解析试函数法分析平面切口问题

本文利用平面切口问题的基本解析解构造单元,分析平面切口问题。通过分析平面切口问题的Williams特征方程的有解区间,使用分区加速lleruM&&法依序无漏地计算了平面V型切口特征值。从Williams应力函数出发,推导了V型切口尖端的应力场基本解析解列式。并用此根据分区混合能量原理构造了含切口解析单元ATF-VN的刚度矩阵。文中还对含切口解析单元的单元尺寸和应力项数等因素对分析结果的影响进行了系统的讨论。     

分布粘聚元的系统理论研究

该文扼要地阐述了一种新型计算方法分布粘聚元的研究意义、理论体系和部分研究进展.粘聚元法通过释放传统有限元的刚性粘聚,将连续体离散为满足连续介质条件的体单元以及位于单元边界处的粘聚元相结合的增广体系.基于分区混合广义变分原理建立了分布粘聚元增广体系的分区广义势能泛函,建立了分布粘聚元的控制方程列式.从动量定理入手建立了分...     

复合材料板壳结构的杂交/混合有限元分析

本文建立了一个9节点Lagrange退化壳杂交/混合有限元模型,以用于复合材料板壳结构的有限元分析。该有限元模型基于修正的Hellinger-Reissner原理,位移和应力均采用分离法思想,使得这一单元不仅具有下列优点:1.位移和应力计算精度都比较高;2.消除了多余零能变形模式;3.具有厚薄通用性;4.具有几何不变性,并且较之一般杂交/混合单元计算工作量进一步降低。单元还考虑了横向剪切影响。计算实例表明,本单元关于复合材料浅壳和深壳的解都与参考解吻合很好,且收敛很快。      

用分区混合有限元法分析框支剪力墙

本文用[1]、[2]、[3]中提出的分区混合能量原理和分区混合有限元法分析框支剪力墙结构。在应力梯度大的区域用应力单元,文中用半无限平面问题的解叠加低次多项式组合出应力函数。在应力梯度小的区域用位移单元,文中用八结点等参数单元。由于针对问题的受力特点,把应力元和位移元加以结合,各自发挥特长,能以较疏的网格取得较高的精度。     

三维热弹性力学问题的混合边界元法

本本文给出了三维无限大域内点热源作用下的位移、应力场基本解。采用基于虚拟热源法的间接边界元法和直接边界元法的混合边界元法求解三维有限域热弹性力学问题,有效地避免了热弹性力学问题中域内积分的处理。数值计算表明混合边界元法求热弹性力学问题具有简单方便、精度较高的优点。     

两种材料平面切口应力强度因子计算

本文先推导两种材料平面切口尖端应力应变场,然后利用分区混合有限元在切口尖端构造奇异应力元,在应力元外围划分常规的位移元,计算不同切口张角和不同材料比值下切口应力强度因子。     

面向宏观基本图的多模式交通路网分区算法

为探究不同模式交通流之间的相互作用关系,提出一种考虑路网多模式属性的分区算法。以社会车和公交车速度和路段邻接关系为划分依据,提出初始子区划分、子区合并、子区边界调整的三步分区算法。以深圳多模式交通数据为例进行了子区划分实验,结果表明本文算法相较于其他分区算法能得到两种模式异质性都较低的交通小区;通过识别路网子区中的多模式宏观基本图,验证了实际交通路网中存在多模式宏观基本图。     

二维正交各向异性结构弹塑性问题的边界元分析

给出了二维正交各向异性结构弹塑性问题的边界元分析方法, 包括相应边界积分方程、内点应力公式、边界元求解格式以及弹塑性应力计算方法。在弹塑性分析中, 引入了Hill-Tsai 屈服准则, 采用初应力法和切向预测径向返回法确定实际应力状态。通过具体算例分析了二维正交各向异性结构的弹塑性应力和塑性区分布情况, 部分数值结果与已有结果进行了比较, 两者基本吻合。结果表明, 本文中给出的边界元法可以有效地用于求解二维正交各向异性结构的弹塑性问题。      

