Elasto-plastic Analysis Method Research Articles

A stochastic LATIN method for stochastic and parameterized elastoplastic analysis

The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or parameterized elastoplastic problems. To this end, the stochastic solution is decoupled into spatial, temporal and stochastic spaces, and approximated by the sum of a set of products of triplets of spatial functions, temporal functions and random variables. Each triplet is then calculated in a greedy way using a stochastic LATIN iteration. The high efficiency of the proposed method relies on two aspects: The nonlinearity is efficiently handled by inheriting advantages of the classical LATIN method, and the randomness and/or parameters are effectively treated by a sample-based approximation of stochastic spaces. Further, the proposed method is not sensitive to the stochastic and/or parametric dimensions of inputs due to the sample description of stochastic spaces. It can thus be applied to high-dimensional stochastic and parameterized problems. Five numerical examples demonstrate the promising performance of the proposed stochastic LATIN method.

Cluster-based Nonuniform Transformation Field Analysis of Gra-phene nanocomposites

Graphene nanocomposites have attracted much attention in materials science due to their superior me-chanical properties. It is difficult for conventional mul-tiscale methods to provide substantial assistance to the research of such materials due to their huge computa-tional costs. Nonuniform transformation field analysis is a very effective reduced order homogenization meth-od for elastoplastic multiscale analysis. However, the reduced order model derived from this method has the shortcoming of low universality and high application threshold. Therefore, an improved reduced order model is proposed by combining the nonuniform transfor-mation field analysis with the k-means clustering algo-rithm. One can embed the required microscopic consti-tutive model into the reduced order homogenization framework without the need to derive a new reduced order model. Based on the cluster-based nonuniform transformation field analysis, the influence of the mi-croscopic plastic strain field evolution on the macro-scopic response of the material under consideration is revealed, while the mechanical properties of graphene nanocomposites are predicted. The numerical results show that the new reduced order model can accurately predict the macroscopic mechanical properties of com-posite materials, and its acceleration rate compared to the traditional finite element computations reaches103-104 .
 Keywords:graphene nanocomposites; reduced order model; multiscale methods; clustering; nonuniform transfomation field analysis

An h-adaptive edge-based smoothed point interpolation method for elasto-plastic analysis of saturated porous media

This study presents the first application of the edge-based smoothed point interpolation method (ESPIM) for adaptive analysis of coupled elasto-plastic problems in saturated porous media. The original ESPIM is enhanced with an adaptive strategy involving an automated h-refinement scheme, a simple, yet effective, recovery-based error indicator, and an efficient data transfer scheme to analyse coupled elasto-plastic problems in geomechanics. The governing equations are presented and discretised in space and time to yield the fully coupled system of equations. The solution strategy is then discussed in terms of handling the material non-linearity, and accommodating the proposed adaptivity procedure in the numerical algorithm. Four numerical examples comprising two different bearing capacity problems, a two-dimensional consolidation problem, and a slope stability analysis are thoroughly investigated. Different adaptive analyses with a range of adaptivity control parameters are investigated in each example and the performances of different techniques are compared in terms of accuracy and the time of the analysis. The results show the ability of the proposed adaptive analyses in yielding accurate and efficient results. Conclusions are drawn in terms of the most efficient numerical set-up to solve non-linear problems in porous media using the proposed numerical scheme.

Active Earth Pressure against Cantilever Retaining Walls with a Long Relief Shelf in Rotation about the Top

A cantilever retaining wall with a long relief shelf (CRW-LRS) is a particular type of retaining wall, but no studies have yet reported on rotation about the top of this type of retaining wall. This work studied failure mechanisms in semi-infinite non-cohesive soils in rotation about the top using the finite element elastoplastic analysis method (FEEA). By considering the influence of both the relief shelf and rotational stress from the soil, a formula for calculating the active earth pressure (Ea) was developed using the horizontal differential layer limit analysis method. Four different parameters were studied, i.e., unloading plate's geometric conditions, heel length and the internal friction angle of the backfill, in terms of their influence on the Ea distribution, resultant force etc. The lowest Ea was found when the relief shelf' relative position m = 0.4.

