Theoretical Stress Research Articles

A new incremental calculated approach to predict maximum contact stress of compressed packer in large deformation

Compressed packer rubber is large deformation material, which endures biaxial contact friction between oil-pipe and casing-pipe in sitting and sealing process. Large-deformation theory analysis of rubber brings huge difficulties to solve, this is due to the material, geometry and contact non-linearity should be considered. In this article, the deformation of compressed packer rubber tube (CPRT) is divided into free deformation, unidirectional and bidirectional constrained deformations. Based on the theory of thick-wall-cylinder and the linear constitutive of rubber material segment, the CPRT mathematical model in different deformation processes is established and the influences of axial load, axial height of CPRT and contact friction coefficient of casing inner wall etc are considered. Based on incremental calculated approach, the mathematical model is solved. By comparing the results of the theoretical model with the results of finite element method and experimental results, it is found that the theoretical maximum contact stress is more conservative than the FEM and experimental solutions, so the sealing reliability of packer effectively predicted under the premise of allowable contact stress and the theoretical results can provide a lower limit reference value for the contact stress of the packer in the actual seal process. Meanwhile, the deviation of contact stress in FEM and theoretical value at z150 height of CPRT is among 1.13%∼4.90%, which can predict the contact stress in the compressed area near the stress concentration upper end-face of CPRT under the low friction factor, the results provide a reference for the compressed packer design.

Tearing behaviors of polytetrafluoroethylene coated fabric under uniaxial in-plane tearing tests

This study conducts alternative-basic-angle trapezoidal tearing and single-edge notch tearing tests on a polytetrafluoroethylene coated woven fabric, where the two methods are related through the basic angle of a trapezoid. The tearing process and failure modes are carefully examined, and load–displacement curves and tearing strength are analyzed. The tearing process comprises three stages, which are distinguished photographically or in different load–displacement curve sections. Corresponding to these stages, failure modes can be classified into three parts with varying extension directions. The effect of the basic angle is clearly illustrated. As the angle increases, three stages and parts appear in sequence; the tearing strength increases, but the larger one changes from weft to warp. The relationship between the tearing process and tearing strength is described. The three stages correspond to the increase in tearing strength, occurrence of the maximum tearing strength, and failure. Because the single-edge notch tearing method is more complex and important, it is the method that is studied mainly. Digital image correlation equipment is used to observe the strain distribution at the crack section. Moreover, the applications of four frequently used models are investigated. The results indicate that Thiele’s empirical formula offers the best simulation among the three tearing strength prediction models, and the theoretical stress distribution model also provides good simulation. Furthermore, a numerical simulation is conducted. The critical tearing strength and load–displacement curves before tearing initiates acquired through the simulation and test agree well. All results may provide basic data for future improvements in design theories.

Psychosocial stress at work and disease risks : Scientific evidence and implications for practice

The modern working world makes a significant contribution to the development of diseases, which goes far beyond the field of traditional occupational diseases. Despite technological progress and successful medical healthcare, distinct widely disseminated psychosocial working conditions contribute to aremarkable burden of work-related diseases. By inducing chronic activation of psychobiological stress reactions, they promote the development of various physical and mental disorders. To identify "toxic" constellations within the complexity and variability of modern work environments, atheoretical model is required. It aims at delineating core critical elements at alevel of generalization that enables their identification in awide range of occupations. This article describes the leading theoretical work stress models in the international research and it demonstrates their contribution towards explaining elevated disease risks among employees. Research based on prospective epidemiologic cohort studies focused specifically on depressive disorders and coronary heart diseases. Two theoretical concepts received particular attention, the demand-control and the effort-reward imbalance models. Results derived from meta-analyses indicate increased relative risks of these disorders in the range of 35-80% among those exposed to these stressors compared to nonexposed groups. Finally, practical implications of this scientific evidence for worksite screening and health promoting activities are discussed.

