Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.

Role of stress,slenderness and foliation on large anisotropic deformations at deep underground excavations

High stress concentrations around underground excavations can result in significant damage to deep hard-rock mines.These conditions can be the result of stopping activities,blasting,seismicity,or other mining activities.Large anisotropic deformation and excavation closure,especially under high-stress conditions,are expected if the excavation is located in a foliated or thin-bedded rock mass.In this research,the behaviour of excavations under deep and high-stress conditions was investigated and categorised.The main purpose was to enhance the existing knowledge of managing large anisotropic deformations and to help prepare suitable measures for handling such contingencies.Numerical simulations using the distinct element method(DEM)and model calibration were performed to reproduce the anisotropic deformation of an ore drive based on the collected field data.Then,the roles of key factors(i.e.stress ratio,slenderness ratio,foliation orientation,and foliation considering excavation orientation)on the large deformation and damage depth of the excavations were investigated.This study found that increasing both the stress ratio and slenderness ratio induced linear increases in wall closure and damage depth,whereas increasing the foliation angle first increases the deformation and damage depth and then reduces them both before and after 45.The wall closure and damage thickness decreased with increasing orientation intercept.The deformation and damage levels were classified based on these factors.

Dynamic analysis of a rotating rigid-flexible coupled smart structure with large deformations

Based on Hamilton＇s principle, a new kind of fully coupled nonlinear dynamic model for a rotating rigid-flexible smart structure with a tip mass is proposed. The geometrically nonlinear effects of the axial, transverse displacement and rotation angle are considered by means of the first-order approximation coupling （FOAC） model theory, in which large deformations and the centrifugal stiffening effects are considered. Three kinds of systems are established respectively, which are a structure without piezoelectric layer, with piezoelectric layer in open circuit and closed circuit. Several simulations based on simplified models are presented to show the differences in characteristics between structures with and without the tip mass, between smart beams in closed and open circuit, and between the centrifugal effects in high speed rotating state or not. The last simulation calculates the dynamic response of the structure subjected to external electrical loading.

GENERALIZED VARIATIONAL PRINCIPLES OF SYMMETRICAL ELASTICITY PROBLEM OF LARGE DEFORMATIONS

This paper is based on the geometrical nonlinear theories of deformationpresented by Chen Zhi-da￣[1], Lagrange’s multiplier mothod is used to study thesymmetry elasticity problems of large deformation. The general rariational priieiplesof potential energy and coinplemenlary energy,and the general variation principle ofdynamic problem have been proved. In the meantme it is also proved that the generalvatiaton principles of potential energy and complementary energy are equivalent.

Case study on the mechanics of NPR anchor cable compensation for large deformation tunnel in soft rock in the Transverse Mountain area,China

A study was conducted to analyze the deformation mechanism of strongly weathered quartz schist in the Daliangshan Tunnel,located in the western Transverse Mountain area.A large deformation problem was experienced during the tunnel construction.To mitigate this problem,a support system was designed incorporating negative Poisson ratio(NPR)anchor cables with negative Poisson ratio effect.Physical model experiments,field experiments,and numerical simulation experiments were conducted to investigate the compensation mechanical behavior of NPR anchor cables.The large deformations of soft rocks in the Daliangshan Tunnel are caused by a high ground stress,a high degree of joint fracture development,and a high degree of surrounding rock fragmentation.A compensation mechanics support system combining long and short NPR anchor cables was suggested to provide sufficient counter-support force(approximately 350 kN)for the surrounding rock inside the tunnel.Comparing the NPR anchor cable support system with the original support system used in the Daliangshan tunnel showed that an NPR anchor cable support system,combining cables of 6.3 m and 10.3 m in length,effectively prevented convergence of surrounding rock deformation,and the integrated settlement convergence value remained below 300 mm.This study provides an effective scientific basis for resolving large deformation problems in deeply buried soft rocks in western transverse mountain areas.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Effect of annealing temperature on microstructure and mechanical properties of Mg-Zn-Zr-Nd alloy with large final rolling deformation