Application of generalized finite difference method for elastoplastic torsion analysis of prismatic bars

In this paper, the generalized finite difference method (GFDM) is employed for the elastic-plastic torsion analysis of prismatic bars, and the generalized finite difference numerical scheme of the elastic-plastic torsion governing equation is derived. This approach divides the computational domain into a series of overlapping sub-domains and constructs a system of linear equations based on Taylor series expansion and moving least squares. With the help of Picard's iterative method, the elastic solution is utilized as the initial guess to reach the elastic-plastic solution. The plastic nonhomogeneous term is then evaluated via radial basis function (RBF) interpolation. Since the generalized finite difference method does not require intra-domain integration and allows random distribution of nodes, it could simply deal with complex computational domain problems. In numerical experiments, the elastic-plastic torsion examples of square-section bars and linear guide rail reveal that the numerically developed generalized finite difference model is a reliable and effective analysis solution for elastic-plastic torsion problems of prismatic bars.

Simplified Elastoplastic Fatigue Correction Factor Analysis Approach Based on Minimum Conservative Margin

ASME and RCC-M codes specify an elastoplastic fatigue analysis technique: a simplified elastoplastic fatigue analysis method based on linear elastic analysis. In this method, the elastic strain range is multiplied by the elastoplastic correction factor (Ke) to envelope the actual plastic strain range for fatigue evaluation. The ASME or RCC-M provide the Ke parameters of typical materials, such as austenitic stainless steel and low alloy steel. However, how can the parameters of the material not included in the codes be determined? Based on the existing material Z2CND18.12 (nitrogen control) in the codes and taking into account various sensitive factors, the minimum conservative margin of Ke for this material is calculated, and then the parameters of nonstandard materials are determined iteratively based on the conservative margin. The sensitive factors include the different structure model, load types, the loading control mode, temperature value and the material constitutive model. Based this approach, the Ke parameters of TA16 are determined and verified by the transient with drastic change in temperature and pressure. The results of the case show that the simplified elastoplastic fatigue analysis can envelope the results of cyclic plastic fatigue analysis. The minimum margin approach established in this paper can reasonably determine the Ke value of materials beyond the ASME and RCC-M codes.

Experimental research on seismic performance of steel fiber-reinforced recycled concrete-filled circular steel tube columns

To study the seismic performance of steel fiber-reinforced recycled concrete-filled steel tube (SRACFST) columns, 14 circular specimens with different replacement rates (Rp) of recycled coarse aggregate (RCA), volume fractions (Vf) of steel fiber, axial compression ratios (n), steel tube thickness (t), and concrete strengths were tested to failure under constant axial and lateral cyclic loads. All the specimens exhibited a similar typical compression bending failure mode. Subsequently, the effect of different parameters on the various seismic characteristics in terms of the lateral load-displacement (P−Δ) hysteresis curve, skeleton curve, ductility, stiffness degradation, strength degradation and energy dissipation were obtained and studied comprehensively. The results indicated that the addition of steel fiber to core concrete can effectively compensate for the marginal negative influence of the defects of recycled aggregate concrete (RAC). Furthermore, the lateral bearing capacity, ductility, and energy dissipation capacity were improved as the steel fiber fraction increased. An increase in the thickness of the steel tube resulted in a remarkable improvement in the overall seismic behaviour. However, a higher axial compression ratio resulted in inferior seismic performance, particularly in terms of the deformation capacity and ductility. The bearing capacity and energy dissipation improved as the concrete strength increased. However, the ductility, stiffness stability, and strength stability weakened. The equivalent viscous damping index corresponding near failure attained 0.281–0.414, and the ductility was higher than 3.0. This demonstrated that the SRACFST columns could be used in load-bearing structures in seismic regions. The Code AIJ-2001 was recommended to calculate the compression bending bearing capacity of SRACFST columns under cyclic seismic loading, with an expansion index of 1.15 for calculation accuracy. Further, the fiber modelling (FM) method was established to predict the skeleton curves. The calculated results matched the experimental results well, and this indicated the relevance of this method for further elastoplastic analysis of SRACFST columns during earthquakes.

Evaluation of Energy Dissipation in Pipe Supports through Parametric Analysis

Elasto-plastic response analysis of pipe systems including the pipe supports is necessary to evaluate the seismic fragility for input seismic motions exceeding the design assumptions. However, the elasto-plastic response analysis method for pipe supports has not been developed yet. In this study, we aim to develop the elasto-plastic response analysis method for pipe supports by focusing on the non-linearity of the load-displacement characteristics. We also conduct parametric analyses on the material properties, etc., for existing loading tests. This paper reports the quantitative computing for energy dissipation with the load-displacement characteristic curves obtained via the analyses, and the comparison between the analytic results and experimental results.

Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region

In order to study the residual strength of buried pipelines with internal corrosion defects in seasonally frozen soil regions, we established a thermo-mechanical coupling model of a buried pipeline under differential frost heave by using the finite element elastoplastic analysis method. The material nonlinearity and geometric nonlinearity were considered as the basis of analysis. Firstly, the location of the maximum Mises equivalent stress in the inner wall of the buried non-corroded pipeline was determined. Furthermore, the residual strength of the buried pipeline with corrosion defects and the stress state of internal corrosion area in the pipeline under different defect parameters was analyzed by the orthogonal design method. Based on the data results of the finite element simulation calculation, the prediction formula of residual strength of buried pipelines with internal corrosion defects was obtained by SPSS (Statistical Product and Service Solutions) fitting. The prediction results were analyzed in comparison with the evaluation results of B31G, DNV RP-F101 and the experimental data of hydraulic blasting. The rationality of the finite element model and the accuracy of the fitting formula were verified. The results show that the effect degree of main factors on residual strength was in order of corrosion depth, corrosion length, and corrosion width. when the corrosion length exceeds 600 mm, which affects the influence degree of residual strength will gradually decrease. the prediction error of the fitting formula is small and the distribution is uniform, it can meet the prediction requirements of failure pressure of buried pipelines with internal corrosion defects in seasonally frozen soil regions. This method may provide some useful theoretical reference for the simulation real-time monitoring and safety analysis in the pipeline operation stage.

Preliminary Design for the First Wall in Low Magnetic Side of HL-2M

Considering the risk of leakage and the complexity of processing technology, a passive cooling first wall has been developed in the low magnetic side. The anticipated heat flux limit of the first wall is about 0.3 MW/m2. In order to enhance thermal transfer, the main materials of the first wall is made of copper alloy (CuCrZr) and graphite tile. A layer of flexible graphite is placed in the interface of CuCrZr and graphite tile to increase thermal contact resistance. Transient thermal analysis has been used to predict the whole heat transfer process for normal operating discharge in a day. Through the simulation, we can get the temperature change history of each component in 24 hours. The temperature and stresses of the passive cooling first wall are found to be within the acceptable limits. The maximum temperature of this first wall is about 307 °C which appears on the graphite tile. The results of the maximum temperature distribution are imported into the structure for calculation. Finally, the elasto-plastic fatigue analysis method is used to check the structural analysis results, and the results show that the structure meets the high parameter discharge mode of more than 480,000 times.

New Elastoplastic Analysis of Two-Dimensional Frames When Some Plastic Hinges Unload Elastically

Two-dimensional frames are made of elastic and perfectly plastic materials. Frames are analized by using the step by step elastoplastic analysis method where the applied loads are gradually increased at each step until a plastic hinge is developed. Then an equivalent frame model is generated by placing a mechanical hinge at the location of the plastic hinge and the increased external loads and the reduced plastic moments acting at the plastic hinge sections are applied to this model and elastoplastic analysis is performed. This elastoplastic analysis is repeated by incrementally increasing the external loads and applying the new reduced plastic moments, until the next plastic hinge is developed. Then a new equivalent frame model is generated to search for the following plastic hinge. This step by step elastoplastic analysis continues until the frame partially or totally collapses. When a plastic hinge is developed, it means that the section is at a fully plastic stress state. In the following small load increment: if this fully plastic stress state moves to another fully plastic stress state then this movement is called plastic flow. But if this fully plastic stress state moves to an elastic–plastic stress state then this movement is called elastic unloading. During the search of the next plastic hinge if one of the plastic hinges begins to unload elastically then the current equivalent frame model must be revised. For this the frame member which contains the elastically unloading plastic hinge is replaced by the equivalent frame member carrying balancing loads.

A Study on the Friction Stir Welding Experiment and Simulation of the Fillet Joint of Extruded Aluminum Material of Electric Vehicle Frame

In the existing automobile manufacturing process, metal inert gas (MIG) and tungsten inert gas (TIG) welding are mainly used. These welding methods are fusion welding, and the heat input in the welding area is very high. Therefore, the deformation of the base material is large, and the residual stress in the vicinity of the welded area is high, resulting in the problem of reduced mechanical strength. In this study, friction stir welding (FSW) was applied to the welding process of the structure constituting the battery frame of a newly developing electric vehicle to compensate for this problem. The welded part is the fillet joint of the side frame and the bottom frame, and experiments and numerical analysis were performed on the welding deformation and residual stress of the full frame structure. A specially manufactured angle head was used for friction stir welding of the fillet joint of extruded type aluminum, not the existing solid type. The optimum process was derived through experiments, and the temperature of the welding center was derived through test correlation between the value of measured temperature and the finite element model. The final deformation result was verified by comparing it with the measured value using a dial indicator. It is expected that the proposed thermal elasto-plastic analysis method will reduce the testing period and the cost of the manufacturing process and increase productivity.