Effects of Co and Co + Mo additions on tensile properties of tungsten heavy alloys: first-principles study and experimental investigations

ABSTRACT The present work illustrates the deformation behaviour of tungsten heavy alloys (WHAs) using first-principles calculation under tensile stress of three virtual alloy systems comprising the matrix phase and a W-grain along with two fcc–bcc interfaces. The energy values of the alloy systems decrease with the additions of Co and Co + Mo in the ternary alloy (W–Ni–Fe). The experimental lattice parameters of the matrix phase of alloys are in good agreement with those of the alloy systems calculated using the first-principles calculation. The lattice constants, yield strength and strength at 20% strain increase with the additions of Co and Co + Mo. The nature of theoretical stress–strain curves of systems is similar to those of the experimental stress–strain curves of typical alloys. The nitty-gritty of virtual alloy systems and the interrelated consequences resulting in closer to real alloys in terms of tensile flow curves have been discussed.

Influence of different corrosion environments on mechanical properties of a roadbed rehabilitation polyurethane grouting material under uniaxial compression

The mechanical properties of the roadbed rehabilitation polyurethane (PU) grouting materials subjected to different chemical corrosion are the theoretical basis for evaluating the long-term performance, which, however, is not clear yet. Here, the PU grouting materials with different densities were immersed in water, H2SO4, HCl, and NaOH solutions for different times, followed by the P-wave velocity tests and uniaxial compression tests. The influences of different corrosion environments on the damage and uniaxial compressive strength of PU samples were analyzed, and the statistical damage constitutive model under the coupling effects of chemical corrosion and the external load was established. Results show that the water brings little influence whereas both the acid and alkaline environments degrade the strength of PU grouting materials, and the longer the chemical corrosion time is, the greater the decrease in strength. The maximum declines in the yield strength of PU samples corroded by H2SO4, HCl, and NaOH solutions are about 32.8%, 31.3%, and 21.4%, respectively. The theoretical stress–strain curves based on the statistical damage constitutive model are in agreement with the experimental ones before yielding (with the average difference of 0.077–1.017 MPa), indicating the rationality of the theoretical model.

Dynamic Cutting Force and Stress Distribution of Carbide Insert during Asymmetric Milling of 508III Steel

In the milling process of water chamber head, the service life of cemented carbide inserts is low, and inserts are prone to premature breakage and impact fracture. Dynamic cutting force is one of the main factors leading to insert failure. In this paper, a dynamic cutting force model is established based on the characteristics of asymmetric milling of water chamber head and the characterization of cutting area variables. By comparing the calculated value with the experimental value, the model can describe the change of dynamic cutting force. Through theoretical analysis and insert stress distribution simulation, it is found that under the impact load of cutting force, the radial tension stress between the compression zone and the stretching zone is the main reason for the insert to crack and break. The results of this paper provide reference for the study of carbide insert failure.

Preparation and characterization of ultra-high-strength and ultra-high-ductility cementitious composites incorporating waste clay brick powder

Large quantities of waste clay bricks from construction and demolition (C&D) waste are currently stockpiled in landfills, which is an environmentally, technically, and economically detrimental procedure. In this work, waste clay bricks powder (WCBP) was assessed to determine its feasibility as an alternative to cement for ultra-high-strength and ultra-high ductility cementitious composites (UHS-UHDCCs). The influences of WCBP on the fluidity, hydration, mechanical properties, fiber/matrix interface performances, autogenous shrinkage, and ecological overload capacity of UHS-UHDCC with different replacement levels ranging from 0 to 50% were investigated. The results indicate that WCBPs reduce the fluidity of the UHS-UHDCC matrix. WCBP content of 20% slightly accelerates the hydration process and exhibits the highest compressive and flexural strength in the specimens. Moreover, all UHS-UHDCCs achieve strain-hardening characteristics and exhibit a tensile strain capacity of 3.18–5.47%. UHS-UHDCC with 20% WCBP obtains excellent ultimate tensile stress and tensile strain capability, reaching around 9.34 MPa and 3.18%, respectively. The performance of the interface frictional bond (τ) with different WCBP content was obtained through single-fiber pullout tests, which reasonably explained the macroscopic tensile properties of UHS-UHDCC. The average interface frictional bond (τ) between the fiber and matrix of UHS-UHDCC reaches the maximum 1.72 MPa in the WCBP20 specimen. The average slip hardening coefficient (β) of UHS-UHDCC is distributed between 0.0031 and 0.0075 and tends to be excellent in the WCBP20 specimen. The theoretical fiber bridging stress vs crack displacement relationship of UHS-UHDCC was calculated through the limitation of interface parameters, which had an excellent correlation with the experimental results. Furthermore, the introduction of WCBP remarkably reduces the autogenous shrinkage of UHS-UHDCC. The ecological overload capacity of UHS-UHDCC is decreased by the introduction of WCBP, which provides an environmentally friendly solution for the C&D and cement industries.

