A quadrilateral membrane hybrid stress element with drilling degrees of freedom

A new kind of quadrilateral assumed stress hy- brid membrane element with drilling degrees of freedom and a traction-free inclined side has been developed based on an extended Hellinger-Reissner principle which is established by expanding the essential terms of the assumed stress field as polynomials in the natural coordinates of the element. The homogeneous equilibrium equations are imposed in a variational sense through the internal displacements which are also expanded in the natural coordinates, while the tractionfree conditions along the inclined side are satisfied exactly. The use of such special element in the finite element solution is shown to be highly accurate when only a very coarse element mesh is used for plates with V-shaped rounded notches or inclined sides.

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

A New Hybrid Stress Element with Fluid

In the process of shale gas exploitation,there exits two difficult problems:one is the real numerical simulation of a tremendous number of holes in actual shale;the other is the fluid–solid coupling problem involved in holes,where the difficulty of transition at the interface between the Eulerian grid and the Lagrangian grid becomes the most important.In response to these two problems,this paper establishes an element model with both fluid and solid.At the fluid–solid interface,the equilibrium condition of the surface force is introduced to obtain the modified complementary energy functional,and a new hybrid stress element with fluid is derived.The comparison of the simulation results with those of the ordinary commercial finite element software verifies the effectiveness and efficiency of this element,and proves its applicability in the problem of shale with numerous holes.Furthermore,this element can be extended to general problems of solid with fluid in.

A New Classification Method of Stress Modes in Hybrid Stress Finite Element

The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient

Special hybrid stress element for stress analyses around circular cutouts in laminated composites

A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.

A hybrid-stress element based on Hamilton principle

A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.

INCREMENTAL ANALYSIS FOR NONLINEAR RUBBER-LIKE MATERIALS BY HYBRID STRESS FINITE ELEMENT

In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.

Modeling thermal and mechanical cancellation of residual stress from hybrid additive manufacturing by laser peening

Additive manufacturing(AM)of metals often results in parts with unfavorable mechanical properties.Laser peening(LP)is a high strain rate mechanical surface treatment that hammers a workpiece and induces favorable mechanical properties.Peening strain hardens a surface and imparts compressive residual stresses improving the mechanical properties of a material.This work investigates the role of LP on layer-by-layer processing of 3D printed metals using finite element analysis.The objective is to understand temporal and spatial residual stress development after thermal and mechanical cancellation caused by cyclically coupling printing and peening.Results indicate layer peening frequency is a critical process parameter affecting residual stress redistribution and highly interdependent on the heat generated by the printing process.Optimum hybrid process conditions were found to exists that favorably enhance mechanical properties.With this study,hybrid-AM has ushered in the next evolutionary step in AM and has the potential to profoundly change the way high value metal goods are manufactured.

准晶问题多项式应力函数及其在有限元中的应用

本文基于广义Lekhnitskii各向异性弹性理论,提出了一种确定准晶问题多项式应力函数的系统性方法,并将之应用于杂交应力函数(HSF)单元的构造.结果表明,对于准晶平面问题,任意齐n次多项式应力函数至多存在6个独立的多项式,且多项式应力函数的一般表达式可以显式地给出.所得的多项式作为解析试函数用于构造准晶问题的新型八节点HSF单元,与传统的有限元相比,HSF单元具有更高的精度和更优异的性能.

Mindlin板理论高阶精化杂交应力元及稳定性分析

基于Mindlin板理论,构造了杂交应力四边形8节点单元QA8-R。采用任意阶的Timoshenko梁函数构造了三阶边界位移插值函数,该函数确保单元能通过严格的收敛检验。利用Airy应力函数构造了单元域内应力插值函数,该函数包含21个最优选择的应力项。通过精化元方法构造了组合几何刚度矩阵,建立了屈曲分析的有限元列式。数值算例结果表明:QA8-R单元不仅可以通过C^(0-1)分片检验,保证了单元的严格收敛性,而且在不同边界条件下对中厚板的计算精度较高,更易于工程应用。

An Arbitrary Polygonal Stress Hybrid Element for Structural Dynamic Response Analysis

This paper constructs a new two-dimensional arbitrary polygonal stress hybrid dynamic(APSHD)element for structural dynamic response analysis.Firstly,the energy function is established based on Hamilton's principle.Then,the finite element time-space discrete format is constructed using the generalized variational principle and the direct integration method.Finally,an explicit polynomial form of the combined stress solution is give,and its derivation process is shown in detail.After completing the theoretical construction,the numerical calculation program of the APSHD element is written in Fortran,and samples are verified.Models show that the APSHD element performs well in accuracy and convergence.Furthermore,it is insensitive to mesh distortion and has low dependence on selecting time steps.

