An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

Influence of High-Density Bedding Plane Characteristics on Hydraulic Fracture Propagation in Shale Oil Reservoir

The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Finite Element Analysis on Plane Stress Crack Growth in a Power-Law Hardening Material

Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.

Modeling shale with consideration of bedding planes by cohesive finite element method

Shale contains distributed directional bedding planes,which make the shale transverse isotropic.To model shale with consideration of the bedding planes,a cohesive finite element method(CFEM)is developed based on the randomized triangular mesh.The interface orientation generated from such mesh tends to be uniformly distributed with the element number increasing.To represent the bedding plane,the interfaces aligned with the bedding plane are assigned the cohesive law that characterizes the bedding plane while the other interfaces are assigned the cohesive law that characterizes the matrix.By this means,the anisotropy characteristics of the stiffness and the strength of shale are well represented.The simulation examples demonstrate that the bedding plane has a significant influence on the fracture trajectory,which is consistent with the observation in the experiment.It is suggested that this modeling method of shale is feasible.It provides an alternative approach to fracture simulation in shale.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD

Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.

Hybrid Post-Processing Procedure for Displacement-Based Plane Elements

In the analysis of high-rise building, traditional displacement-based plane elements are often used to get the in-plane internal forces of the shear walls by stress integration. Limited by the singular problem produced by wall holes and the loss of precision induced by using differential method to derive strains, the displacement-based elements cannot always present accuracy enough for design. In this paper, the hybrid post-processing procedure based on the Hellinger-Reissner variational principle is used for improving the stress precision of two quadrilateral plane elements. In order to find the best stress field, three different forms are assumed for the displacement-based plane elements and with drilling DOF. Numerical results show that by using the proposed method, the accuracy of stress solutions of these two displacement-based plane elements can be improved.

AN EXACT ELEMENT METHOD FOR PLANE PROBLEM

In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.

蓝宝石晶体纳米压入本构方程

应用有限元方法(FEM)结合神经网络优化及无量纲模型,建立了可统一描述蓝宝石不同晶面纳米压入行为的本构方程。采用纳米压痕方法对蓝宝石晶体的四个典型晶面(C、A、R、M)的表面微力学行为进行了研究,本构方程计算结果与实测结果对比表明:加载、卸载曲线均可由压入深度h的二次函数表达;加载曲线是压入面弹性模量E、屈服应力Y和加工硬化指数n的函数,卸载曲线则除此三个因素之外还与卸载位置(最大深度)h_(max)有关;对同一晶面而言,残余深度hr正比于h_(max),塑性功正比于h_(max)的三次方。结果还表明,对蓝宝石晶体这类难以应用常规力学性能试验研究手段的超硬高脆材料,利用本构方程结合纳米压痕试验,可以比较有效地获得其基本力学性能。

增强蜂窝结构面外力学行为研究

在传统六边形蜂窝结构的基础上添加加强筋,提出了增强蜂窝结构,通过有限元模拟的方法对其在准静态压缩过程中的面外力学行为进行研究,并与传统六边形蜂窝结构进行了对比。研究发现,加强筋的加入显著提高了其面外抗压强度与吸能性,其中对边强化蜂窝结构的平均压缩力最多可提高166.8%,比吸能最多可提高38.53%。增强蜂窝结构在压缩过程中的变形模式均为渐进折叠式,与传统六边形蜂窝结构相比其叠缩褶皱数量增多,变形过程更为稳定,并且具有更多的塑性应变集中区。此外,通过开展参数化研究发现,比吸能与单胞壁厚呈正相关,与单胞边长呈负相关关系。通过对增强蜂窝结构力学性能进行综合分析,发现对边强化峰窝结构是最优的强化方式。

钢筋混凝土夹板墙加固石砌体片墙力学性能分析

为保护福州市平潭地区传统石头厝建筑的独特风格,本研究拟采用钢筋混凝土夹板墙对其进行加固并对其力学性能加以分析。为明确该加固技术对内、外墙的不同加固效果,首先,利用有限元数值分析软件ABAQUS分别建立了未加固、单侧加固和双侧加固的石砌体片墙试件的数值分析模型;然后,通过面外单向加载分析了混凝土加固层厚度及配筋率对加固墙体性的影响。结果表明,钢筋混凝土夹板墙能大幅度提高石砌体片墙的承载力,且随着加固层混凝土厚度的增加,墙体承载能力不断增大,但配筋率对加固效果的提高作用不明显。