On the relationship between right‐wing attitudes, conspiracy beliefs, and intergroup threat: Introducing an indirect measure for intergroup threat

Recent theoretical models stress the importance of both personal and contextual factors in the development of political extremism. One such theory is the Intergroup Threat Theory (ITT) that suggests a relationship between extremism and intergroup threat (i.e., the perception that one's ingroup is threatened by a particular social outgroup). Using an adaptation of the Semantic Misattribution Procedure (SMP), the present research aimed at replicating the results of previous studies using a novel measure. In a first study (N = 88, 77% female), self-reported intergroup threat was significantly and positively related to two types of extreme political attitudes, namely, right-wing authoritarianism and generic conspiracy beliefs. The SMP score, in contrast, was only significantly correlated to right-wing authoritarianism. In a second study, these results were replicated in a larger sample (N = 243, 68% female). Moreover, both self-reported and indirectly measured intergroup threat were related to hostile attitudes and stereotypes against immigrants. When compared to explicit intergroup threat, however, the SMP score was not incremental in the prediction of hostile attitudes against immigrants. These results support the validity of the SMP for the assessment of intergroup threat. Replications should explore the practical utility of the SMP in other samples using additional validation criteria.

Constitutive relations of micro-arc oxidation coated aluminum alloy

The stress and displacement of the coating and substrate were analyzed according to the constructive relations of the micro-arc oxidation (MAO) coated aluminum alloy. Effect of the yielding of the interlayer and substrate on the constructive relations was explored. This study revealed the changes in displacement relationship between the coating and substrate under high and low tensile stresses. The yielding of the interlayer resulted in the displacement of the coating to be lower than that of the substrate. The results provided a theoretical basis for the residual stress relaxation, the larger plastic deformation zone found in the substrate adjacent to the MAO coating, and the disappearance of pores and the closure of cracks on the coating surface. The strain of the coating surface was measured using the YE2539 high-speed strain gauge and BX120-5AA strain gauge. The theoretical stress of the coating surface was compared with the measured results, exhibiting good consistency. Furthermore, the results of the in-situ observation test in previous study verified the rationality of the theoretical model analysis. In addition, the effect of the residual stress on the mechanical properties of the MAO coated samples was discussed. The residual compressive stress in MAO coating was beneficial to the improvement of the mechanical properties.

Simulation Analysis and Experimental Study on the Working State of Sinking Headframe in the Large Underground Shaft

Based on the newly developed sinking headframe for the deep and large shaft, the finite element model of the full-scale headframe was established by using SAP2000. Through the calculation, the theoretical stress of the headframe at sinking depths of 40 m, 143 m, 223 m, 518 m, 762 m, 1000 m, 1250 m, and 1503 m was obtained and then compared with the field measured stress. The results show that with the increase of shaft sinking depth, the theoretical stress of finite element simulation and the field measured stress of each member of the sheave wheel platform and the headframe increase linearly, and for the maximum member stress in the upper, middle, and lower layers of the headframe, the numerical simulation value is greater than the field measured value and less than the designed steel strength. In other words, under normal working conditions, headframe members are in the elastic stress stage and meet the design requirements, and instability failure of headframe members will not occur. The end-restraint mode of the supporting bars has a great influence on the force of the top member. The reasonable selection of the restraint mode in the simulation is the key to the accuracy of the calculation results. The simulation results well reflect the actual stress of the headframe and provide a reliable guarantee for the follow-up work of the project.

Investigation of the effect of blank holder force distribution on deep drawing using developed blank holder divided into double rings

A new blank holder divided into double rings is proposed, in which the blank holder force (BHF) can be independently and effectively applied on different flange regions. In this paper, the principle and characteristics of the new blank holder technique are expatiated by theoretical derivation and stress analysis. All results indicate that the distribution of BHF applied by the double rings blank holder is more reasonable than a single blank holder under the condition of proper parameter selection, and the wrinkling can be better suppressed. The effectiveness of the double rings blank holder has been proven by deep drawing experiments. Using the new blank holder technique, the flange wrinkling was demonstrated to be more eliminated than that using the single blank holder. Moreover, experimental results also corroborate that the parameters of BHF distribution ratio and the boundary diameter of the two rings have a great influence on the effects of the new blank holder technique.

