Incremental Load Method Research Articles

Compressibility Characteristics of Peat Soil Treated with MUF-P Resin

Peat is commonly described as a soil that is possess to high rate of compressibility due to present of high organic substance derived from plant origins. Peat soil naturally associated with settlement and consolidation characterized by its high initial void ratio, organic content and water holding capacity. This paper presents the performance of peat soil treated with powdered melamine urea formaldehyde resin (MUF-P) in term of compression and consolidation behaviour under standard compressibility test. In this study, series of one-dimensional oedometer test were carried out with the load increment method from 12.5 to 400 kPa after 24 hours of each loading. Peat soils under high moisture condition were mixed with MUF-P within 3 days of stipulated periods of curing times. The results indicate that increasing the MUF-P proportion has improved the compressibility characteristics of peat soil. The result shows the values of compression index (Cc) decreased from 4.12 to 0.9, and secondary compression index (Cα) were also decreased from the range of 0.026 to 0.320 to the range of 0.080 to 0.161 with the increase of peat MUF-P proportions up to maximum 350 kg/m3.

A Cyclic Plasticity Model with Martensite Transformation for S30408 and Its Finite Element Implementation

The ability of the constitutive model to simulate the ratcheting behavior of metastable austenitic stainless steel S30408 is significant to ensure the safety of the liquefied natural gas (LNG) semi-trailer tanks in the lightweight process of the inner containers. This is because the lightweight inner vessels often encounter cyclic stresses due to the road inertia loads together with high mean stresses due to internal pressures. In this study, we performed cryogenic uniaxial tension experiments and a series of ratcheting experiments to investigate the cyclic plasticity behavior of the metastable austenitic stainless steel S30408. Based on the Ohno-Wang II model, we proposed a new cyclic plasticity constitutive model with martensitic transformation, which relates the content of deformation-induced martensite with isotropic hardening and kinematic hardening. The ratcheting behaviors of S30408 were first simulated by the proposed model with the incremental loading method using MATLAB. The results showed that the model could reasonably predict the ratcheting behavior of S30408, and the evolution law of martensite content could well predict the content of deformation-induced martensite. Under the assumption of the von Mises yield criterion and normal plasticity flow rule, we developed a numerical algorithm of plastic strain with the proposed model to implement the finite element calculation of the model. Internal iteration in the numerical algorithm was implemented with the Euler backward method, which calculated the trial strain for each equilibrium iteration using the consistent tangent matrix. With a user subroutine, the proposed model was programmed into ANSYS for a user - executable version. By simulating the uniaxial ratcheting of a S30408 round bar, we found that the calculated results were in good agreement with the experimental results, which promises further applications in the design of structures, such as LNG semi-trailer tanks.

A novel methodology for structural robustness assessment of offshore platforms in progressive collapse

Accidental events may cause a chain of local damages of offshore platforms and eventually result in an overall collapse of platform structures, which exposes the structural vulnerability in resisting non-proportional failure. In addition, due to the redundancy of structure and the uncertainty of failure response, there may exist a series of different potential failure paths for offshore platforms. Therefore, this paper proposes a novel methodology for structural robustness assessment considering multi-failure paths to quantify the robustness of offshore platforms. By using the generalized bearing-capacity-ratio method combined with the incremental-loading method, all possible failure paths could be sought out and the most possible failure sequence be identified. Based on failure paths analysis, three novel robustness indices are established from different perspectives, respectively: (1) path-dependent & state-dependent robustness index RI, (2) overall dynamic robustness index RP, (3) and comprehensive robustness index RW for structural pre-evaluation. Also, by introducing the maintenance reinforcement into the structural robustness simulation, the effects of the whole reinforcement and the critical path reinforcement on structural robustness are studied. Robustness analysis results show that the differences of robustness of different failure paths are significant, although the accidental events occur in small probability path, its impact on the structural robustness is serious so it should be paid more attention. Besides, strengthening the critical path could significantly improve the structural robustness and achieve the goal of robustness control.