In this study,the Mg-3Zn-0.5Zr-χNd(χ=0,0.6)alloys were subjected to final rolling treatment with large deformation of 50%.The impact of annealing temperatures on the microstructure and mechanical properties was investigated.The rolled Mg-3Zn-0.5Zr-0.6Nd alloy exhibited an ultimate tensile strength of 386 MPa,a yield strength of 361 MPa,and an elongation of 7.1%.Annealing at different temperatures resulted in reduced strength and obviously increased elongation for both alloys.Optimal mechanical properties for the Mg-3Zn-0.5Zr-0.6Nd alloy were achieved after annealing at 200℃,with an ultimate tensile strength of 287 MPa,a yield strength of 235 MPa,and an elongation of 26.1%.The numerous deformed microstructures,twins,and precipitated phases in the rolled alloy could impede the deformation at room temperature and increase the work hardening rate.After annealing,a decrease in the work hardening effect and an increase in the dynamic recovery effect were obtained due to the formation of fine equiaxed grains,and the increased volume fraction of precipitated phases,which significantly improved the elongation of the alloy.Additionally,the addition of Nd element could enhance the annealing recrystallization rate,reduce the Schmid factor difference between basal and prismatic slip systems,facilitate multi-system slip initiation and improve the alloy plasticity.

Development of the rolling extrusion rock bolt with constant resistance and large deformation

With the increasing excavation depth of underground engineering,engineering problems such as large deformation and rock burst caused by high geo-stress brings new challenges to the excavation and reinforcement of surrounding rock in deep underground engineering.The traditional rock bolt is prone to brittle fracture under high geo-stress due to its low elongation.Therefore,this work aims to develop a novel energy-absorbing bolt with constant resistance and large displacement to reinforce the surrounding rock with a risk of large deformation or rockburst.The novel energy-absorbing bolt refereed as rolling extrusion rock bolt(RE bolt)is mainly consists of sleeve tube with a variable cross-section,energy absorption slider with steel balls embedded,steel bar connected with the energy absorption slider.The rolling extrusion is adopted to produce the resistance force of the RE bolt,which avoids the sudden attenuation of resistance force and the abrasion of the energy absorption slider.The static pull test is conducted to study the resistance force and deformation characteristics of the RE bolt with different specifications.Results imply that the RE bolt has higher resistance force,larger deformation capacity and energy absorption capacity.The work of this study provides an effective solution for the reinforcement of surrounding rock in deep rock engineering.

Compensation excavation method control for large deformation disaster of mountain soft rock tunnel

In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.

Characteristics of microseismic b-value associated with rock mass large deformation in underground powerhouse caverns at different stress levels

Rock mass large deformation in underground powerhouse caverns has been a severe hazard in hydropower engineering in Southwest China.During the development of rock mass large deformation,a sequence of fractures was generated that can be monitored using microseismic(MS)monitoring techniques.Two MS monitoring systems were established in two typical underground powerhouse caverns featuring distinct geostress levels.The MS b-values associated with rock mass large deformation and their temporal variation are analysed.The results showed that the MS bvalue in course of rock mass deformation was less than 1.0 in the underground powerhouse caverns at a high stress level while larger than 1.5 at a low stress level.Prior to the rock mass deformation,the MS b-values derived from both the high-stress and low-stress underground powerhouse caverns show an incremental decrease over 10%within 10 d.The results contribute to understanding the fracturing characteristics of MS sources associated with rock mass large deformation and provide a reference for early warning of rock mass large deformation in underground powerhouse caverns.

