THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

LOCKING-FREE DEGENERATED ISOPARAMETRIC SHELL ELEMENT

An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.

ON THE STABILITY ANALYSIS OF PLATES AND SHELLS USING A QUADRILATERAL,16-DEGREES OF FREEDOM PLAT SHELL ELEMENT DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral,16-degrees of freedom flat shell element (called DKQ16).The geometrical stiffness matrix was established.Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.

A novel enriched CB shell element method for simulating arbitrary crack growth in pipes

In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.

Modeling stationary and moving cracks in shells by X-FEM with CB shell elements

The continuum-based(CB)shell theory is combined with the extended finite element method(X-FEM)in this paper to model crack propagation in shells under static and dynamic situations.Both jump function and asymptotic crack tip solution are adopted for describing the discontinuity and singularity of the crack in shells.Level set method(LSM)is used to represent the crack surface and define the enriched shape functions.Stress intensity factors(SIFs)are calculated by the displacement interpolation technique to prove the capability of the method and the maximum strain is applied for the fracture criterion.Also,an efficient integration scheme for the CB shell element with cracks is proposed.

A RECTANGULAR SHELL ELEMENT FORMULATION WITH A NEW MULTI-RESOLUTION ANALYSIS

A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level （RL） to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.

A Smoothed Finite Element Method for the Static and Free Vibration Analysis of Shells

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

Geochemistry of trace elements and Sr-Nd isotopes of foraminifera shell from the Okinawa Trough

Trace elemental associations and Sr-Nd isotopic compositions are of important to recognition of biogenic material from mixed marine sediments. The foraminifera shell from the Okinawa Trough strongly enriches Sr,P,Mn and Ba, enriches Li,U,Th,Sc,Co,Cu,Pb,Zn,Cr,Rb,Y,Sb and light rare earth elements,slightly enriches V,Ga,Zr,Nb,Cd and middle rare earth elements,is short of Mo,In,Sn,Cs,Hf,Ta,W,Ti,Bi and heavy rare earth elements. The mechanism of elemental enrichment in forminifera is the concentrations of trace elements in sea water and selective absorption of trace elements during foraminifera living, as well as the geochemical affinity between major elements and trace elements.The REE (rare earth elements)partition pattern of foraminifera shell of the Okinawa Trough shows enrichment of middle rare earth elements with slightly negative Ce anomaly,which are different from those of foraminifera of the Pacific Ocean.The Sr,Nd isotopic ratios of the Okinawa Trough foraminifera are 0 709 769 and 0 512 162,respectively, which are different not only from those of oceanic water, but also from those of river water of China's Mainland, the former is slightly higher than those of oceanic water,but much lower than those of river water;the latter is slightly lower than those of oceanic water,but higher than those of river water,demonstrating that the Okinawa Trough sea water has been influenced by river water of China's Mainland.

A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures

This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid ele- ment, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method

An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.

Numerical Simulation of Stress-Strain State for Nonhomogeneous Shell-Type Structures Based on the Finite Element Method

Projective-iterative version of finite element method has developed for numerical simulation of the stress-strain state of nonhomogeneous shell-type structures (shells with openings). Plastic deformation of the material is taken into account when using the method of elastic solutions that reduce the solution of elastoplastic problems to solution of elastic problems. Developed PIV’s significant savings of computer calculation has been compared with the calculation on a fine mesh of traditional FEM. Designed scheme allows analysis of the mutual influence of openings. Analysis of the transformation zone of plastic deformation is developed. For definiteness, the cylindrical shell structures with several rectangular openings are considered.

Difference in Number of Electrons in Inner Shells of Charged or Uncharged Elements in Organic and Inorganic Chemistry: Compatibility with the Even-Odd Rule

The recently introduced even-odd rule has been shown to successfully represent chemical structures of ions and molecules. While comparing available drawings in the scientific literature with the list of compounds predicted by the even-odd rule, it became however obvious that existing compounds are fewer than expected. Several predicted compounds involving many covalent bonds have apparently never been experimentally observed. Neutral oxygen for instance is expected to have 6 valence electrons, whereas oxygen can only build a maximum of two bonds, as in water. This specificity is observed for elements in the top-right corner of the periodic table. For compounds to contain only single covalent bonds, and thus follow the even-odd rule, further explanations are necessary. The present paper proposes that those specific elements experience a transfer of electrons from the valence shell into the inner shell, making them unavailable for further bonding. These elements will be described as organic, hereby providing a clear and hopefully unifying definition of the term. In opposition, inorganic elements have a constant inner shell no matter their electrical state or the number of bonds they maintain. More than 70 compounds involving 11 elements of the main group are studied, revealing a progression from fully inorganic elements at the left of the periodic table to fully organic elements. The transition between inorganic or organic elements is made of few elements that take an organic form when negatively charged;they are labelled semi-organic. The article concludes that the fully organic elements of the main group are Oxygen and Fluorine, whereas semi-organic elements are more numerous: C, N, S, Cl, Se, Br and I. Thus, the even-odd rule becomes fully compatible with scientific knowledge of compounds in liquid or gaseous phase.