New approach in constitutive modelling of commercially pure titanium thermo-mechanical processing

The pure titanium, as a biomaterial destined for production of load-demanding prostheses, requires thermo-mechanical processing to increase its strength. The most common way to achieve this is the method of grain fragmentation. Thermo-mechanical deformation of titanium is a complex process, which makes it very difficult to describe it by means of constitutive equations. Such constitutive relations are very useful as they can be implemented in the finite element method tools in order to simulate and optimize the whole process. Cylindrical specimens were compressed at elevated temperatures on a thermo-mechanical simulator. The tests were performed at four different strain rates (from 10^{mathrm {-2}} s^{mathrm {-1}} to 10 s^{mathrm {-1}}) and at 775 K and 875 K temperatures. The collected data allowed us to create strain–stress graphs characterizing the process. Observations on the scanning electron microscope and scanning transmission electron microscope were done as well as the electron backscatter diffraction analysis, revealing significant grain fragmentation. The aim of the studies described in the paper was to verify and select a proper mathematical model for the process of titanium grain fragmentation obtained in a thermoplastic process. Four different constitutive models were considered. The calculation of theoretical stress values based on the Arrhenius-type equation, Anand viscoplastic model, Johnson–Cook model and Khan Huang-Liang model was done and compared to experimental results. The theoretical curves were generated and fitted to experimental, which made it possible to calibrate the constants in the mathematical models. The curve-fitting analyses showed that the Anand constitutive model described the titanium behaviour best.

Dynamic strain aging of an AISI 1025 steel coil and its relationship with macroscopic responses during the upsetting process

In this paper, dynamic strain aging (DSA) of an AISI 1025 steel coil and related strain hardening behavior are described, including their macroscopic effects. A cylinder compression test was conducted for various sample temperatures and strain rates ranging from 20°C to 500°C and 1/s to 20/s, respectively. The experimental flow stress data were indicative of typical DSA, which caused serrated flow; this was verified by the strain hardening rate obtained from the Kocks-Mecking hardening model. The experimental data were mathematically fitted by a simple but general power law model, with piecewise bi-linear functions of sample temperature and strain for both the strength constant and strain rate sensitivity exponent. The flow stresses extracted from JMatPro were used as the theoretical flow stresses for comparison with fitted flow stresses associated with DSA, to characterize the effects. The fitted flow stresses were validated experimentally by compression tests conducted at various sample temperatures and strain rates; the varying conditions had a negligible effect despite the complexities in the flow stress due to DSA. An instability index was proposed to evaluate the macroscopic effect of DSA on upsetting processes in non-isothermal cylinder compression tests. This index was used to quantify the macroscopic plastic deformation behavior of the material with DSA.

Dynamic Analysis Of Hydraulic Actuated Mandrel

Machining is an important part of the manufacturing process, as it involves precise metal removal to achieve quality, accuracy, and precision. The proper selection of cutting tools and work holding devices is essential in machining. In the manufacturing process, a work holding device is crucial. A mandrel is a work holding device that is used to grip a component during machining at high speeds and low feeds. The current work describes the design of a Hydraulic Actuated Mandrel, which is a useful work-holding device that firmly grips the work piece. The proposed material for the mandrel manufacture is Chromium Vanadium steel, because it provides uniform gripping forces and leaves no residual stresses on the work piece. Empirical relationships are used to calculate the forces and pressures exerted by the cutting tool on the work piece and the work holding device. The theory of thin cylinders is used to calculate the theoretical maximum hoop and longitudinal stresses. ANSYS software is used to create the statical model. The developed model was assessed by applying forces and pressures to the mandrel, which results in deformations and stresses. The theoretical stresses on the mandrel are compared to the stresses obtained from ANSYS. The correlation between the two analyses is found to be satisfactory. Modal analysis is used to obtain the natural frequencies and mode shapes for the same model, which are also useful for dynamic analysis. To determine the dynamic response of a structure under the action of dynamic loads, the “Mode Superposition Transient Dynamic Analysis” method is used. By using the natural frequencies and mode shapes obtained from modal analysis the dynamic analysis is done in ANSYS on the model. At various nodes, time-varying deformations are obtained. The deformations obtained in dynamic analysis at various nodes are compared to those obtained in static analysis. The level of agreement between them is deemed to be reasonable.

