Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

New tangent stiffness matrix for geometrically nonlinear analysis of space frames

A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.

New Formula for Geometric Stiffness Matrix Calculation

The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

The Matrix Stiffness and Physical Confinement of Hydrogel Microchannel Jointly Induce the Mesenchymal-Amoeboid Transition for Cancer Cell Migration

The migration mode transition of cancer cell enhances its invasive capability and the drug resistance,where physical confinement of cell microenvironment has been revealed to induce the mesenchymal-amoeboid transition(MAT).However,most existing studies are performed in PDMS microchannels,of which the stiffness is much higher than that of most mammalian tissues.Therefore,the amoeboid migration transition observed in these studies is actually induced by the synergistic effect of matrix stiffness and confinement.Since the stiffness of cell microenvironment has been reported to influence the cell migration in 2D substrate,the decoupling of stiffness and confinement effects is thus in need for elucidating the underlying mechanism of MAT.However,it is technically challenging to construct microchannels with physiologically relevant stiffness and channel size,where existing microchannel platforms with physiological relevance stiffness are all with>10μm channel width.Such size is too wide to mimic the physical confinement that migrating cancer cells confront in vivo,and also larger than the width of PDMS channel,in which the MAT of cancer cell was observed.Therefore,an in vitro cell migration platform,which could mimic both stiffness and confinement of the native physical microenvironment during cancer metastasis,could profoundly contribute to researches on cancer cell migration and cellular mechanotransduction.In this paper,we overcome the limitations of engineering soft materials in microscale by combining the collagen-alginate hydrogel with photolithography.This enables us to improve the accuracy of molded microchannel,and thus successfully construct a 3D microchannel platform,which matches the stiffness and width ranges of native environmental confinement that migrating cancer cells confront in vivo.The stiffness(0.3~20 kPa),confinement(channel width:3.5~14μm)and the adhesion ligand density of the microchannel can be tuned independently.Interestingly,using this platform,we observed that the migration speed of cancer cell is influenced by the synergistic effect of channel stiffness and width,and the increasing stiffness reverses the effect of channel width on the migration speed of cancer cells.In addition,MAT has a strong correlation with the channel stiffness.These findings make us reconsider the widely accepted hypothesis:physical confinement can induce MAT.Actually,this transition can only occur in stiff confined microenvironment not in soft one.For soft microchannels,the compliance of the channel walls could cause little cell/nucleus deformation,and the MAT could not be induced.To further investigate the mechanism of MAT,we developed a computational model to simulate the effect of nucleus deformation on MAT.With the model,we found that deforming the cell nuclear by decreasing the nucleus stiffness will reduce the cellmigration speed.This implies that nuclear stiffness plays an important role in the regulation of cancer migration speed and thus MAT in microchannels.The effect of channel stiffness on MAT and migration speed as observed in our experiment could partially explain previous findings reported in the literature,where the increasing matrix stiffness of tumor microenvironment promotes cancer metastasis.Our observations thus highlight the critical role of cell nuclear deformation not only in MAT,but also in regulating cellular mechanotransduction and cell-ECM interactions.This developed platform is capable of mimicking the native physical microenvironment during metastasis,providing a powerful tool for high-throughput screening applications and investigating the interaction between cancer migration and biophysical microenvironment.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

Time-varying stiffness analysis of double-row tapered roller bearing based on the mapping structure of bearing stiffness matrix

Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

An elastic-plastic analysis of short-leg shear wall structures during earthquakes

Short-leg shear wall structures are a new form of building structure that combine the merits of both frame and shear wall structures. Its architectural features, structure bearing and engineering cost are reasonable. To analyze the elastic-plastic response of a short-leg shear wall structure during an earthquake, this study modified the multiple-vertical-rod element model of the shear wall, considered the shear lag effect and proposed a multiple-vertical-rod element coupling beam model with a new local stiffness domain. Based on the principle of minimum potential energy and the variational principle, the stiffness matrixes of a short-leg shear wall and a coupling beam are derived in this study. Furthermore, the bending shear correlation for the analysis of different parameters to describe the structure, such as the beam height to span ratio, short-leg shear wall height to thickness ratio, and steel ratio are introduced. The results show that the height to span ratio directly affects the structural integrity; and the short-leg shear wall height to thickness ratio should be limited to a range of approximately 6.0 to 7.0. The design of short-leg shear walls should be in accordance with the ＂strong wall and weak beam＂ principle.

Stiffness Matrix Derivation of Space Beam Element at Elevated Temperature

Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient temperature, and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation. However, the material stress-strain relationship is very complicated at elevated temperature, and its form is not unique, which brings great difficulty to the derivation of element stiffness equation. Referring to the derivation method of element stiffness equation at ambient temperature, by using the continuous function of stress-strain-temperature at elevated temperature, and based on the principle of virtual work, the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper, which provide basis for finite element analysis on structures at elevated temperature.