Stochastic Finite Element Analysis of Plate and Shell Construction

The response of random plate and shell construction is analyzed with the stochastic finite element method (SFEM). Random material properties and geometric dimensions of construction are involved in this paper. A simplified isoparametric local average model is used to describe the random field. Numerical results of the examples indicate that the approach presented herein is an economical and efficient solution for such an analysis compared with Monte Carlo simulation (MCS).

超协调元

该文提出一类超协调的单元理论。不同于在普通协调元中采用的线位移协调插值格式,超协调元的单元插值函数首先引入转角自由度等线位移导数的高阶协调假设,并通过积分推导,进而获得超协调的线位移模型。基于超协调元理论,该文构造了一类新型的三结点三角形平板壳元SCT。数值算例表明:与其他类型单元相比,基于超协调元理论的单元具有计算精度高和计算效率好的优势。该文所提出单元理论构造简单,超协调元理论可以成为构造高性能数值算法的一种新的通用理论。

仿生犁铧耐磨性能仿真分析与试验研究

目的解决传统犁铧耐磨性差、使用寿命短等问题。方法以栉孔扇贝壳为仿生原型,对其表面几何特征进行提取,将棱纹几何结构特征应用于犁铧的设计。设计6种不同仿生棱纹方向及3种不同仿生棱纹间距的犁铧试样,建立离散元模型,分析土壤颗粒运动速度场以及犁铧耕作阻力图。结果表面仿生结构设计改变了土壤颗粒的流动方向,减小了土壤堆积量,降低了所需牵引力,从而提高了耐磨性能。不同仿生棱纹方向犁铧试样中,F-1竖棱纹结构试样的平均耕作阻力最小,平均耕作阻力值为1681.73 N;不同仿生棱纹间距犁铧试样中,棱纹间距为5 mm的F-1-1仿生表面接触的土壤颗粒的运动速度分布和趋势最佳。通过田间试验得出,同种仿生棱纹方向结构设计下,棱纹间距为5 mm的F-1-1试样的耐磨性能最佳,相比传统犁铧试样磨损量减少17.25%。结论合理改变表面仿生棱纹方向与间距设计可显著提高犁铧耐磨性,为仿生技术在农业机械方向上的应用提供参考。

BOUNDARY ELEMENT METHOD FOR ARBITRARY ELASTIC THIN SHELL

In this paper,a boundary element scheme for arbitrary elastic thin shells is elaborated,Based on BEM of 3D linear elasticity and Kirchhoff's hypothesis,boundary integral equations for shells are deduced. As a result,only Kelvin's solution is used,the difficulty,in finding a fundamental solution of arbitrary shells is successfully avoided.

锂离子电池三元正极核-壳结构的电化学-力学模拟

利用有限元模拟技术构建了电化学-力学耦合的三维多物理场锂离子电池模型,进而获得了核-壳正极在放电过程中Li+浓度、应变和应力的分布与演变情况,并研究了放电结束时不同放电倍率、壳厚度和核粒径对应变和应力的影响.结果表明,颗粒中心及核-壳界面处的应力在放电初期迅速达到最大值,然后随着Li+扩散过程的进行,应力逐渐减小.另外,黏结剂和相邻颗粒对电极应力分布有显著影响.减小放电速率和核粒径以及增加壳厚度能够降低电极中的应力.研究结果可为核-壳正极结构的设计与优化以及锂离子电池放电策略提供参考.

山核桃破壳裂纹试验与仿真分析

研究山核桃在冲击力下裂纹产生和发展的规律。用万能力学试验机进行冲击破壳试验,分别对山核桃在长轴、斜向和短轴加载方向各进行3种不同高度的15次重复试验。结果表明,无论加载方向如何,破壳冲击力的最大值都在240 N左右,且越靠近横轴方向力越小,越靠近长轴方向力越大。以此为依据,将山核桃横向截面简化为圆形,通过在传统弹塑性元素接触模型基础上增加强结合力的方法,构建压头—山核桃离散单元模型。仿真结果显示,水平压头会造成山核桃模型对称裂纹形式被压溃;与此同时,竖直状态压头会以S型裂纹形式分裂山核桃模型。通过高速摄像机拍摄山核桃破壳裂纹产生过程,与仿真结果基本一致。为山核桃破壳机械的设计、优化与深入地理解山核桃裂纹产生与发展机理提供重要参考。