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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation. The model is inspired by the distribution of the measured in-plane and out-of-plane deformation. The in- plane displacement of crack-tip fields under both Mode 1 and mixed-mode （Mode I-II） fracture conditions is measured by using the digital Moir6 method. The deformation character- istics and experimental sector division mode are investigated by comparing the measured displacement fields under differ- ent fracture modes. The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimen- tal observations and the classical relation between indenta- tion force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.