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1.
黄若煜  吴长春 《力学学报》2004,36(4):419-426
借助于Cosserat连续介质模型,探讨了应力函数和位移对避免有限元C$^{1}$ 连续性困难的互补性作用. 通过对应力函数对偶理论的深入分析,为将应力函数列式得到的 余能单元转化为具有一般位移自由度的势能单元提供了严格的理论基础,在此基础上, 给出应用应力函数构造有限元的一般方法.  相似文献   

2.
修正的偶应力线弹性理论及广义线弹性体的有限元方法   总被引:1,自引:0,他引:1  
以含偶应力的弹性理论为基础,考虑小变形情况下变形体的平动变形和旋转变形,提出关于偶应力与曲率张量的线性本构关系,建立一般弹性体的线性模型。为满足有限单元C1连续性要求,考虑转角为独立变量,利用罚方法引入约束条件,构造一般弹性体的约束变分形式。应用8节点48个自由度的实体等参元,建立一般弹性体力学响应分析的有限元方程。对悬臂梁的静力和动力分析表明,一般弹性体模型较之经典弹性力学更适合结构分析;较之Timoshenko梁模型,一般弹性体模型能够计及结构尺度对结构动力特性和动力响应造成的显著影响。  相似文献   

3.
应用膜板比拟关系 ,可以避开 c1 连续性的困难 ,为板单元的构造提供了一种新的途径 ,并已成功地构造出一系列相应的板单元。本文构造了一个四节点二十四自由度的平板壳单元 ,该单元由平面四节点理性元 RQ4(膜部分 )和由膜板比拟理论构造的一个四节点十二自由度的板单元 (弯曲部分 )构成。该单元构造简单 ,数值结果表明具有很好的收敛性和精度。  相似文献   

4.
基于偶应力理论剪切带问题的弹塑性有限元分析   总被引:3,自引:0,他引:3  
对于软化材料的剪切带问题,传统弹塑性有限元分析遇到了困难,进入弹塑 性阶段,计算结果对网格划分敏感,出现所谓的有限元网格依赖性问题,随着网格的细分, 计算常常因不收敛导致失效. 用有限元软件ABAQUS计算了3个例题,证实了传统弹塑性 有限元分析软化材料剪切带问题的局限性,同时证实对于无剪切带的厚壁筒问题不会出现上 述问题. 进一步引入细观非局部化理论,对非局部理论含有的细观参数\ell 进行了深入讨论,并采用可通过C0 -1分片检验的18参偶应力三角形单元, 重新计算了3个例题,结果避免了上述问题,说明 细观偶应力有限元尤其适用于分析剪切带问题.  相似文献   

5.
基于Hellinger-Reissner变分原理的应变梯度杂交元设计   总被引:2,自引:0,他引:2  
李雷  吴长春  谢水生 《力学学报》2005,37(3):301-306
从一般的偶应力理论出发,基于Hellinger-Reissner变分原理,通过对有限元 离散体系的位移试解引入非协调位移函数,得到了偶应力理论下有限元离散系统的能量相容 条件,并由此建立了应变梯度杂交元的应力函数优化条件. 根据该优化条件,构造了一 个C0类的平面4节点梯度杂交元,数值结果表明,该单元对可压缩和不可压缩状态的 梯度材料均可给出合理的数值结果,再现材料的尺度效应.  相似文献   

6.
基于偶应力模型的连续体结构拓扑优化设计   总被引:1,自引:0,他引:1  
经典连续介质理论不包含材料尺度参数,因而基于经典理论的结构拓扑优化无法显现尺度效应.本文在偶应力理论的框架下,构造了四节点四边形离散偶应力单元,将传统的SIMP方法推广至偶应力介质.结果表明,在以结构的最大刚度为目标的设计中,偶应力介质的最优结果取决于宏观结构尺寸与材料微结构尺寸(或者特征长度)的比值,最优结果具有明显的尺度效应,具体为,二者比值较大将产生与传统理论相似的结构,而二者比值相当则产生独特的偶应力主导的结构.  相似文献   

7.
无网格伽辽金法求解平面偶应力问题   总被引:2,自引:2,他引:0  
提出采用无网格伽辽金法(EFGM)求解偶应力问题,以避免有限元求解中因C1连续要求可能引起的不便。推导了基于二次基和移动最小二乘技术的EFGM计算公式,通过计算受轴向均匀拉伸的带中心小孔无限大板和细长杆的偶应力问题,对所提方法进行了数值验证,与解析解相比结果令人满意,此外还讨论了节点密度和权函数对计算结果的影响。数值结果表明,所提算法可有效地求解平面偶应力问题。  相似文献   

8.
本文利用[1]的方法,构造了一个九节点非协调三角形平面单元.与一般有限元相比可以提高一阶收敛精度,应力可直接在单元节点上得到.形成单刚矩阵时,不需要在单元域内进行数值积分,容易构造曲边单元.文末的算例表明,仅用很少的单元,位移和应力即可获得较高的精度.  相似文献   

9.
1.引言在经典的连续介质力学中,物体是假设由无穷小的质点所组成,因而不能承受分布的体力偶及面力偶的作用,不然的话就要导致无限大应力的出现.在此假设下,得到的应力张量是对称的.1887年W.Voigt 设想过物体是由非常小但不为零的体积元素所组成,内面力偶的存在是可能的.1909年Cosserat 兄弟提出了一个偶应力(couple-stresses)的理论,但长期内,这个理论没有受到应有的注意.1910年C.Somigliana,1953年S.Bodaszewski 考虑了非对称应力的情况,但他们的结果是错误的.1956年R.Tiffen 和A.C.Stevenson 研究了受有体力偶的弹性体的无  相似文献   

