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.

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.

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.

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.

Anchorage performance of large-diameter FRP bolts and their application in large deformation roadway

In underground coal mines, fibre reinforced polymer(FRP) bolt is ideal for mined rib reinforcements as it can prevent gas explosions caused by shearer frictional spark. With increasing mining depth, small diameter FRP bolts used in shallow underground mining cannot fulfil the rib support requirements. Under the engineering background of deep underground shortwall mining in Wudong coal mine, this paper systematically studies Φ27 mm FRP bolt support for large deformation coal rib. Specimens with a fan-shaped cross-section were used to enable the tensile testing of the bolt rod, the measured average tensile strength of the studied FRP bolt was(486.1 ± 9.6) MPa with a maximum elongation of 5.7%±0.6%.The shear strength of the bolt was measured as approximately 258 MPa using a self-made double shear testing apparatus. Based on the equivalent radial stiffness principle, a laboratory short encapsulation pullout test(SEPT) method for rib bolting has been developed undertaken consideration of the mechanical properties of the coal seam. Results showed that the average peak anchorage forces of the Φ27 mm FRP bolt and Φ20 mm steel rebar bolt were 108.4 and 66.4 k N, respectively, which were agreed with the theoretical calculations and field measurements. Based on theoretical analysis of the loading states of the bolt under site conditions, bolting method of full-length resin grouting was adopted to offset the weaknesses of the FRP bolt. Numerical method was employed to compare the bolting effect using Φ27 mm FRP bolts and steel rebar bolts. Large diameter FRP bolting was determined as the optimum rib support scheme to increase the productivity of the coal mine and to enhance the ground control capability for+425 level mining roadways. This study provides the laboratory testing design and theoretical prediction of large diameter FRP bolts used for rib support in large deformation roadways.

Excavation compensation theory and supplementary technology system for large deformation disasters

Given the challenges in managing large deformation disasters in energy engineering,traffic tunnel engineering,and slope engineering,the excavation compensation theory has been proposed for large deformation disasters and the supplementary technology system is developed accordingly.This theory is based on the concept that“all destructive behaviors in tunnel engineering originate from excavation.”This paper summarizes the development of the excavation compensation theory in five aspects:the“theory,”“equipment,”“technology,”the design method with large deformation mechanics,and engineering applications.First,the calculation method for compensation force has been developed based on this theory,and a comprehensive large deformation disaster control theory system is formed.Second,a negative Poisson's ratio anchor cable with high preload,large deformation,and super energy absorption characteristics has been independently developed and applied to large deformation disaster control.An intelligent tunnel monitoring and early warning cloud platform system are established for remote monitoring and early warning system of Newton force in landslide geological hazards.Third,the double gradient advance grouting technology,the two-dimensional blasting technology,and the integrated Newton force monitoring--early warning--control technology are developed for different engineering environments.Finally,some applications of this theory in China's energy,traffic tunnels,landslide,and other field projects have been analyzed,which successfully demonstrates the capability of this theory in large deformation disaster control.

Numerical simulation of rockburst disaster and control strategy of constant resistance and large deformation anchor cable in Gaoloushan tunnel

The Gaoloushan Tunnel in Longnan City,Gansu Province,China,frequently experiences rockburst disasters due to high in-situ stress.Managing rockburst in deep-buried tunnels remains a challenging issue.This paper employs RFPA(Rock Failure Process Analysis)software to establish a calculation model of constant resistance and large deformation(CRLD)anchorages and analyzes the effects of different support methods and pre-stress levels on rockburst.We simulate the process of tunnel rockburst disasters and find that ordinary anchor support incurs rockburst on the right arch waist and arch top,forming a V-shaped explosion pit.CRLD anchor support has several advantages in rockburst control,such as more uniform stress distribution in the surrounding rock,a uniform distribution of plastic zones,less noticeable damage to the tunnel,and effective control of the arch top displacement.The effectiveness of the CRLD anchor support under varying pre-stress conditions shows that a higher prestress results in a smaller plastic zone of the surrounding rock and arch top displacement and a lower number of acoustic emission signals,which better explains the excavation compensation effect.Moreover,adding long anchorages in the deep surrounding rock area can better control rockburst and reduce surrounding rock deformation.Based on these findings,we propose a comprehensive control system that combines long and short anchorages and provides the optimal scheme based on calculations.Therefore,by using high-prestress CRLD anchor support and the combination of long and short anchorages at critical positions,we can enhance the integrity of the surrounding rock,effectively absorb the energy released by the surrounding rock deformation,and reduce the incidence of rockburst disasters.

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.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

Failure mechanism and safety control technology of a composite strata roadway in deep and soft rock masses:a case study

The construction of coal mines often encounters deep composite soft rock roadways,which is characterized by significant deformation and poor stability.To deeply study the failure mechanism and large deformation challenges of a composite strata roadway in deep and soft rock masses,a numerical model of 3DEC tetrahedral blocks was established based on the method of rock quality designation(RQD).The results showed that original support cannot prevent asymmetric failure and large deformation due to the adverse geological environment and unsuitable support design.According to the failure characteristics,a coupling support of“NPR bolt/cable+mesh+shotcrete+steel pipe”was proposed to control the stability of the surrounding rock.The excellent mechanical properties of large deformation(approximately 400 mm)and high constant resistance force(bolt with 180 k N;cable with 350 k N)were evaluated by the tensile tests.The numerical results showed that the maximum deformation was minimized to 243 mm,and the bearing capacity of the surrounding rock of the roadway was enhanced.The field test results showed that the maximum deformation of the surrounding rock was 210 mm,and the forces of the NPR bolt and cable were stable at approximately 180 k N and 350 k N,respectively.This demonstrated the effectiveness of the coupling support with the NPR bolt and cable,which could be a guiding significance for the safety control of large deformation and failure in deep composite soft rock roadways.

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.

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.

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.