Analysis of Finite Elasto-Plastic Strains: Integration Algorithm and Numerical Examples

The paper is devoted to the development of a calculation technique for elasto-plastic solids with regard to finite strains. The kinematics of elasto-plastic strains is based on the multiplicative decomposition of the total deformation gradient into elastic and inelastic (plastic) components. The stress state is described by the Cauchy stress tensor. Physical relations are obtained from the equation of the second law of thermodynamics supplemented with a free energy function. The free energy function is written in an invariant form of the left Cauchy–Green elastic strain tensor. An elasto-plasticity model with isotropic strain hardening is considered. Based on an analog of the associated rule of plastic flows and the von Mises yield criterion, we develop the method of stress projection onto the yield surface (known as the radial return method) with an iterative refinement of the current stress-strain state. The iterative procedure is based on the introduction of additional virtual stresses to the resolving power equation. The constitutive relations for the rates and increments of the true Cauchy stresses are constructed. In terms of the incremental loading method, the variational equation is obtained on the basis of the principle of possible virtual powers. Spatial discretization is based on the finite element method; an octanodal finite element is used.We present the solution to the problem of tension of a circular bar and give a comparison with results of other authors.

An informed user equilibrium dynamic traffic assignment problem in a multiple origin-destination stochastic network

We develop in this paper a comprehensive linear mathematical framework to study the benefit of real-time information and the impact of resulting user adaptive route choice behaviours on network performance. The framework formulates the information-based stochastic user equilibrium (ISUE) dynamic traffic assignment (DTA) problem for a multiple origin-destination (OD) network. Using the framework, we prove the linkage between the user equilibrium (UE) and system optimal (SO) solutions underpinned by the first-in-first-out (FIFO) principle. This important property then enables us to develop an incremental loading method to obtain the ISUE solutions efficiently by solving a sequence of linear programs. Moreover, the proposed method is more scalable that avoids a huge enumeration of paths in large-scale networks as done in path-based methods of the existing literature on this topic. We show via numerical examples the impact of information on both route choices and network performance, and demonstrate the significant improvements in the obtained ISUE solution both in terms of accuracy and computational complexity.

Dynamics of a rotor system coupled with water-lubricated rubber bearings

Dynamic behaviour is significantly important in the design of large rotor systems supported on water-lubricated rubber bearings. In this study, the mathematical model of elastohydrodynamic lubrication of the bearing is established based on the theory of hydrodynamic lubrication after considering the elastic deformation of rubber, and the dynamic characteristics of water-lubricated rubber bearings are analysed under small perturbation conditions according to the load increment method and the finite difference method. Next, the differential equation of rotor systems coupled with the water-lubricated rubber bearing is deduced using Lagrange’s approach, and its critical speeds, stability, and unbalanced responses are analysed in detail. The numerical results show that several parameters, such as the eccentricity, length–diameter ratio, and clearance of bearing and the rotating speed of the rotor, have a great impact on the dynamic performance of water-lubricated rubber bearings, and this influence cannot be ignored, especially in the case of large eccentricity ratios. The dynamic characteristics of rotor systems guided by water-lubricated rubber bearings reveal that the critical speeds are much lower than the ones under the rigid supports because of the elastic deformation, and they also indicate that the rotor system supported on water-lubricated rubber bearings has a weaker stability. In addition, the steady-state responses of the rotor system are analysed when the mass unbalance of the propeller exists, and the effect of the thickness of the rubber liner is also considered.

Three-dimensional simplified slope stability analysis by hybrid-type penalty method

In this study, we propose a three-dimensional simplified slope stability analysis using a hybrid-type penalty method (HPM). In this method, a solid element obtained by the HPM is applied to a column that divides the slope into a lattice. Therefore, it can obtain a safety factor in the same way as simplified methods on the slip surface. Furthermore, it can obtain results (displacement and strain) that cannot be obtained by conventional limit equilibrium methods such as the Hovland method. The continuity condition of displacement between adjacent columns and between elements for each depth is considered to incorporate a penalty function and the relative displacement. For a slip surface between the bottom surface and the boundary condition to express the slip of slope, we introduce a penalty function based on the Mohr-Coulomb failure criterion. To compute the state of the slip surface, an r-min method is used in the load incremental method. Using the result of the simple three-dimensional slope stability analysis, we obtain a safety factor that is the same as the conventional method. Furthermore, the movement of the slope was calculated quantitatively and qualitatively because the displacement and strain of each element are obtained.

