Theory and numerics of three‐dimensional beams with elastoplastic material behaviour

A theory of space curved beams with arbitrary cross‐sections and an associated finite element formulation is presented. Within the present beam theory the reference point, the centroid, the centre of shear and the loading point are arbitrary points of the cross‐section. The beam strains are based on a kinematic assumption where torsion‐warping deformation is included. Each node of the derived finite element possesses seven degrees of freedom. The update of the rotational parameters at the finite element nodes is achieved in an additive way. Applying the isoparametric concept the kinematic quantities are approximated using Lagrangian interpolation functions. Since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells. Due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load‐carrying capacity of beam structures. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite‐deformation irreversible cohesive elements for three‐dimensional crack‐propagation analysis

We develop a three‐dimensional finite‐deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of a drop‐weight dynamic fracture test similar to those reported by Zehnder and Rosakis. The ability of the method to approximate the experimentally observed crack‐tip trajectory is particularly noteworthy. © 1999 John Wiley & Sons, Ltd.     

A particle‐in‐cell solution to the silo discharging problem

The problem of flow of a granular material during the process of discharging a silo is considered in the present paper. The mechanical behaviour of the material is described by the use of the model of the elastic–plastic solid with the Drucker–Prager yield condition and the non‐associative flow rule. The phenomenon of friction between the stored material and the silo walls is taken into account—the Coulomb model of friction is used in the analysis. The problem is analysed by means of the particle‐in‐cell method—a variant of the finite element method which enables to solve the pertinent equations of motion on an arbitrary computational mesh and trace state variables at points of the body chosen independently of the mesh. The method can be regarded as an arbitrary Lagrangian–Eulerian formulation of the finite element method, and overcomes the main drawback of the updated Lagrangian formulation of FEM related to mesh distortion. The entire process of discharging a silo can be analysed by this approach. The dynamic problem is solved by the use of the explicit time‐integration scheme. Several numerical examples are included. The plane strain and axisymmetric problems are solved for silos with flat bottoms and conical hoppers. Some results are compared with experimental ones. Copyright © 1999 John Wiley & Sons, Ltd.     

功能梯度铁电铁磁复合材料弯曲模态下的磁电效应

基于磁致伸缩相与压电相的本构方程,应用弹性力学的方法,建立了功能梯度铁电铁磁复合材料弯曲模态下的磁电耦合静态力学模型。假设铁电和铁磁材料的物理参数均为沿厚度方向的线性或指数函数,分析计算了由PZT作为铁电材料和CoFe2O4作为铁磁材料的双层复合材料的磁电效应。结果表明,在弯曲模态下,磁电电压系数出现两个峰值。负梯度的铁电(或铁磁)材料提高磁电效应,正梯度的铁电(或铁磁)材料降低磁电效应。同号梯度的铁电铁磁材料对磁电效应的影响更大。     

隧道软弱围岩挤压大变形非线性流变力学特性研究

 讨论高地应力条件下隧道软弱围岩发生挤压大变形的复杂力学行为,将挤压大变形归属为变形速率快而收敛速率慢的非线性流变变形范畴。在分析挤压大变形流变力学机制的基础上,分别提出非线性二维黏弹塑性本构模型和大(小)变形三维弹黏塑性本构模型,并进行相关专用程序的研发。运用所研发的材料子程序,对相关流变模型进行理论分析,就乌鞘岭铁路隧道软弱围岩施工开挖大变形问题进行工程应用研究。     

Shanghai center project excavation induced ground surface movements and deformations

Empirical data on deep urban excavations can provide designers a significant reference basis for assessing potential deformations of the deep excavations and their impact on adjacent structures. The construction of the Shanghai Center involved excavations in excess of 33-m-deep using the top-down method at a site underlain by thick deposits of marine soft clay. A retaining system was achieved by 50-m-deep diaphragm walls with six levels of struts. During construction, a comprehensive instrumentation program lasting 14 months was conducted to monitor the behaviors of this deep circular excavation. The following main items related to ground surface movements and deformations were collected: (1) walls and circumferential soils lateral movements; (2) peripheral soil deflection in layers and ground settlements; and (3) pit basal heave. The results from the field instrumentation showed that deflections of the site were strictly controlled and had no large movements that might lead to damage to the stability of the foundation pit. The field performance of another 21cylindrical excavations in top-down method were collected to compare with this case through statistical analysis. In addition, numerical analyses were conducted to compare with the observed data. The extensively monitored data are characterized and analyzed in this paper.     

