An improved complex variable element-free Galerkin method for two-dimensional elasticity problems

In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.

An improved interpolating element-free Galerkin method for elasticity

Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.

An elastic mechanics model and computation method for geotechnical material

Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time. However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils. We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted. Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation. By assuming that the friction coefficient is proportional to the strain,the internal friction is computed. At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant. The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation. The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.

A Fast Element-Free Galerkin Method for 3D Elasticity Problems

In this paper,a fast element-free Galerkin(FEFG)method for three-dimensional(3D)elasticity problems is established.The FEFG method is a combination of the improved element-free Galerkin(IEFG)method and the dimension splitting method(DSM).By using the DSM,a 3D problem is converted to a series of 2D ones,and the IEFG method with a weighted orthogonal function as the basis function and the cubic spline function as the weight function is applied to simulate these 2D problems.The essential boundary conditions are treated by the penalty method.The splitting direction uses the finite difference method(FDM),which can combine these 2D problems into a discrete system.Finally,the system equation of the 3D elasticity problem is obtained.Some specific numerical problems are provided to illustrate the effectiveness and advantages of the FEFG method for 3D elasticity by comparing the results of the FEFG method with those of the IEFG method.The convergence and relative error norm of the FEFG method for elasticity are also studied.

Non-pneumatic mechanical elastic wheel natural dynamic characteristics and influencing factors

Non-pneumatic tire appears to have advantages over traditional pneumatic tire in terms of flat proof and maintenance free.A mechanical elastic wheel(MEW) with a non-pneumatic elastic outer ring which functions as air of pneumatic tire was presented.The structure of MEW was non-inflatable integrated configuration and the effect of hinges was accounted for only in tension. To establish finite element model of MEW, various nonlinear factors, such as geometrical nonlinearity, material nonlinearity and contact nonlinearity, were considered. Load characteristic test was conducted by tyre dynamic test-bed to obtain force-deflection curve. And the finite element model was validated through load characteristic test. Natural dynamic characteristics of the MEW and its influencing factors were investigated based on the finite element model. Simulation results show that the finite element model closely matched experimental wheel. The results also show that natural frequency is related to ground constraints, material properties, loads and torques. Influencing factors as above obviously affect the amplitude of mode of vibration, but have little effect on mode of vibration shape. The results can provide guidance for experiment research, structural optimization of MEW.

Mechanical analysis of double-layered circular graphene sheets as building material embedded in an elastic medium

Possessing the unique and highly valuable properties, graphene sheets(GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concrete and other building materials. In this work, the nonlocal elastic theory and classical plate theory(CLPT) are used to derive the governing equations. The element-free framework for analyzing the buckling behaviors of double layer circular graphene sheets(DLCGSs) relying on an elastic medium is proposed. Pasternak-type model is adopted to describe the elastic medium. Accordingly, the influences of boundary conditions, size of GSs and nonlocal parameters on the buckling behavior of DLCGSs are investigated. The results show that the OP buckling modes are only sensible to the van der Waals forces.

Discrete element method of improved performance of railway ballast bed using elastic sleeper

With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method(DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.

TOPOLOGY SYNTHESIS OF GEOMETRICALLY NONLINEAR COMPLIANT MECHANISMS USING MESHLESS METHODS

This paper presents a new method for topology optimization of geometrical nonlinear compliant mechanisms using the element-free Galerkin method （EFGM）. The EFGM is employed as an alternative scheme to numerically solve the state equations by fully taking advantage of its capability in dealing with large displacement problems. In the meshless method, the imposition of essential boundary conditions is also addressed. The popularly studied solid isotropic material with the penalization （SIMP） scheme is used to represent the nonlinear dependence between material properties and regularized discrete densities. The output displacement is regarded as the objective function and the adjoint method is applied to finding the sensitivity of the design functions. As a result, the optimization of compliant mechanisms is mathematically established as a nonlinear programming problem, to which the method of moving asymptotes （MMA） belonging to the sequential convex programming can be applied. The availability of the present method is finally demonstrated with several widely investigated numerical examples.

Probabilistic analysis of linear elastic cracked structures

This paper presents a probabilistic methodology for linear fracture mechanics analysis of cracked structures. The main focus is on probabilistic aspect related to the nature of crack in material. The methodology involves finite element analysis; sta- tistical models for uncertainty in material properties, crack size, fracture toughness and loads; and standard reliability methods for evaluating probabilistic characteristics of linear elastic fracture parameter. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly when the crack size has a large coefficient of variation. Numerical example is presented to show that probabilistic methodology based on Monte Carlo simulation provides accurate estimates of failure prob- ability for use in linear elastic fracture mechanics.