A linear framework for dynamic user equilibrium traffic assignment in a single origin-destination capacitated network

The dynamic traffic assignment (DTA) problem has been studied intensively in the literature. However, there is no existing linear framework to solve the user equilibrium (UE) DTA problem. In this paper, we develop a novel linear programming framework to solve the UE-DTA problem in a dynamic capacity network that exploits the linkage between the UE and system optimal (SO) solutions underpinned by a first-in-first-out (FIFO) principle. This important property enables us to develop an incremental loading method to obtain the UE solutions efficiently by solving a sequence of linear programs. The proposed solution methodology possesses several nice properties such as a predictable number of iterations before reaching the UE solution, and a linear system of equations to be solved in each of the iterations.In contrast to the related iterative methods, such as Frank–Wolfe algorithm, successive average (MSA) or projection and their extensions where the purpose of iteration is to seek the solution convergence, whereas ours is to solve a linear problem over multiple iterations but only for a single unit of demand in each iteration. Furthermore, we provide a theoretical proof that in the limit, the SO objective can be used to obtain the UE solution as the system time step goes to zero given the satisfaction of the FIFO constraint. We show via numerical examples the significant improvements in the obtained UE solutions both in terms of accuracy and computational complexity.

Discussion of the Method to Determine the Ultimate Bearing Capacity of Soil Foundation

Combining literature examples, this paper has carried out Contrastive analysis of the theoretical formula method and finite element method about the ultimate bearing capacity of foundation, To verify rationality and superiority of the incremental load method in finite element ABAQUS in solving the bearing capacity of foundation soil. The study can provide certain reference for practical engineering calculation and analysis of foundation bearing capacity.

Dynamic behavior of fluid‐structure coupling of hydrostatic spindle under effect of oil film slip

AbstractTo better understand the dynamic characteristics of a hydrostatic spindle in fluid‐structure coupling, the impact of oil film slip on the 4 dynamic stiffness and damping coefficients of the spindle is studied. On the basis of modified Reynolds equation, which considers the microscale velocity slip effect, rotation error of the spindle is calculated. To solve the rotor axis orbit under the existence of eccentric quality, 4 dynamic stiffness and damping coefficients of the oil film, which describe the dynamics of a rotor axis orbit, are calculated by using load increment method and the pressure perturbation method. The research results show that velocity slip caused a certain impact on dynamics of bearing stiffness and damping performance. The experiment of the measuring path of the shaft verifies the correct and effect of the orbit of shaft center model.

Incremental algorithm for acoustoelastic theory of large static pre-deformed fluid-saturated porous media

The incremental acoustoelastic equations for fluid-saturated porous media (FSPM) under the large static pre-deformation are derived in this paper by incremental loading method based on classic acoustoelastic theory of FSPM, which provides quantitative acoustoelastic relation of FSPM with arbitrary constitutive equation. Isotropic FSPM with third-order constitutive equation are taken as an example to give the relation between wave velocity and confining pressure and discuss the effect of loading step on acoustoelastic relations of isotropic FSPM under closed-pore jacketed condition and opened-pore jacketed condition.

A Parallel Elastoplastic Reanalysis Based on GPU Platform

An efficient parallel elastoplastic reanalysis method is suggested. The main backbone of the suggested method is based on combined approximation (CA) reanalysis. GPU parallel computation is used to accelerate assembling the stiffness matrix. Assembling process is divided into the offline part for strain matrix and online part for element stiffness matrix, which makes the structure of the program more reasonable and efficient. Pseudo elastic analysis is introduced and extended to load increment method to make the CA method more feasible. The numerical examples show that the suggested method can improve the efficiency of elastoplastic analysis significantly and the accuracy of results can also be ensured.