混凝土结构三维弹塑性开裂分析

本文指出了Ｗ．Ｆ．Ｃｈｅｎ应变强化弹塑性模型在应状态分区方面的局限性，建立了能够普遍适用的应力状态分区法则，使之能够准确地运用三维应力状态，在此基础上编制了三维弹塑性有限元分析程序，对混凝土破坡后性状采用分布裂缝模型模拟，区别脆性开裂，延性开裂和粘结压碎分别进行了处理，利用所编程序，结合国家八．五攻关项目对拉西瓦拱坝进行了计算分析，得到了有益的结果。     

真实梁板壳局部应力分析的高性能边界元法

经过数十年的发展边界元法在学术界已被看成有限元法的重要补充,但是要使这种补充成为工程界的实际需要还必须用它解决一些有限元法和其他方法难以解决的问题,这就是要充分发挥其高精度的优势,对一些复杂问题得到可靠的结果。为此作者近年通过误差分析提出了一种高精度边界元法计算方案,它在没有解析解和其他数值解做比较的情况下也能求得边界元法的收敛解。这种新方法的一个重要应用领域就是真实梁板壳结构的局部应力分析,即考虑梁板壳结构边缘实际几何、和基座或周围构件联合进行三维高精度边界元分析。该文给出了两个二维高精度边界元分析的算例,一个是真实悬臂薄板梁的横向弯曲,另一个是承受内压的无限长加肋圆柱壳,其中前一个算例揭示了真实悬臂薄板梁端部的局部应力远高于由梁弯曲理论所得到的应力。该文同时建立了悬臂薄板梁三维分析的边界元模型,其边界自由度数已经超出了在微机上用常规边界元法能够求解的规模。因此必须将高精度边界元法结合快速算法才能胜任此类分析,这就是作者提出的高性能边界元法的含义。最后作者展望了这两个相关新领域将要开展的研究内容,希望起到抛砖引玉的作用。     

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

This paper presents two hybrid stress four‐node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allman's rotation is employed, the elements are plagued by zero‐energy rotation modes which induce no strain. A modified Hellinger–Reissner functional that treats the rotation and the skew symmetric stress as independent fields is employed to formulate a stabilization scheme. Particular effort has been made to reduce the number of stress modes to minimum without sacrificing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non‐constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi‐field element which, however, is not frame invariant and exhibits unsuppressed zero‐energy deformation modes. Copyright © 2000 John Wiley & Sons, Ltd.     

A novel 3D mixed finite‐element model for statics of angle‐ply laminates

Analysis of angle‐ply laminates becomes critical and computationally involved because of the presence of extension–shear coupling. A refined three‐dimensional, mixed, 18‐node finite element (FE) model has been developed to analyse angle‐ply laminates under static loading. The minimum potential energy principle has been used for the development of the mixed FE model, where the transverse stress components (τ_xz, τ_yz and σ_z, where z is the thickness direction) have been incorporated as the nodal degrees of freedom, in addition to the three displacement fields. Further, continuity of transverse stress fields through the thickness of the plate and layerwise continuity of displacement fields have been enforced in the formulation. Because all the constitutive and the compatibility conditions have been ensured within the continuum, the present formulation is unique amongst the family of mixed FE models. Results have been obtained for various angle‐ply laminates and compared with analytical and finite‐element solutions, which have been found to be in good agreement with them. Some new results on angle‐ply with clamped–clamped support condition have also been presented to serve as benchmark results. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis of adaptive plate structures by mixed layerwise finite elements

In this paper, a mixed layerwise finite element model for adaptive plate structures is presented. Static and free-vibration analysis of piezoelectric laminated plate structures is considered. A modified Reissner mixed variational principle is used to formulate the finite element model. The mixed functional is formulated using transverse stresses, displacement components and electrical potential as primary variables. The present model, in contrast with the standard layerwise displacement finite element model, fulfils the continuity of all primary variables across the interface between adjacent layers. The in-plane stress components and the electric displacements are evaluated in the post-computation through the piezolaminate constitutive equations. Two illustrative examples are presented for comparison. The predictions of the primary variables and the efficiency of the model, mainly with reference to the interlaminar stresses are discussed and compared with alternative three-dimensional solutions. The present solutions are found to be in good agreement with the benchmark solutions for the static and modal analysis problems.     