当今新平面设计的特征及发展趋势

目的对当今中国新平面设计的特征及发展趋势进行分析,更好地服务于平面设计领域。方法对当今中国新平面设计中的“中国风”视觉元素、艺术动线的视觉符号、充满生机与活力的图案、三维立体空间的视觉表现、图文蒙版的设计手法、单色处理的设计风格、金属质感的设计风格、字体与版式的设计风格、孟菲斯风格的设计、未来主义这10种不同热潮的视觉元素及设计风格进行了简要阐述,梳理了不同设计风格的特点和应用方法。结果传统的平面设计已经无法满足当今人们视觉审美的需求。平面设计的领域发生了本质的变化,已经从传统的平面设计迈入了新平面设计的领域,视觉传达与时代背景息息相关,因而形成了各个阶段多元化的设计风格,探寻不同热潮的视觉元素及设计风格已成为了必然。结论设计师不仅要熟悉和掌握新平面设计发展的脉搏,还要大胆地探寻新平面设计的未知领域。

考虑车轮多边形的动车组车轴疲劳寿命预测

以某型高速动车组车轴为研究对象,基于考虑轮轨柔性的车辆轨道刚柔耦合动力学模型、轮对有限元模型和多轴疲劳模型,以实测多边形磨耗为输入,在速度300 km/h下分析了多边形磨耗对车轴疲劳损伤的影响。研究表明:在多边形磨耗的影响下,轮对受载状态剧烈波动并具有显著的周期性,且受载波动情况与多边形磨耗阶次相关。在18阶多边形磨耗影响下,高速动车组车轴的服役寿命降低至22年,小于《铁路动车组运用维修规程》规定的车轴设计寿命。

考虑地震波输入差异的二维兰州盆地地震效应研究

利用谱元法和多次透射边界相结合的数值模拟方法,探讨了不同地震波输入时,具有大盆地内嵌小盆地特征的二维兰州盆地构造对地表地震波传播、地表峰值加速度(PGA)及其放大系数,以及频域放大特征等影响,分析了地表地震动的放大特征与盆地横向不均匀构造之间的关系。结果表明:1)当输入波的卓越频率接近小盆地最深处的一阶自振频率时,小盆地发生整体共振现象,进而显著改变地震动或放大系数的分布特征。大盆地边缘形成的次生面波在进入更为松散的小盆地时分化为波速差别显著的两阶面波,且盆地较陡一侧边缘形成的面波强度更大。2)无论何地震波入射,盆地内的最强烈地震动集中于小盆地边缘区域,大盆地较陡一侧边缘上方的区域是次强烈地震动放大区,而盆地基底倾角较缓的一侧边缘区域基本无边缘效应。3)兰州盆地基底形状对地震动的分布特征影响强烈,盆地地表地震动的放大系数受输入波的影响明显。4)水平和垂直分量的地震动及放大系数分布特征差别显著,垂直分量上在大盆地较陡一侧边缘及小盆地内形成两个显著放大区,最强烈放大效应区域靠近小盆地中心,而水平分量上的强烈放大区域主要出现在小盆地内的边缘区域。此外,地表不同位置处的频域放大特征也存在明显差别。

米字形填充正方形蜂窝异面平台应力

目的研究冲击速度和结构参数对米字形填充正方形蜂窝异面平台应力的影响规律。方法利用ANSYS/LS-DYNA建立该蜂窝可靠的基于胞元阵列的异面冲击分析有限元模型;基于简化的超折叠单元理论推导该蜂窝的准静态平台应力理论公式,理论值与仿真值相吻合验证理论公式的正确性。对不同壁厚边长比的蜂窝,在不同冲击速度下进行异面冲击仿真分析,利用LS-PrePost软件处理得到相应的接触力-位移曲线,进一步处理得到变形模式和平台应力,并以图表的形式加以展示与分析。结果不同冲击速度下结构参数固定的蜂窝表现出LS、MS和HS等3种不同的异面冲击变形模式,从LS模式转变到MS模式再到HS模式的临界速度分别约为20 m/s和150 m/s;壁厚边长比对变形模式的影响可忽略。结论该蜂窝动态平台应力随冲击速度(或壁厚边长比)的增加而增大,且增长速率不断提高。当其他参数固定时,LS模式和MS模式下该蜂窝的动态平台应力与冲击速度呈二次函数关系,HS模式下动态平台应力与冲击速度的平方呈线性关系;动态平台应力与壁厚边长比呈幂函数关系。基于仿真计算结果,得到了该蜂窝动态平台应力的经验表达式。