基于电测法测量弹性模量和泊松比的实验研究

测量材料的弹性模量和泊松比是材料力学实验的一项重要实验项目。为了丰富材料力学实验教学手段和教学内容,把理论计算、有限元仿真技术和电测法测试技术有机地融合在一起。分别通过电测法、ABAQUS软件模拟和理论计算方法得到低碳钢的弹性模量和泊松比。结果表明:模拟结果和理论计算结果几乎相等,但是电测法实验测试结果与理论计算结果之间的误差相对较大,主要是由于电阻应变片在试样表面的粘贴质量不高和试样的几何尺寸测量不精确造成的。

An interpolating boundary element-free method (IBEFM) for elasticity problems

The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.

The interpolating element-free Galerkin method for elastic large deformation problems

This paper presents an interpolating element-free Galerkin(IEFG) method for solving the two-dimensional(2D) elastic large deformation problems. By using the improved interpolating moving least-squares method to form shape function, and using the Galerkin weak form of 2D elastic large deformation problems to obtain the discrete equations, we obtain the formulae of the IEFG method for 2D elastic large deformation problems. As the displacement boundary conditions can be applied directly, the IEFG method can acquire higher computational efficiency and accuracy than the traditional element-free Galerkin(EFG)method, which is based on the moving least-squares approximation and can not apply the displacement boundary conditions directly. To analyze the influences of node distribution, scale parameter of influence domain and the loading step on the numerical solutions of the IEFG method, three numerical examples are proposed. The IEFG method has almost the same high accuracy as the EFG method, and for some 2D elastic large deformation problems the IEFG method even has higher computational accuracy.

混合边界护顶层力学模型及应用

对于直接顶板稳固性较差的矿山,通常需留设护顶层以防止直接顶板的垮塌。为了保证矿山的安全开采,确定合理的护顶层厚度至关重要。针对房柱法开采的采空区顶板进行结构力学解析,将护顶层视作四边中部自由其余部分固支的薄板,即混合边界薄板;利用功的互等法推导出混合边界薄板的挠曲面方程,构建混合边界护顶层力学模型,在此基础上得到护顶层安全厚度的计算公式。将混合边界薄板与四边固支薄板的变形情况进行对比时发现,混合边界薄板的挠度整体大于四边固支薄板挠度,混合边界自由段长度与最大挠度值呈正相关。将理论分析和数值模拟结合应用在某铝土矿No.9采场上,确定了护顶层安全厚度为1 m,验证了力学模型的准确性。

煤矿充填开采下顶板沉降研究

充填采矿可以有效控制岩层移动、抑制地表沉陷、减轻地质灾害,并且能够处理或利用一定的固体废弃物,有效改善矿山上覆岩层的力学环境,减轻顶板压力。以平凉某煤矿为工程背景,研究煤矿充填开采条件下坚硬顶板沉降变形情况,构建了顶板力学模型,对于初期来压采用四边固支的边界条件,利用变分法中伽辽金变形方程求选用不同挠度表达式的解;另对周期来压选用三边固支一边自由的边界条件,采用变分法中里兹变形方程进行求解,得出充填后顶板挠度显著减小,初期来压时减小38.74%,周期来压时减小66.84%。并得到充填开采顶板沉降变形规律,随着充填体弹性模量k值增大,顶板下沉位移显著减小。

基于超声纵横波原位法的螺栓预紧力检测研究

针对超声纵横波的螺栓预紧力原位测量精度受几何层面和材料层面因素的影响,通过声弹力学的理论推导,提出了基于形状因子和材料因子的螺栓预紧力超声原位检测模型,并对多种规格、等级、厂商的螺栓的形状因子和材料因子的影响进行试验。结果表明,本测量方法具有较高的拟合度,且可将形状因子λ<0.3作为适用条件。由此得出,通过测量验证了理论推导的正确性,定量地获得了各种因素对测量精度的影响范围,为建立纵横波虚拟标定曲线算法和数据库提供了坚实的基础。