Development of steel dampers for bridges to allow large displacement through a vertical free mechanism

Isolation bearings and dampers are often installed between piers and superstructures to reduce the seismic responses of bridges under large earthquakes. This paper presents a novel steel damper for bridges. The damper employs steel plates as energy dissipation components, and adopts a vertical free mechanism to achieve a large deformation capacity. Quasi-static tests using displacement-controlled cyclic loading and numerical analyses using a finite element program called ABAQUS are conducted to investigate the behavior of the damper, and a design methodology is proposed based on the tests and numerical analyses. Major conclusions obtained from this study are as follows： （1） the new dampers have stable hysteresis behavior under large displacements; （2） finite element analyses are able to simulate the behavior of the damper with satisfactory accuracy; and （3） simplified design methodology of the damper is effective.

Two-Dimensional Large Deformation Finite Element Analysisfor the Pulling-up of Plate Anchor

Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the deterruination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay arc simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

Application of MLPG in large deformation analysis

Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.

Anchoring effect and energy-absorbing support mechanism of large deformation bolt

To research the anchoring effect of large deformation bolt,tensile and drawing models are established.Then,the evolution laws of drawing force,bolt axial force and interfacial shear stress are analyzed.Additionally,the influence of structure element position on the anchoring effect of large deformation bolt is discussed.At last,the energy-absorbing support mechanism is discussed.Results show that during the drawing process of normal bolt,drawing force,bolt axial force and interfacial shear stress all gradually increase as increasing the drawing displacement,but when the large deformation bolt enters the structural deformation stage,these three values will keep stable;when the structure element of large deformation bolt approaches the drawing end,the fluctuation range of drawing force decreases,the distributions of bolt axial force and interfacial shear stress of anchorage section are steady and the increasing rate of interfacial shear stress decreases,which are advantageous for keeping the stress stability of the anchorage body.During the working process of large deformation bolt,the strain of bolt body is small,the working resistance is stable and the distributions of bolt axial force and interfacial shear stress are steady.When a rock burst event occurs,the bolt and bonding interface cannot easily break,which weakens the dynamic disaster degree.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel

Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.

Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Effects of liquefaction-induced large lateral ground deformation on pile foundations

The pile-soil system interaction computational model in liquefaction-induced lateral spreading ground was established by the finite difference numerical method.Considering an elastic-plastic subgrade reaction method,numerical methods involving finite difference approach of pile in liquefaction-induced lateral spreading ground were derived and implemented into a finite difference program.Based on the monotonic loading tests on saturated sand after liquefaction,the liquefaction lateral deformation of the site where group piles are located was predicted.The effects of lateral ground deformation after liquefaction on a group of pile foundations were studied using the fmite difference program mentioned above,and the failure mechanism of group piles in liquefaction-induced lateral spreading ground was obtained.The applicability of the program was preliminarily verified.The results show that the bending moments at the interfaces between liquefied and non-liquefied soil layers are larger than those at the pile＇s top when the pile＇s top is embedded.The value of the additional static bending moment is larger than the peak dynamic bending moment during the earthquake,so in the pile foundation design,more than the superstructure＇s dynamics should be considered and the effect of lateral ground deformation on pile foundations cannot be neglected.

Behavior of large post-liquefaction deformation in saturated Nanjing fine sand

Laboratory tests on the large post-liquefaction deformation of saturated Nanjing fine sand were performed by using a hollow cylinder apparatus. The stress-strain responses and the characteristics of excess pore water pressure after liquefaction were studied. It was found that the relationship between deviatoric stress and axial strain presented a sigmoid curve, and there was a good linearity relationship between normalized pore water pressure and deviatoric stress. On this basis, a constitutive model of stress-strain responses and a dissipation model of excess pore water pressure were established. It was found that the results predicted by the two models were in good agreement with the experimental data. The influence of relative densities and confining pressure on the characteristics of liquefied soil were studied, The results showed the relative densities and initial effective confining pressure all had an important influence on the stress-strain responses of liquefied saturated Nanjing fine sand. However, the dissipation model of excess pore water pressure after liquefaction was only affected by the confining pressure.