A New Type of Hierarchical Honeycomb in-Plane Impact Study.

Honeycomb materials have low density, high specific strength and stiffness, impact resistance, and good sound insulation effect, and therefore are widely used in aerospace, automobile, and ship field applications. In this paper, we study the in-plane impact response of a second-order hierarchical honeycomb (SHH) material. Its main structure is a hexagonal honeycomb, and the substructure is composed of an augmented double arrow honeycomb (ADAH) negative Poisson’s ratio unit. Through a finite element simulation, the failure stress of an hierarchical honeycomb in two directions of quasi-static crushing and dynamic crushing was analyzed; the failure stress of the hierarchical honeycomb under different densities, different speeds, and different substructures was discussed; and the theoretical failure stress was verified. The numerical analysis results show that a second-order hierarchical honeycomb (SHH) has better collapse stress than a first-order regular hexagonal honeycomb (FHH) and an augmented double arrow honeycomb (ADAH).

Stress–Strain Behaviour of Bacterial Concrete Incorporated With Sugarcane Fibres

Bacterial concrete is one of the methods of rectifying the micro-cracks developed in the structural elements made of concrete. The gram-positive type bacteria Bacillus subtilis when acquainted with concrete produces calcite precipitation which heals the micro cracks in the concrete. Bacillus subtilis was used with a cell concentration of 106. The optimised percentage replacement of fine aggregates with sugarcane fibres of grain size less than 4.75 mm was 0.1 %. The effect of sugarcane fibres on the durability of bacterial concrete is presented in this paper.To study the Stress -Strain behaviour of Sugarcane based Bacterial concrete (SBC), appropriate analytic SS model is developed that resembles the experimental behaviour of the various samples such as Conventional Concrete (CC), Bacterial Concrete (BC) and SBC. This work mainly targets on utilizing the earlier models and offers a new SS model that can well represent the actual SS behaviour of SBC samples. After finding the SS behaviour of CC, BC and SBC specimens experimentally, equations are developed to characterise axial SS behaviour of CC, BC and SBC samples. From these mathematical equations, theoretical stress for CC, BC and SBC are calculated and compared with test values. The proposed equations have exposed good connection with test values authorizing the mathematical model developed.

Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques

Machine parts always work under different types of stresses or loading conditions. The sudden dimensional changes lead to sudden increase in stress on the critical section of the machine parts. This state is defined as stress concentration factor (SCF). The strength of the machine part decreases on the located point at maximum stress. In this study, SCFs of circular/elliptical holes with bead reinforcement in an infinite panel under uniaxial and biaxial stresses were modeled, simulated, calculated and verified using analytical, finite element analysis (FEA) and artificial neural networks (ANN) techniques. This study presents a new model for predicting SCF for panels using artificial intelligence techniques under uniaxial and biaxial loading conditions. Theoretical SCF (Kt) values for different shapes and loading conditions have been compiled and graphical forms of these experimental results were published by Peterson (Peterson’s stress concentration factors, 3rd edn. Wiley, Hoboken, 2007). There is a need to convert these curves into a numerical data set to be used in machine part design easily. Theoretical SCF (Kt) was obtained from the Peterson’s charts in numerical form according to dimensional parameter ratios using high-accuracy graphical computer software. Using these dimensional parameter ratios, a parametric finite element model (FEM) was created. Uniaxial and biaxial boundary conditions were applied to the FEM model. Mesh optimization was accomplished to the parametric FEM model. Mesh formation is compatible with the model according to dimensional sizes and ratios. Mesh optimization was provided to element size and per unit volume. Numerical and FEA results were tested, approved and confirmed with Peterson’s original data using statistical methods. A code was created for the improvement of the ANN model in the Matlab ANN Toolbox Editor. Different ANN model variations were tested and the best-performing ANN model was determined among the tried models. Numerical, FEA and ANN model results were compared and confirmed with one another. The developed model provides an easy method to predict and calculate the stress in defining the Kt according to dimensional ratios and applied loading states (uniaxial/biaxial).