Thermal–structural analysis of large deployable space antenna under extreme heat loads

Large deployable space antennas may be exposed to severe thermal environments in future space missions; extreme heat loads will result in considerable thermal stresses and deformations which seriously affects the accuracy of the antenna's parabolic surface. In this study, thermal–structural finite element analysis of a deployable AstroMesh antenna under extreme heat loads was presented. Considering position and orientation with respect to the Sun and Earth, the antenna's temperature changing law under orbital heat fluxes was first evaluated to find the worst condition as loading point. Analyses for the antenna under different levels of extreme heat loads were then performed to obtain the temperature distributions utilizing an equivalent quarter antenna model. Based on the temperature calculation results and prestress designs, structural analyses were finally made to gain the resulting stresses and deformations. The analysis results show that the existing antenna may generate significant performance distortion under extreme thermal environments; so attentions for reliability and safety under such conditions should be taken seriously in future antenna works. Modeling and analysis method proposed in this article was validated to be contributive in antenna's thermal and precompensation designs.     

电场活化聚合物（DE）平面弯曲致动器设计

电场活化聚合物在电场力作用下会产生大幅度的形变,可用做微型致动器的理想材料。文章探索电场活化聚合物（DE）平面弯曲致动器的设计方法,为将来更为复杂致动器的设计和应用提供理论依据;阐述了电场活化聚合物卷筒型平面弯曲致动器的工作原理,建立了力学模型,设计了致动器的结构几何参数,推导了圆柱螺旋弹簧横向弯曲刚度及其挠度、转角的计算公式。数值模拟结果表明所设计的平面弯曲致动器可以实现预期的平面弯曲运动,从而验证了这种设计方法的正确性。     

The deflection of a circular parabolic telescope mirror on an elastic foundation

In this article we describe the deflection due to gravity of a parabolic mirror, supported by an annular shaped elastic foundation. We calculate the deflection by solving the thin plate equation for plates with a non-constant thickness numerically. It will be shown that a central hole in the elastic foundation of a certain diameter will minimize the deflection of the mirror and will result in minimal RMS values. We compare the mirror deflection caused by 18 and 27 axial point support to the deflection of a mirror on an annular shaped elastic foundation. It will be shown that an annular shaped elastic foundation results is much less deflection and smaller RMS values compared to the multiple point axial support for mirrors smaller than 1 m diameter and F# ratios larger than 2. Using this foundation method, mirrors may become thinner which results in lightweight constructions.     

In vivo optic nerve head biomechanics: performance testing of a three-dimensional tracking algorithm

Measurement of optic nerve head (ONH) deformations could be useful in the clinical management of glaucoma. Here, we propose a novel three-dimensional tissue-tracking algorithm designed to be used in vivo. We carry out preliminary verification of the algorithm by testing its accuracy and its robustness. An algorithm based on digital volume correlation was developed to extract ONH tissue displacements from two optical coherence tomography (OCT) volumes of the ONH (undeformed and deformed). The algorithm was tested by applying artificial deformations to a baseline OCT scan while manipulating speckle noise, illumination and contrast enhancement. Tissue deformations determined by our algorithm were compared with the known (imposed) values. Errors in displacement magnitude, orientation and strain decreased with signal averaging and were 0.15 µm, 0.15° and 0.0019, respectively (for optimized algorithm parameters). Previous computational work suggests that these errors are acceptable to provide in vivo characterization of ONH biomechanics. Our algorithm is robust to OCT speckle noise as well as to changes in illumination conditions, and increasing signal averaging can produce better results. This algorithm has potential be used to quantify ONH three-dimensional strains in vivo, of benefit in the diagnosis and identification of risk factors in glaucoma.