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应用于弹性问题的重心坐标有限元法 总被引:1,自引:1,他引:0
通过几何的方法构造了在任意多边形上的具有重心型格式的平均值插值函数,并利用Galerkin法提出了应用于弹性问题的重心坐标有限元法.重心坐标有限元法的插值函数在多边形单元间是协调的,能够方便的施加本质边界条件.重心坐标有限元法的插值函数对于不同边数的多边形单元具有统一的表达形式,编程实现简便易行,能够方便的应用于复杂几何区域的求解.通过重心坐标有限元法分别进行了小片试验、悬臂梁和复合材料的有效模量的数值模拟.小片试验的计算精度达到了机器精度;悬臂梁的计算结果与解析解的吻合程度较高;复合材料的有效模量的数值模拟结果与传统有限元和解析解吻合得较好,变化趋势合理. 相似文献
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多边形有限元研究进展 总被引:10,自引:0,他引:10
有限元法是数值求解偏微分方程边值问题的重要方法,采用不规则多边形单元网格, 可以方便有效地模拟材料的力学性能, 又使得区域网格剖分变得灵活方便. 特别是对于复杂的几何形状, 多边形单元网格具有更大的优势. 本文对国内外有关多边形有限元法的最新进展作了初步的总结和评述, 主要以基于位移法的多边形有限元为主.论述了多边形有限元的发展历史, 给出了多边形单元上的Wachspress插值、Laplace插值和重心坐标的一些最新研究成果. 与经典有限元法形函数为多项式形式不同, 多边形单元的形函数为有理函数或者无理函数形式. 多边形单元插值形函数满足线性完备性, 可以再现线性位移场, 像经典有限元法一样直接施加本质边界条件; 插值函数在多边形的边界上是线性的,确保不同单元间的自动协调. 不同单元的插值形函数表达公式形式统一, 方便混合单元网格计算的程序编写. 提出了多边形有限元法今后需要研究的问题. 相似文献
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常规单元的插值函数通常仅考虑单元的几何形状与节点位置,而忽略了反映物理问题关键特性的物性参数,从而降低了其数值分析的效果。相反,理性有限元法是取问题微分控制方程的多项式基本解作为单元内的插值函数,其所形成的刚度阵与问题的物性参数紧密相关,因此它避免了常规有限元法对物理问题和数学问题的割裂,可显著提高数值分析的稳定性和精度。本文利用空间各向异性问题的基本解,构造出满足分片实验要求的八节点理性块体单元。数值算例表明,本文给出的理性单元不仅具有较高的求解精度,而且具有良好的数值稳定性,尤其是对较为畸形的单元反应不敏感。 相似文献
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常规单元的插值函数通常仅考虑单元的几何形状与节点位置,而忽略了反映物理问题关键特性的物性参数,从而降低了其数值分析的效果。相反,理性有限元法是取问题微分控制方程的多项式基本解作为单元内的插值函数,其所形成的刚度阵与问题的物性参数紧密相关,因此它避免了常规有限元法对物理问题和数学问题的割裂,可显著提高数值分析的稳定性和精度。本文利用空间各向异性问题的基本解,构造出满足分片实验要求的八节点理性块体单元。数值算例表明,本文给出的理性单元不仅具有较高的求解精度,而且具有良好的数值稳定性,尤其是对较为畸形的单元反应不敏感。 相似文献
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将风力发电塔视为带有附加质量的变截面悬臂梁,进行横向振动的自振特性分析.采用直接模态摄动法建立风力发电塔自振特性的近似求解方法,与采用梁单元模型和壳单元模型的有限元法的计算结果相比较.数值计算结果表明直接模态摄动法具有较好的精度,形成了半解析解形式. 相似文献
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平面夹杂模型在纤维增强型复合材料中有广泛应用.复合材料内部通常含有不规则形状夹杂,而夹杂物的存在能严重影响材料的机械力学性能,往往导致应力集中及裂纹萌生等失效先兆.先前关于多边形夹杂的研究大多数关注受均匀本征应变下的应力/应变解,而对位移的分析较少. 基于格林函数方法和围道积分,本文给出了平面热夹杂边界线单元的封闭解析解,可方便应用于受任意分布本征应变的任意形状平面热夹杂位移场的数值计算.当夹杂受均匀本征应变时, 只需将该夹杂边界进行一维离散,因而本文方法可直接得出受均匀分布热本征应变的任意多边形夹杂位移场的封闭解析解.当夹杂区域存在非均匀分布本征应变时,可将该区域划分为足够小的三角形单元进行数值计算. 众所周知,应力应变场在多边形夹杂顶点处具有奇异性,容易导致数值计算上的处理困难及相应的数值稳定性问题; 然而本文工作表明,在多边形顶点处位移场是连续有界的, 因而数值稳定性较好.本文算法可以便捷高效地通过计算机编程实现. 文中给出的验证算例,均体现了本文离散方法的高精度、以及计算编程的鲁棒性. 相似文献
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普通截锥壳单元是分析旋转壳结构的常用单元,但应力计算的精度较差;而渐近传递函数解在圆锥壳的应力分析方面具有很高的计算精度。本文针对一般截锥壳单元应力计算精度不高的缺点,将传递函数法与有限元法进行结合,以圆锥壳的渐近传递函数解为插值函数,直接构造了一种高精度的截锥壳单元,该单元位移插值模式满足相容性和完备性要求,并具有力学概念清楚、计算精度高等特点。数值算例表明,采用该单元进行圆锥壳的内力和自由振动 相似文献
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Based on the concept of the base forces by Gao, a new finite element method – the base force element method (BFEM) on complementary energy principle for two-dimensional geometrically non-linear problems is presented. A 4-mid-node plane element model of the BFEM for geometrically non-linear problem is derived by assuming that the stress is uniformly distributed on each sides of a plane element. The explicit formulations of the control equations for the BFEM are derived using the modified complementary energy principle. The BFEM is naturally universal for small displacement and large displacement problems. A number of example problems are solved using the BFEM and the results are compared with corresponding analytical solutions and those obtained from the standard displacement finite element method. A good agreement of the results, and better performance of the BFEM, compared to the displacement model, in the large displacement and large rotation calculations, is observed. 相似文献
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《International Journal of Solids and Structures》2006,43(10):2868-2903
The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations. 相似文献
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《International Journal of Solids and Structures》2005,42(11-12):3261-3287
In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of composite beams of arbitrary constant cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross-section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable. 相似文献
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IntroductionBecauseoftherequirementofc1continuity ,itisverydifficulttoconstructconformingKirchhoffplatebendingelements.Inordertoovercomethedifficulty ,manyapproacheshavebeenpresented .Intheseapproaches,therequirementofc1isreleasedonconditionoftheconvergen… 相似文献