A CATENARY ELEMENT FOR THE ANALYSIS OF CABLE STRUCTURES

Based on analytical equations, a cat ena ry element is presented for the finite element analysis of cable structures. Com pared with usually used element(3_node element, 5_node element), a program with the proposed element is of less computer time and better accuracy.

Gershgorin and Rayleigh Bounds on the Eigenvalues of the Finite-Element Global Matrices via Optimal Similarity Transformations

The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

A Finite Element Method for Cracked Components of Structures

In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.

GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES

Geometrically nonlinear stiffness matrix due to large displacement small strain was firstly formulated explicitly for the basic components of pantographic foldable structures,namely, the uniplet, derived from a three node beam element.The formulation of the uniplet stiffness matrix is based on the precise nonlinear finite element theory and the displacement harmonized and internal force constraints are applied directly to the deformation modes of the three node beam element. The formulations were derived in general form, and can be simplified for particular foldable structures, such as flat, cylindrical and spherical structures.Finally, two examples were presented to illustrate the applications of the stiffness matrix evolved.

基于共旋坐标法的几何非线性裂纹梁单元

现有有限元软件模拟裂纹结构主要采用指派裂纹的实体和壳单元,但缺少梁单元。因此,在弹性梁单元的曲率函数中引入Dirac-δ函数表征局部损伤的曲率变化,得到位移分布函数;推导出应变矩阵和单元刚度矩阵,提出了裂纹梁单元。基于共旋坐标法理论进一步发展了考虑裂纹损伤的几何非线性裂纹梁单元,给出了单元的具体算法及流程。利用课题组开发的有限元求解框架,在程序中实现了裂纹梁单元及共旋列式裂纹梁单元。经过典型算例,对比分析了裂纹位置、裂纹深度及外荷载对裂纹梁弯曲性能的影响。结果表明:该单元能够准确描述裂纹结构的挠度变化,同时与现有模拟裂纹结构弯曲变形的单元相比,提出的裂纹梁和共旋列式裂纹梁在精度分别提高了约1%和4%,并且能够退化成无损伤的梁单元和几何非线性梁单元。

基于滑动元法的连续拉索滑移分析

实际工程中,拉索在索撑节点处滑移十分普遍。考虑滑移的影响,索撑节点不能简单地用铰接模拟。现有的拉索滑移分析方法往往需要迭代,计算过程复杂且收敛性无法保证。本文提出一种拉索滑移分析新方法——滑动元法,以预应力鱼腹梁为例进行理论推导,介绍了滑动元法的基本原理和计算步骤。结合有限元软件,利用滑动元法对算例进行计算分析,结果表明,滑动元法计算快速无需迭代,可以较为准确地分析拉索滑移。

基于Feon-Abaqus的杆梁混合结构的有限元分析与应用

由于不同类型单元的结合处其结点自由度不一致,在杆梁混合结构的内力分析过程中整体刚度矩阵的集成存在效率较低、存储空间较大等问题.Feon框架采用的集成方式在运算速度和存储经济性等方面仍存在改进空间,且Feon目前仅能处理线性情形.Abaqus虽能处理各种非线性问题,但缺少针对混合结构的参数化建模解决方法.将Feon与Abaqus进行结合,可以为杆梁混合结构的线性及非线性有限元分析提供更为有效的方法.该文首先改进Feon中整体刚度矩阵的集成方法,新方法显著减小了计算中的过渡矩阵和最终刚度矩阵规模,提高了处理速度和存储经济性.其次基于对Feon框架的改进,提供了在Python平台上直接对杆梁混合结构进行有限元分析的方法,将处理范围由线性拓展到非线性,并编写了相应的Feon-Abaqus转换程序,提供了Abaqus处理混合结构参数化建模解决方法.最后通过算例验证了改进方法在确保计算精度的同时能提高计算速度,验证了基于Feon-Abaqus在杆梁混合结构线性和非线性分析中的有效性.

有限元总体刚度矩阵集成的教学

单元刚度矩阵组装到总体刚度矩阵的原理和方法是有限元教学中基本而重要的内容,因涉及的节点平衡方程问题简单而讲解不够深入,容易导致留下认知隐患。文中介绍了有限元总体刚度矩阵集成的两种教学设计,一种涉及节点平衡方程,另一种不涉及节点平衡方程。针对由节点平衡方程引出的似是而非的认知问题展开教学。教学过程中采用提问、讨论、推导、动画演示等方式以加深学生的认知和理解。

一种复合驱动并联机构刚度分析

针对直升机旋翼支撑平台,设计了一种复合驱动四自由度并联机构,利用复合驱动分支增大了并联机构工作空间。推导了并联机构中各驱动分支和动平台之间的运动关系式,考虑约束力、驱动力和驱动力矩综合作用下复合驱动分支的横向变形、轴向变形和扭转变形,结合机构的运动学方程推导了复合驱动并联机构的刚度矩阵。利用有限元软件验证了并联机构整体刚度矩阵的正确性。仿真结果表明该并联机构的刚度满足使用需要,为含复合驱动并联机构的应用和推广奠定了理论基础。