Research on a Novel Non-contact Metrology Technology of Stress Measurement Based on Deflection Method

With the aerospace and aviation industry development, machining deformation is the most prominent and urgent problem in the production process. Studies have shown that initial residual stress (RS) is the main factor causing the deformation of this type of part. Since residual stresses must be analyzed quantitatively, a series of measurement methods have been developed for this purpose. Remarkably, a series of measurement technologies inevitably need to include the corresponding calibration process, which is the fundamental element to ensure RS measurement accuracy. In this investigation, we developed a non-contact stress calibration method based on deflection value to study the measurement deviation of forging residual stress in the aerospace field. The constant stress beam (CSB) mechanical and finite element models of Ti6Al4V titanium alloy were established. The deflection measurement method was implemented using the visual system based on pattern speckle technology. A high precision loading device was developed to provide an accurate external load for CSB. A novel calibration technology based on the deflection method was proposed to realize RS measurement’s calibration process. We have successfully applied the CSB bending test campaigns and deflection metrology method to calibrate the stress values measured by the Static strain measuring instrument of Sigma and the Stress measuring instrument of Proto-ixrd. The results of theoretical and simulation stress are highly consistent with the calibration experiment. Calibration experiments combining the pattern speckle technology and the deflection method allow the stress measurement process’s calibration according to the correction factor. The research provides a great impetus to the development of precise quantitative measurement of RS.

Failure analysis of an in-vivo fractured patient-specific Ti6Al4V mandible reconstruction plate fabricated by selective laser melting

Fatigue fracture of titanium alloys fabricated by Selective Laser Melting (SLM) in engineering has been studied in recent years, but an underlying understanding of the in-vivo fatigue fracture of SLM-fabricated titanium patient-specific implants (PSIs) is rarely revealed due to the complex in-vivo biomechanical behaviour and biological environment combined. This paper provides a multidimensional and comprehensive analysis of the in-vivo fatigue failure mechanism of an SLM-fabricated Ti6Al4V mandible reconstruction plate, by macro-scaled Finite Element Analysis (FEA) of biomechanical behaviours, static force analysis and micro-scaled metallurgical investigation. FEA indicates maximal tensile stress of 392.6 MPa locally on the implant with high stress gradients around. Although the theoretical stress is far below the fatigue strength of SLM-fabricated Ti6Al4V material, indicating low potential of plate failure, the site with maximal stress and high stress gradients successfully determine the failure route of the plate, which coincides with the factual crack growth mode on the plate. The followed analysis of stress and force conditions theoretically confirms the failure condition on the implant. Metallurgical investigations further show β and α/α’ phases and tiny pores at implant (sub)surface, together with typical features (striations, cleavage facets and dimples) of metal fatigue failure in fractography analysis. Taken together these can conclude that the fatigue crack initiates from the implant surface subjected to surface defects and maximal stress caused by implant design, and propagates radially, showing a combined brittle/ductile fracture mode. The process is synergistically influenced by Ca/P/O deposits and hydrogen embrittlement under the biological environment. Practical measures for the improvement of in-vivo fatigue life of implants are finally provided.

Failure Mechanical Characteristics of Rock with Different Hole Shapes

Due to the role of geological structure, the underground rock contains a large number of holes. In order to study the influence of the hole on the mechanical characteristics of the rock failure, the numerical simulation analysis of the intact rock and the rock with three shapes holes(circle, square, triangle) are carried out by using PFC2D. The results show that the rock strength varies with the shape of the hole. Circular holes have the least impact on strength and triangles have the greatest impact. At the same time, different holes shapes have different failure morphology, the intact rock sample forms a penetrating fracture zone inclined by 60°. For the circular hole, forms a through-fracture zone along the upper left and lower right corners. The square hole sample forms an "X"-shaped fracture zone along the four corners. For the triangular holes sample, the damage occurs first at the two positions of the left and right foot of the hole, and then the fracture zone is formed along the upper right corner and the two feet of the sample. Finally, theoretical analysis of stress distribution characteristics around the rock with circular holes is carried out. The compressive stress concentration occurs on the left and right sides of the circular hole, the tensile stress concentration occurs at the top and bottom boundary of the hole. And the tensile crack occurs at the top and bottom of the hole, tensile and shear mixed cracks appear on the left and right sides of the hole from numerical simulation. The crack distribution of numerical simulation is consistent with the theoretical stress analysis results.