A New Semi-Analytical Method for Elasto-Plastic Analysis of a Deep Circular Tunnel Reinforced by Fully Grouted Passive Bolts

The use of fully grouted passive bolts as a reinforcement technique has been widely applied to improve the stability of tunnels. To analyze the behaviors of passive bolts and rock mass in a deep circular tunnel, a new semi-analytical solution is presented in this work based on the finite difference method. The rock mass was assumed to experience elastic–brittle–plastic behavior, and the linear Mohr–Coulomb criterion and the nonlinear generalized Hoek–Brown criterion were employed to govern the yielding of the rock mass. The interaction and decoupling between the rock mass and bolts were considered by using the spring–slider model. To simplify the analysis process, a bolted tunnel was divided into a bolted region and an unbolted region, while the contact stress at the bolted–unbolted interface and the rigid displacement of the bolts were obtained using two boundary conditions in combination with the bisection method. Comparisons show that the results obtained using the proposed solution agree well with those from the commercial numerical software and the in situ test. Finally, parametric analyses were performed to examine the effects of various reinforcement parameters on the tunnel’s stability. The proposed solution provided a fast but accurate estimation of the behavior of a reinforced deep circular tunnel for preliminary design purposes.

A new semi-numerical method for elastoplastic analysis of a circular tunnel excavated in a Hoek–Brown strain-softening rock mass considering the blast-induced damaged zone

Abstract Drill and blast method is mostly used method for excavation of tunnels throughout the world. This tunneling method involves the use of explosives. Compared with bored tunneling by Tunnel Boring Machine, blasting generally results in the development of a blast-induced damaged zone around the tunnel boundary. Theoretically, the presence of this zone, with its reduced strength and stiffness, will affect the overall performance of the tunnel, as well as its construction and maintenance. In fact, the extent of the damaged zone is finite. However, the effect of this zone is traditionally considered by a damage factor D applied to the entire rock mass surrounding the tunnel. This is a common modeling method which can greatly underestimate the strength and stability of the overall rock mass. In this paper, a semi-analytical solution is proposed for analysis of tunnels considering the damaged zone. The solution is presented for circular tunnels excavated in rock masses obeying a new proposed non-linear strain-softening behavior and the non- linear Hoek–Brown failure criterion. The damaged zone is assumed to have a cylindrical shape with reduced strength and deformability parameters.

Study on Static Elastoplastic Analysis of a High-Rise Frame-Shear Wall Structure

Static elastoplastic analysis is a widely used method to evaluate the seismic performance of structures. The project example in this paper is the high-rise frame-shear wall structure of the second phase (Yongsheng homeland) of the Baisha resettlement area in Zhengdong New Area. The three-dimensional integral model is used to calculate the force of the building under earthquake using the static elasto-plastic analysis method. Analysis was conducted to obtain the stress conditions of high-rise buildings against plastic deformation, and the sequence of the plastic hinges, and the unfavorable floors of the high-rise structure were identified, which provided guidance for the design of such structures.

Automatic scaled boundary finite element method for three-dimensional elastoplastic analysis

This paper introduces an automatic way of performing 3D static and dynamic elastoplastic analyses in the framework of the scaled boundary finite element method (SBFEM), which only requires the boundary discretization and thus can provide high flexibility in automatic mesh generation. The input models in this paper are described by Standard Tessellation Language (STL) format due to its simplicity and popularity in computer-aided design. The automatic mesh generation from any input geometry is achieved by utilizing the octree decomposition algorithm and boundary trimming. An efficient approach for 2D static image-based elastoplastic analysis based on SBFEM is extended to 3D static and dynamic elastoplastic analyses in this present work. In this improved approach, the return mapping algorithm is only required to be performed at the scaling center of each subdomain in the yield zone. Constant elastoplastic constitutive matrix and internal stresses are used within each yielded subdomain as well. This will greatly simplify the implementation of elastoplastic formulation and reduce the costs involved in the elastoplastic analysis as the return mapping algorithm is computationally expensive. Meanwhile, stabilization matrix is also introduced in the elastoplastic stiffness matrix to eliminate the spurious modes. Numerical examples are presented in this paper to show the feasibility and accuracy of the proposed approach as well as its capability of modelling complex structures in practical applications.