基于有限元法的半桥IGBT混合模块的可靠性分析与优化设计

为了避免过高的温度和热应力使IGBT模块内部材料疲劳失效,建立了硅基IGBT与碳化硅基JBS组成的半桥IGBT混合模块的有限元仿真模型,通过改变芯片排列位置、各层结构的厚度,以及焊料和陶瓷基板的材质,研究模块结温及最大热应力变化规律,并对模块封装结构进行优化。优化后模块的结温与最大热应力分别下降18℃和80.2 MPa,提高了模块的可靠性。

混合梁斜拉桥钢混结合段剪力连接件受力特性分析

以某大跨混合梁斜拉桥钢混结合段为研究背景,通过ABAQUS有限元软件建立钢混结合段模型,分析最不利轴力荷载工况作用下和最不利弯矩工况作用下钢混结合段剪力连接件受力特性。研究结果表明:在最不利轴力荷载工况和最不利弯矩荷载工况作用下,钢混结合段剪力连接件的承载能力满足设计要求,且腹板和加劲肋处PBL剪力连接件可有效抑制该处钢混界面间相对滑移。

AN ADAPTIVE HYBRID STRESS TRANSITION QUADRILATERAL FINITE ELEMENT METHOD FOR LINEAR ELASTICITY

In this paper, we discuss an adaptive hybrid stress finite element method on quadri- lateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5- node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lam~ constant A. We introduce~ for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.

碳/玻混杂复合材料层合板单钉螺栓连接孔边应力分析

基于经典层合板理论和复合材料机械连接结构螺栓孔边应力计算公式,推导了碳/玻混杂复合材料单钉螺栓连接结构孔边应力的计算方法。以碳/玻混杂复合材料层合板单钉螺栓连接结构为例,计算了各纤维铺层孔边径向应力、环向应力和剪切应力的分布规律。同时,采用ABAQUS有限元软件建立了碳/玻混杂复合材料层合板单钉螺栓连接结构的有限元模型,分析了层合板孔边的应力。结果表明,理论计算结果与有限元结果吻合较好,验证了解析方法的有效性。

基于面积坐标的四边形杂交有限元法

本文针对二维线弹性问题提出了一种基于面积坐标的新型杂交应力四边形有限元法AGQ-LQ 6.该方法基于广义Hellinger-Reissner变分原理,位移逼近采用含内部位移的四节点广义协调元,应力逼近则采用九参数线性应力模式.数值算例表明,本文构造的有限元既能保持面积坐标广义协调元对网格畸变不敏感及粗网格精度较高的优点,又能有效克服泊松闭锁现象.

交叉裂隙岩体裂纹扩展试验及混合有限-离散元数值模拟研究

对预制交叉裂隙岩石试样进行裂纹扩展试验,研究了裂纹萌生、扩展、聚合过程,分析了主裂隙和轴向载荷夹角及主次裂隙夹角对裂纹起裂应力和聚合应力的影响,并用混合有限元-离散元程序,即图形处理器并行化的3D Y-HFDEM代码对试验进行了仿真计算,实现了岩石破坏从连续介质向非连续介质的过渡,对裂纹类及损伤破坏模式进行了识别,捕捉到了试验中难以发现的现象。研究表明:随主裂隙与轴向载荷夹角增加,裂纹聚合区的拉伸裂纹数量增加;裂纹起裂和聚合应力与主裂隙与轴向载荷夹角成正比;主次裂隙夹角增加,岩石的破坏模式由拉伸破坏转为剪切破坏,交叉裂隙加剧岩石破碎程度;主裂隙尖端萌生扩展的拉伸-剪切混合裂缝引起的破坏在岩石破坏中占主导地位,是导致岩体失去承载能力的主控裂纹;混合有限元-离散元仿真软件GPGPU并行化的3D Y-HFDEM IDE在岩石裂纹扩展研究中具有优势,可以捕捉实验室难以发现的损伤断裂类型,可以作为岩石裂纹扩展研究的有力工具。

Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.