Elastic-plastic secondary indeterminate problem for thin-walled pipe through the inner-wall loading by three-point bending

ABSTRACTThe inner-wall loading by three-point bending about thin-walled pipe is an elastic-plastic secondary indeterminate problem in the symmetrical three-roller setting round process. In this study, the shifting of the tangent point between the pipe and lower roller is ignored. The bilinear hardening material model is adopted, and the static equilibrium condition, physical relationship of elastic-plastic deformation, and deformation compatibility condition are taken into account. Based on the geometrical discrete idea, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with same geometric parameters along the circumferential direction. Deformation characteristics of each element are calculated, and then the deformation history response of the whole pipe is resolved by the load increment method. The finite element model of static bending in three-roller setting round process is established by using the software package ABAQUS. The theoretical and simulated results show that the cross section of pipe has two positive bending regions and two reverse bending regions; the maximum bending curvature appears in the bottom section of pipe, the minimum bending curvature appears in the section corresponding to the tangent point of the pipe and lower roller. The quantitative relationships between the upper roller load, maximum(minimum) bending curvature and reduction are given. Finally, the reliability of theoretical calculation is proved by numerical simulation.

Fiber Effects on Compressibility of Peat

Fibers found in the soil, especially in peaty soil play an important role in the determination of soil compressibility. Peat soils are the results from the decomposition of organic matter and the type of peat can be classified based on the fibrous material in the soil. In the engineering field, peat soil was mostly known as soils that has a serious settlement with high compressibility index. From the previous research, fibers in the soil were influenced in compressibility in terms of size, shape, fibric, soil arrangement and etc. Hence, this study attempts the determination of fibers effects on the compressibility of peat using a 1-D oedometer consolidation test. The reconstituted peat samples of different particle sizes were used to determine the consolidation parameters and the results obtained from reconstituted samples were also compared with the undisturbed sample. 1-D oedometer consolidation tests were performed on the samples by using the load increment method. The results shows, the higher particle size (R3.35), give higher moisture content (w = 401.20%) and higher initial void ratio (eo = 5.74). In settlement prediction, the higher the fiber content will results the higher the compression index, therefore, it will cause high of settlement.

A mechanical model of symmetrical three-roller setting round process: The static bending stage

The static bending deformation of three-roller setting round process is an elastic–plastic secondary indeterminate problem, and belongs to the plane bending deformation. This paper adopts a bilinear material model. In consideration of shifting of the tangent points between the pipe and the lower rollers, the static equilibrium conditions, the physical relationships of elastic–plastic deformation, the deformation compatibility conditions, and the constraint conditions are analyzed comprehensively. By applying the discrete method, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with the same geometric parameters. Deformation characteristics of each micro-pipe-wall element are calculated, and then the deformation history responses of the whole pipe are resolved by applying the load increment method, based on the variable step size, and the experimental apparatus is further designed to verify the theoretical model. Finally, the effects of various process parameters on the upper roller load and bending curvature are studied. The results show that the static bending deformation can be assumed to be a pure bending process; the cross section of the pipe has two positive bending regions and two reverse bending regions; the upper roller diameter and the lower rollers spacing are the major factors for the upper roller load and the bending curvature; the dynamic roll bending process can be simplified into a static to-and-fro bending process.

Continuation Newton methods

Severely nonlinear problems can only be solved by some homotopy continuation method. An example of a homotopy method is the continuous Newton method which, however, must be discretized which leads to the damped step version of Newton’s method.The standard Newton iteration method for solving systems of nonlinear equations F(u)=0 must be modified in order to get global convergence, i.e. convergence from any initial point. The control of steplengths in the damped step Newton method can lead to many small steps and slow convergence. Furthermore, the applicability of the method is restricted in as much as it assumes a nonsingular and everywhere differentiable mapping F(⋅).Classical continuation methods are surveyed. Then a new method in the form of a coupled Newton and load increment method is presented and shown to have a global convergence already from the start and second order of accuracy with respect to the load increment step and with less restrictive regularity assumptions than for the standard Newton method. The method is applied for an elastoplastic problem with hardening.