三种岩体变形试验方法及其工程应用研究

现场岩体变形参数的准确测量对于岩体工程的合理设计至关重要.为了研究承压板法、钻孔弹模法和隧洞液压枕径向加压法三种岩体变形原位测试方法的适用性,详细阐述三种岩体变形测试方法的试验原理、使用范围及影响因素,探讨了不同方法的优缺点,在此基础上以东庄水利枢纽工程坝体两岸灰岩的现场实测为例,对不同方法测量结果进行了对比分析.结果表明,刚性承压板法所测得水平方向和垂直方向岩体变形试验结果相近,而柔性承压板法试验结果中PD18洞和PD409洞具有较大差异;刚性承压板法所测岩体变形模量要略大于钻孔弹模法所测试验结果;与其他方法相比,隧洞液压枕径向加压法能计算岩体变形模量和单位抗力系数等力学参数,可以更好地反映现场岩体各向异性和地质条件等特征.研究结果可为工程岩体力学参数的科学测量提供参考,确保工程设计的合理性.

基于响应面法和Weibull分布的不锈钢纤维再生混凝土抗冻性能研究

【目的】在我国严寒地区,冻融损伤会使再生混凝土(RAC)结构提前达到耐久性极限甚至导致构件失效,为了延长再生混凝土(RAC)结构在严寒地区的使用寿命,【方法】对再生混凝土(RAC)、天然混凝土(NC)、普通钢纤维再生混凝土(PFRAC)和不锈钢纤维再生混凝土(SFRAC)进行冻融循环试验。经过冻融循环后,测得RAC、NC、PFRAC、SFRAC的质量损失及相对动弹性模量,分析冻融循环过程中混凝土内部的损伤机理及劣化规律。以相对动弹性模量为损伤变量,基于响应面模型(RSM)和Weibull分布建立了钢纤维再生混凝土冻融损伤模型,研究冻融循环次数、PF和SF的掺量对再生混凝土抗冻性的影响。【结果】结果表明,SF的掺入能有效延缓RAC质量的损失和相对动弹性模量的降低。冻融循环150次时,掺量为2%的SFRAC质量损失和相对动弹性模量分别下降3.01%和19.57%。SFRAC与RAC相比,质量损失率降低了0.4%,相对动弹性模量提高了14.17%。【结论】Weibull分布和响应面模型(RSM)的预测结果 基本一致,但RSM预测值的相对误差要低于Weibull分布的预测值。两种模型的相关系数R2均在0.94以上,预测结果较为准确,可为钢纤维再生混凝土在寒冷地区的使用提供理论参考。

混合式三稳态压电能量俘获器动力性能分析

为了提高压电能量俘获器在低强度外界激励下的俘能表现,基于三稳态压电悬臂梁能量俘获器模型,在U形框架和基底之间以及压电悬臂梁固定端与U形框架之间分别装置一个弹性放大器,提出一种混合式三稳态压电能量俘获器(TPEH+DEM)模型。基于Hamilton原理建立了TPEH+DEM系统的非线性力电耦合运动方程,并利用谐波平衡法分析了弹性放大器的质量和弹簧刚度、磁铁之间相对距离、负载电阻等对TPEH+DEM系统能量收集水平的影响。结果表明:在一定的外界激励频率范围内,TPEH+DEM系统的响应输出功率存在两个峰值,合理调节弹性放大器的质量和刚度能使系统在较低的外界激励强度下进入阱间运动,产生很高的输出功率。相比于仅带有弹性基底的传统三稳态压电能量俘获器,TPEH+DEM模型在低频外界激励下具有更好的俘能表现。

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

FURTHER RESEARCH ON THE SPLINE MODEL METHOD OF KED ANALYSIS IN A PLANAR FLEXIBLE LINKAGE

This paper relates to the deep research on the Splinc Model Method of KED analysis. With the use of cubic B-splinc function as a link’s transverse deflection interpolation function, the principle of virtual displacement is presented as a basic theory for the general formulation of the equations of motion, and thus abandoned the kinematic assumption and the instantaneous structure assumption which arc used in the Spline Model Method. In thc same time, the nonlinear terms sue as coupling terms between thc rigid body motion and elastic deformation arc included. New member’s spline models are established. Mass matrix, Coriolis mass matrix, normal and tangential mass matrix, linear stiffness matrix, nonlinear stiffness matrix and rotation matrix arc derived. The kinematic differential equations of a member and system are deduced in the end. The Newmark direct integration method is used as the solution scheme of the kinematic differential equations to get the periodic response.