含裂纹声子晶体能带分析的改进局部径向基函数配点法

基于直接法局部径向基函数配点法(local radial basis function collocation method,LRBFCM)提出了含裂纹声子晶体反平面弹性波的能带结构计算方法,分析了其能带结构特性,并通过有限元法计算对比验证该数值结果的准确性和有效性.在边界上采用直接法沿方向取局部节点,解决了边界求解不稳定问题,讨论了数值方法的处理技巧对结果的影响.并通过考虑不同声阻抗比、散射体形状(方形、圆形)和裂纹情况,验证了该方法计算含裂纹声子晶体能带结构的适用性.研究了形状参数、配点数对计算结果的影响.最后深入分析了不同长度和位置的裂纹对声子晶体能带结构的影响特性,并进行了对比分析.文章的创新性在于用直接法局部径向基函数配点法解决了含裂纹声子晶体能带结构计算的问题,极大增加了声子晶体的应用价值.研究结果显示:随着裂纹的扩展,能带结构带隙逐渐变窄;当裂纹扩展到一定程度时,金散射体的声子晶体带隙数量会增加,且新增带隙会随着裂纹扩展而变宽,但铝散射体的声子晶体带隙数量会减少;直接法局部径向基函数配点法可以大大提高含裂纹声子晶体能带结构的计算效率和计算精度.

基于离散元法的生态茶园开沟抛土刀设计与参数优化

【目的】旨在设计一种用于生态茶园环境作业的开沟抛土刀。【方法】以正切面折弯角、抛土片面积、抛土片与侧切面夹角为试验因素,以功耗和区域抛土质量为评价指标,采用Box-Benknken中心组合设计法进行离散元仿真试验。【结果】(1)正切面弯折角、抛土片面积、抛土片与侧切面夹角3个因素对功耗和区域抛土质量的影响均显著。(2)仿真试验得出的最优参数组合:正切面弯折角112.7°,抛土片面积3566 mm^(2),抛土片与侧切面夹角132.5°。在最优参数条件下,功耗为1.121 kW,区域抛土质量为11.45 kg。(3)刀具功耗平均误差为12.25%,区域抛土质量平均误差为12.67%,说明该仿真模型较为可靠。

日照市海滩沉积物地球化学元素特征及物源研究

海滩是大自然赋予人类宝贵的自然资源,作为著名的海滨旅游城市,日照市拥有丰富的海滩资源。目前,国内对日照市海滩沉积物地球化学特征和物源的研究相对薄弱,掌握海滩沉积物特征对后续海滩保护、海洋管理和滨海旅游业的发展具有重要意义。本文对日照市自北向南4个海滩5个探槽所采集的73个海滩样品,进行了沉积物粒度、常微量和稀土元素测试分析,系统地研究了日照市海滩沉积物的地球化学元素在平面上的变化特征与其物质来源。结果显示,日照市海滩沉积物普遍较粗,以粗砂和中砂为主,自北向南沉积物呈现细-粗-细的变化特征。常量元素以二氧化硅(SiO2)为主,其次为三氧化二铝(Al2O3)和氧化钾(K2O)、氧化钠(Na2O)、氧化钙(CaO)等;微量元素以钡(Ba)、锶(Sr)、锆(Zr)为主;稀土元素呈现明显的轻稀土元素富集、重稀土元素亏损,球粒陨石标准化曲线呈现左高右低的“V”形曲线,铕(Eu)异常变化范围较大,从正异常-负异常,无明显铈(Ce)异常。通过与长江、黄河及周边中小型入海河流沉积物的稀土元素对比分析,发现研究区内沉积物物质来源较复杂,主要为陆源物质,受到黄河及周边中小河流的影响程度较高。