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《Acta Mechanica Solida Sinica》2015,(6)
A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can be applied to nonlinear problems. The weak patch test guarantees the convergence of the element. Then the linear element is extended to the geometrically nonlinear analysis in the framework of Total Lagrangian(TL) formulation. The numerical tests indicate that the present element is accurate and insensitive to mesh distortion. 相似文献
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经典连续体理论不包括物质内部尺度,当考虑应变软化问题时,有限元结果对网格具有很强的依赖性。与经典连续介质力学理论不同,Cosserat连续体模型在传统平动自由度的基础上添加了一独立的旋转自由度,在本构模型中引入了内尺度参数。本文研究了基于Cosserat理论的平面4和8节点等参元以及8(4)节点线、角位移混合插值等参单元,给出Cosserat单元分片试验的实施过程。最后将单元运用到小孔应力集中问题的分析当中,通过计算结果与理论解的比较,表明了4和8节点以及8(4)节点等参元的适用性,为问题的非线性分析打下基础。 相似文献
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本文导出一种等参协调元位移函数的新的表示方法,在此基础上建立起了构造等参非协调元的新方法。作为实例,构造出两个可以给出单刚显式的四结点平面非协调新单元。 相似文献
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12结点三维等参奇异单元的构造和应用 总被引:1,自引:0,他引:1
通过改变三维8结点六面体等参单元的结点位置、结点数目和形函数,构造了一种12结点三维等参奇异单元,该单元的应力场具有1/(√r)奇异性,可以模拟裂缝前沿的奇异应力场;该单元的位移模式在其中两个坐标方向是线性变化的,因此,该单元与线性单元连接时不需要过渡单元,仍能保证交界面位移协调,克服了20结点三维等参奇异单元不能与线性单元协调连接的缺陷;文章最后将该奇异单元布置在裂缝前沿,应用有限元法计算了三点弯曲梁预制裂缝前沿的应力强度因子,该结果与规范公式计算值基本一致. 相似文献
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为了研究层合壳脱层,本文首先建立了柱坐标系下Hamilton 正则方程的8 节点等参元列式;然后分别采用了"先分后合" 模型和"弱粘接" 模型对开口壳的脱层损伤进行了模拟;通过利用层间的力学关系建立了整个壳的求解方程;最后分别从粘接完好和脱层两类情况对开口壳进行研究,并计算脱层前缘裂纹扩展的能量释放率. 数值实例的分析结果表明环向脱层受外载荷影响大于轴向脱层外载荷影响,脱层深度对两类脱层模型影响较大. 相似文献
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Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area. 相似文献
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The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the Bnet method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian coordinates. In this paper, a thin plate spline element is developed based on the spline element L8 and the refined technique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes. 相似文献
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4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.The project supported by the National Natural Science Foundation of China (10225212, 50178016, 10421002) and the Program for Changjiang Scholars and Innovative Research Team in University of China The English text was polished by Keren Wang. 相似文献
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拟协调元研究综述 总被引:1,自引:0,他引:1
拟协调元是有限元中十分重要的、具有特色的一种列式体系. 拟协调元列式简单、灵活, 统一了协 调元、非协调元等列式方法. 在列式中, 拟协调元将几何方程和平衡方程同时弱化, 并强调基函数在有限元空 间中的重要作用; 借助对位移和应变离散精度的控制, 拟协调元保障了单元的收敛性, 并可以利用泰勒展开校 核进行简便直接的收敛性分析. 研究者们利用拟协调元已经构造了大量的优秀的单元, 并广泛地应用到结构问 题、流体流动问题、非线性分析、稳定性和破坏分析等方面. 这些工作集中体现了拟协调元的理论价值和工程 应用价值. 对拟协调列式方法、列式理论和已发表文献中的主要拟协调单元进行了总结. 最后对拟协调的研究 工作进行了展望. 相似文献
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In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements. 相似文献
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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. 相似文献
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Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the triangular area coordinates and the B-net method, which can exactly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The numerical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions. 相似文献
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密闭腔体声-结构耦合系统的动力灵敏度分析 总被引:5,自引:0,他引:5
以密闭空腔为对象,开展了声-结构耦合系统的动力分析和灵敏度计算,为系统性态优化设计提供理论和算法基础。分别把结构和声场进行离散化,推导了声-结构耦合系统的有限元方程,求解了耦合系统的频率和声压级响应。在此基础上,以结构尺寸为设计变量,计算了耦合系统的固有频率和声压级响应的灵敏度,解决了声-结构耦合系统动力灵敏度的数值算法问题。 相似文献
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Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method.
Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion.
In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order
shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the
element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized
conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric
coordinates. Furthermore, the hybrid post-processing procedure, which was firstly proposed by the authors, is employed again
to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC,
exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method,
the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple,
effective and reliable finite element models.
The project is supported by the National Natural Science Foundation of China (10502028), the Special Foundation for the Authors
of the Nationwide (China) Excellent Doctoral Dissertation (200242), and the Science Research Foundation of China Agricultural
University (2004016). 相似文献
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The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam element. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approximately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l2) and when regular elements are used l is the element length.The Project Supported by National Natural Science Foundation of China. 相似文献
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First order shear deformation theory is applied to analyze the behavior of one-side (unbalanced) and two-side (balanced) patched lap joints containing initial through cracks. The joints are made of adherends bonded together by adhesives. An adhesive interface plate element is introduced; it consists of an adhesive layer weighted by influence of the adherend. The thin adhesive layer is assumed to behave elastically and modelled as a simple tension-shear spring. The mathematical model contains layers of adherend and weighted adhesive layer.Finite elements are employed to model the adherend with an 8-node isoparametric plate element and interface layer with a 16-node plate element. Numerical results are obtained for one-side and two-side patches the width of which could be narrower or wider than the crack length. The former leads to bulging and possible peeling while the latter provides better bonding. Stresses and crack-tip stress intensity factors are calculated for different patch thickness. Effectiveness of the weighted adhesive layer model is exhibited by comparing the present results with those found in previous work where the adhesive is modelled as an individual layer. 相似文献