Welding Deformation Analysis, Using an Inherent Strain Method for Friction Stir Welded Electric Vehicle Aluminum Battery Housing, Considering Productivity

With the rise of electric vehicles, the use of battery modules, which are key units that drive vehicles, is increasing. The battery housing is the final form of a battery system mounted on electric vehicles, and is generally made of aluminum alloys, located at the bottom of the vehicle. The aluminum housing has a special shape to accommodate the battery module and is produced by welding extruded panels. This study applied friction stir welding (FSW) to weld 2.5 mm thin aluminum plates in order to improve the weldability and productivity. To increase productivity, we compared the mechanical properties after performing experiments under various FSW conditions. As a result, it was possible to derive speed-enabling welding conditions that can improve productivity without decreasing tensile strength. Deformation occurred in the structure during welding, causing gaps in the structure. Since these gaps have a significant influence on the degradation of mechanical properties after welding, the welding deformation at each step of welding must be calculated and reflected in the process. This study used the inherent strain method to calculate the deformation of each step of welding to apply automatic welding, and reduced the analysis time to 1/30 compared to the thermal elasto-plastic analysis method. Finally, this study verified the validity of the analysis method by comparing the experimental results with the numerical results using the inherent strain method.

Elastoplastic analysis of anchored tunnel under seepage

In order to study the stress and displacement distribution of surrounding rock of full-length bonded anchor support tunnel under seepage. The surrounding rock is regarded as a uniform and continuous porous medium. The supporting reaction force and seepage force of the surrounding rock are converted into the axisymmetric radial volume force of the circular tunnel and act on the stress field. Considering the reinforcement of the surrounding rock parameters by the bolt, the mechanical model is established. The elastoplastic analysis method is used to derive the analytical solution of the stress and displacement elasticity of the surrounding rock and plastic analytical solution based on Mohr-Coulomb yield criterion, which can be used to obtain the expression of the radius of the plastic zone of the tunnel and the displacement of the wall. Finally, the calculation results of this paper are compared with the numerical simulation analysis. The results show that the influence of the seepage on the plastic zone range and the wall displacement is more serious. The length and pretension of the bolt are inversely related to the plastic zone range and the displacement of the wall. The bolt row spacing is positively correlated with the plastic zone range and the displacement of the wall. Under the same conditions, considering the seepage requires the anchor to provide greater support. In order to avoid the instability of tunnel caused by seepage, the length of the bolt can be reasonably increased, the bolt spacing can be reduced, and the bolt pretension can be increased.

Elastoplastic Solutions to Predict Tunneling-Induced Load Redistribution and Deformation of Surface Structures

AbstractIn this paper, an elastoplastic two-stage analysis method is proposed to model tunneling-induced soil-structure interaction and incorporated into a computer program called Analysis of Struc...

Evaluation of seismic behavior of box culvert buried in the ground through centrifuge model tests and numerical analysis

Japan has yet to establish a seismic design for road box culverts (RBCs) because past major earthquakes did not damage them. In recent years, structures with enlarged sectional dimensions (the purpose of which is to optimize the internal space in RBCs) have become common. However, the unknown seismic strength of such large RBCs makes RBC seismic designs increasingly necessary. Several seismic design methods have been developed for and applied to rectangular underground structures, e.g., cut-and-cover tunnels, which are structurally similar to RBCs. Although these methods are applicable to RBCs, it is uncertain whether they can be applied directly because there are currently no evaluation results from model tests on RBCs, which have unique structural features, e.g., no haunch at the bottom of the sidewalls. Therefore, we verify a seismic behavior of an RBC and develop a method for evaluating it in order to establish a seismic design for RBCs. We conducted centrifuge model tests subjected to seismic force and a numerical analysis using an elastoplastic finite analysis method, in addition, we validated this analysis by comparing the test and analytical results. The test results show RBCs will most likely develop rocking rotation when the ground strain exceeds approximately 0.08%. A comparison of the numerical and experimental results shows that this analysis can estimate the shear deformation behavior with approximately 90% accuracy in square cross-section cases. Meanwhile, this analysis has tendency to underestimate the axial forces in each case and to overestimate the bending moments of some members in the case of wide cross-sections.