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Edoardo Artioli Paolo Bisegna Franco Maceri 《International Journal of Solids and Structures》2010,47(3-4):383-397
This paper presents a closed-form expression for the homogenized longitudinal shear moduli of a linear elastic composite material reinforced by long, parallel, radially-graded circular fibres with a periodic arrangement. An imperfect linear elastic fibre-matrix interface is allowed. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the fibre domain is solved in closed form by applying the theory of hypergeometric functions, for new wide classes of grading profiles defined in terms of special functions. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. A parametric analysis investigating the influence of microstructural and material features on the effective moduli is presented. The feasibility of mitigating the shear stress concentration in the composite by tuning the fibre grading profile is shown. 相似文献
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In this paper the non-linear analysis of a composite Timoshenko beam with arbitrary variable cross section undergoing moderate large deflections under general boundary conditions is presented employing the analog equation method (AEM), a BEM-based method. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson's ratio and are firmly bonded together. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the AEM. Application of the boundary element technique yields a system of non-linear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy, the range of applications of the developed method and the influence of the shear deformation effect. 相似文献
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为了提高有限元的性能,弹性力学的解析解(齐次方程的通解)常常可用作有限元的试探函数。然而单元自由度数与完备的直角坐标解析解个数并不匹配,不完备的试函数会导致单元有方向依赖性。利用新型局部自然坐标——第二类四边形面积坐标QACM-II(S,T),给出了平面问题对应任意方向纯弯曲状态的应力函数解析解,即S3和T3的线性组合,并推导出了这两组应力函数对应的应力、应变和位移解析解。之后,利用QACM-II表示的解析解构造了非对称的平面4节点8自由度单元USQ4,该单元可以同时通过常应力/应变分片检验和纯弯测试,从而破解了MacNeal局限定理对平面低阶单元的限制。 相似文献
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《International Journal of Solids and Structures》2003,40(9):2215-2248
The objective of this research is to develop a macroscopic theory, which can provide the connection between macro-mechanics and micro-mechanics in characterizing the micro-stress of composite laminates in regions of high macroscopic stress gradients. The micro-polar theory, a class of higher-order elasticity theory, of composite laminate mechanics is implemented in a well-known Pipes–Pagano free edge boundary problem. The micro-polar homogenization method to determine the micro-polar anisotropic effective elastic moduli is presented. A displacement-based finite element method based on micro-polar theory in anisotropic solids is developed in analyzing composite laminates. The effects of fiber volume fraction and cell size on the normal stress along the artificial interface resulting from ply homogenization of the composite laminate are also investigated. The stress response based on micro-polar theory is compared with those deduced from the micro-mechanics and classical elasticity theory. Special attention of the investigation focuses on the stress fields near the free edge where the high macro-stress gradient occurs. The normal stresses along the artificial interface and especially, the micro-stress along the fiber/matrix interface on the critical cell near the free edge where the high macro-stress gradient detected are the focus of this investigation. These micro-stresses are expected to dominate the failure initiation process in composite laminate. A micro-stress recovery scheme based on micro-polar analysis for the prediction of interface micro-stresses in the critical cell near the free edge is found to be in very good agreement with “exact” micro-stress solutions. It is demonstrated that the micro-polar theory is able to capture the micro-stress accurately from the homogenized solutions. 相似文献
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本文分析了含有界面相纤维增强复合材料热残余应力的空间分布。针对材料实际微结构几何特点,建立含有界面相的三维三相单丝模型,用均匀和梯度函数描述界面相模量随空间变化规律,由轴对称体弹性力学理论得到单丝热残余应力分布,结果表明梯度界面降低了残余应力。通过碳纤维电阻法测出T300/环氧树脂单丝体系固化后的纤维轴向应变,与梯度界面的分析结果基本一致。用叠加方法得到密排六方结构代表性体积元(RVE)中纤维间相互偶合的应力场,同时应用有限元法分析RVE中纤维间的残余应力分布,两者结果相互验证。 相似文献