Consolidation Parameters of Reconstituted Peat Soil: Oedometer Testing

This paper presents the consolidation parameters of reconstituted peat soils with different peat soil particle sizes. The reconstituted peat sample was used to determine the consolidation parameters since the undisturbed samples were difficult to collect. The selected sizes of soil particles passing have been collected and formed the reconstituted peat samples by preloaded a pressure to remove the extra water. The testing involve was one-dimensional oedometer consolidation test with the load increment method (5 – 320kPa). It is important to gather the information about a soil profile, especially on consolidation properties which were important in predicting the settlement of soil. Based on the results, compression index (Cc) and swell index (Cs), the values were increased with the increasing peat particles size.

A method for predicting approximate lateral deflections in thin glass plates

In the present paper a three-dimensional non-linear truss element and a short computer program for the modeling and predicting approximate lateral deflections in thin glass plates by the method of incremental loading are proposed. Due to the out-of-plane large deflections of thin glass plates compared to the plate thickness within each loading increment, the equilibrium and stiffness conditions are written with respect to the deformed structure. An application is presented on a thin fully tempered monolithic rectangular glass plate, laterally supported around its perimeter subjected to uniform wind pressure. The results of the analysis are compared with published experimental results and found to have satisfactory approximation. It is also observed that the large deflections of a glass plate lead to a part substitution of the bending plate behavior by a tensioned membrane behavior which is favorable.

Constant rate of strain consolidation of organic clay: in Kolkata region

Constant rate of strain (CRS) consolidation test is an alternative testing method to estimate the consolidation parameters of fine grained soils, which has gained popularity in countries, such as USA, Japan, Hong Kong, and Canada, because of its several merits over conventional incremental loading (IL) method. Constant rate of strain test is also important to study the effect of strain rate on consolidation behavior of soils. Organic soils are considered problematic soils because of their low strength and higher compressibility. In this paper, an attempt has been made to determine consolidation parameters of a number of undisturbed and remolded organic soils in the Kolkata region with organic content 14–45% by testing them at different strain rates (1·2, 0·24, 0·12, 0·048, and 0·012% min−1) using an indigenously built CRS cell. Incremental loading tests were also conducted to verify the dependability of CRS results. Results indicate that 1·2 and 0·24% min−1 strain rates generate high pore pressure ratio (PPR), which are beyond the recommended values. Present investigation revealed that vertical effective stresses, pre-consolidation pressure, coefficient of consolidation, coefficient of volume change, hydraulic conductivity, etc., are strain-rate dependent. Higher strain rate is found to produce higher effective stress and consolidation parameters. Constant rate of strain test results obtained from undisturbed organic clays (OCs) and a number of remolded organic and inorganic soils particularly at 0·12, 0·048, and 0·012% min−1 strain rates are in line with that of IL tests.

A numerical study of the overall stability of flexible giant crane booms

Flexible giant crane boom is a statically indeterminate mixed structure equipped in giant boom cranes. It has a soaring complex geometry consisting of a giant combined boom and a flexible luffing structure, and the overall plastic instability is apt to happen under large hoisting, gravity and wind loads. As dually (geometrically and materially) nonlinear buckling analysis for flexible giant crane booms has not been well studied in literature, a detailed investigation is presented in this paper. Prior to carrying out a dually nonlinear buckling analysis, this paper first undertakes a geometric buckling analysis for a better understanding of the buckling behavior. A method of applying temporary constraints is proposed to prevent the non-convergence issue caused by boom tilting. The incremental load method, the incremental displacement method, and the Newton–Raphson method are applied to evaluate the complete load–deflection response and the accurate critical load. Numerical analyses using the proposed method agree well with the conventional Arc-Length method and the survey results of a crane boom collapse accident. Results show that material nonlinearity is a remarkable factor that weakens the overall stability of the structure. The plastic development of the structure happens mainly in chord members of standard sections. The P−∆ effect of gravity load on the structure determines the first fracture position in the boom. The methodology developed in this paper can be easily extended for the development and applications of other performance-based approaches for enhancing the stability of flexible giant crane booms.