion subjected to the prescribed incremental displacement, it can also be observed that the pathologically mesh-dependent problem can be partially or even completely removed by employing CosFEM-SOCP, as long as the mesh is fine enough so that the average element size in the mesh discretization is smaller than lc.

Quadrilateral 2D linked-interpolation finite elements for micropolar continuum

Quadrilateral finite elements for linear micropolar continuum theory are developed using linked interpolation. In order to satisfy convergence criteria, the newly presented finite elements are modified using the Petrov–Galerkin method in which different interpolation is used for the test and trial functions. The elements are tested through four numerical examples consisting of a set of patch tests, a cantilever beam in pure bending and a stress concentration problem and compared with the analytical solution and quadrilateral micropolar finite elements with standard Lagrangian interpolation. In the higher-order patch test, the performance of the first-order element is significantly improved. However, since the problems analysed are already describable with quadratic polynomials, the enhancement due to linked interpolation for higher-order elements could not be highlighted. All the presented elements also faithfully reproduce the micropolar effects in the stress concentration analysis, but the enhancement here is negligible with respect to standard Lagrangian elements, since the higher-order polynomials in this example are not needed.