Deviatoric hybrid model and multivariable elimination at element level for incompressible medium

A deviatoric hybrid element approach, in which the deviatoric stress σ′, the pressure p and the displacement u are independently dealt with as the element variables, is suggested. The present approach is naturally universal for compressible and fully incompressible mediums. Moreover, it can be extended to the simulation of Stokes flow directly. The resulting hybrid model is able to meet the zero volumetric strain constraint in terms of the incompatible displacement mode only. Therefore an incompressible elimination can be carried out within an individual element, and the complex system elimination for nodal displacements is then avoided. The present 3‐field hybrid model maintains the important features of current hybrid stress elements—finally resulting in a set of displacement‐type discrete equations which can be easily solved, while not a set of u ‐p mixed‐type equations resulted. Regarding the numerical stability of the element, an effective strategy is offered to suppress all the zero energy modes hidden in the model. Copyright © 1999 John Wiley & Sons, Ltd.     

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

In this study, we present free vibration analysis of shells of revolution using the hybrid‐mixed finite element. The present hybrid‐mixed element, which is based on the modified Hellinger–Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes. Copyright © 2001 John Wiley & Sons, Ltd.     

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

In this paper, we present a non‐linear finite element formulation for piezoelectric shell structures. Based on a mixed multi‐field variational formulation, an electro‐mechanical coupled shell element is developed considering geometrically and materially non‐linear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference in the electric potential in the thickness direction of the shell. Incorporating non‐linear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner–Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three‐dimensional transversal isotropic material law, thus the kinematic in the thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields. Accounting for material non‐linearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperature‐dependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature‐dependent hysteresis curves. Copyright © 2011 John Wiley & Sons, Ltd.     

Three-dimensional finite element analysis of fracture modes for the pull-off test of a thin film from a stiff substrate

A three-dimensional geometrically nonlinear finite element analysis model is presented to study the interfacial delamination for the pull-off test of a thin film strip debonded from a stiff substrate. The strain energy release rates of all three modes (mode I, mode II, and mode III) along the debond front are considered and calculated to investigate the mixed fracture modes for the entire deformation regime from bending plate to stretching membrane. These results indicate that the individual strain energy release rates and the total energy release rate vary along the width of the debond front and strong three-dimensional edge effects exist near the free edges of the film. Interestingly, residual stress also plays an important role in controlling mixed fracture modes and the variation of the energy release rates. Finally, the three-dimensional finite element model is compared with an analytical solution developed earlier. The three-dimensional finite element model is found to provide additional insights for interfacial delamination for the pull-off test.     

A mixed solid‐shell element for the analysis of laminated composites

This paper presents a versatile low order locking‐free mixed solid‐shell element that can be readily employed for a wide range of linear elastic structural analyses, that is, from thick isotropic structures to multilayer anisotropic composites. This solid‐shell element has eight nodes with only displacement degrees of freedom and few assumed stress parameters that provide very accurate interlaminar stress calculations through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The element formulation is based on the well‐known Fraeijs de Veubeke–Hu–Washizu mixed variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid‐shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar stress field in multilayer structures, which is achieved by the introduction of a constraint equation on the interlaminar stresses in the Fraeijs de Veubeke–Hu–Washizu principle‐based enhanced assumed strains formulation. The intelligent computer coding of the present formulation makes the present element appropriate for a wide range of structural analyses. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, and shell and laminated composite analyses are investigated and the results are compared with those available in the literature. These benchmark examples reveal that the proposed formulation provides very good results for the structural analysis of shells and multilayer composites. Copyright © 2011 John Wiley & Sons, Ltd.     

A mixed finite element for the nonlinear analysis of in-plane loaded masonry walls

A mixed membrane eight-node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history-dependent 2D stress-strain constitutive law is used to model masonry material, the element derivation is based on a Hu-Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral-type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement-based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.