10.
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   

11.
带旋转自由度C^0类任意四边形板(壳)单元   总被引:5,自引:0,他引:5  
朱菊芬  郑罡 《计算力学学报》2000,17(3):287-292300
基于Reissner-Mindilin板弯曲理论和Von-Karman大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Allman膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点C^0类板单元。大量算例表明:该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。  相似文献   

12.
本文全面讨论了基于平面弹性--板弯曲模拟关系的薄板有限单元的理论和方法,由于直接对弯矩函数进行插值,c1连续性的要求得以自然避免,薄板单元可以直接在c0连续的层面上加以构造,无需借用Reissner-Mindlin的中厚板理论,由之引发的闭锁问题也得以避免,本文系统地阐明了平面弹性膜单元与薄板弯曲单元的对应关系,及由平面弹性膜单元的向薄板弯曲单元转换的一整套方法。为薄板单元的构造提供了一条新的有余的途径,文中给出了对应于平面弹性膜单元CST,LST,Q4,Q8的薄板单元,我们称之为MPS板单元,MPS板元以挠度和转角为自由度,便于实际应用,和其它板单元相比具有非常高的精度。  相似文献   

13.
加强板的弯矩函数列式   总被引:1,自引:0,他引:1  
本文首先谇薄板弯曲问题矩函数的物理意义,据此,将弯矩函数列式推广到具有加强条的薄板弯曲问题,给出了与平面弹性问题完全对应的余能原理。  相似文献   

14.
In the present article, axisymmetric bending and stretching of functionally graded (FG) circular plates subjected to uniform transverse loading based on fourth-order shear deformation plate theory (FOST) have been studied. Using a fourth-order shear deformation theory, the solutions for deflection and rotation functions of FG plates are presented in terms of the corresponding quantities for a homogeneous plate using the classical plate theory (CPT), from which solutions one can easily obtain the FOST solutions for axisymmetric bending of FG circular plates. It is assumed that the effective mechanical properties of the functionally graded plates through the thickness are continuous functions of the volume fractions of the constituent parts which are themselves defined by a power-law function. Numerical results for maximum deflection and shear stress are presented for various percentages of ceramic–metal volume fractions. These results are also compared with those obtained from the first-order shear deformation plate theory of Mindlin (FST), the third-order shear deformation plate theory of Reddy (TST) as well as the exact three-dimensional elasticity solution. It is found that although the maximum deflections obtained using FOST and TST are close to each other, the through-thickness shear stress is predicted more accurately by the FOST formulation than by the TST.  相似文献   

15.
板弯曲求解新体系及其应用   总被引:41,自引:3,他引:38  
钟万勰  姚伟岸 《力学学报》1999,31(2):173-184
建立平面弹性与板弯曲的相似性理论,给出了板弯曲经典理论的另一套基本方程与求解方法,然后进入哈密顿体系用直接法研究板弯曲问题.新方法论应用分离变量、本征函数展开方法给出了条形板问题的分析解,突破了传统半逆解法的限制.结果表明新方法论有广阔的应用前景.  相似文献   

16.

In this study, an analytical procedure for the bending problem of a viscoelastic sandwich plate with a corrugated core is presented. Reissner–Mindlin plate theory and N-termed Prony series are employed to define the elastic and time-dependent contributions of the governing equations, respectively. Three different corrugation patterns, i.e., rectangular, trapezoidal, and triangular, are examined. Moreover, the structure is analyzed under both simply support and clamp boundary conditions. The calibrated material parameters of polymethyl methacrylate (PMMA) for the Generalized Maxwell rheological model are employed to show the viscoelastic response of the structure. A 3D finite element simulation of the problem is also conducted to confirm the accuracy of the analytical formulation. The two well-known creep and stress relaxation phenomena of the viscoelastic materials are examined for the mentioned corrugation cores and both boundary conditions analytically and numerically. The time-dependent dimensionless deflection and resultant von Mises stress distributions are provided. Besides, the variation of the results with various rise-times and applied load are studied in detail. The von Mises stress contours of the upper surface of the structure at the end of the creep test are also presented. The finite element method outcomes verify the analytical results with excellent compatibility. The proposed analytical procedure can be used as an efficient tool to study the effects of various parameters such as material, geometrical constants, and corrugation pattern on bending of viscoelastic sandwich plates with corrugated core problems for design and optimization, which involves a high number of simulations.

  相似文献   

17.
In the first part (Lebée and Sab, 2010a) of this two-part paper we have presented a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff–Love theory (3 in-plane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called Bending-Gradient plate theory is an extension to arbitrarily layered plates of the Reissner–Mindlin plate theory which appears as a special case when the plate is homogeneous. Moreover, we demonstrated that, in the general case, the Bending-Gradient model cannot be reduced to a Reissner–Mindlin model. In this paper, the Bending-Gradient theory is applied to laminated plates and its predictions are compared to those of Reissner–Mindlin theory and to full 3D (Pagano, 1969) exact solutions. The main conclusion is that the Bending-Gradient gives good predictions of deflection, shear stress distributions and in-plane displacement distributions in any material configuration. Moreover, under some symmetry conditions, the Bending-Gradient model coincides with the second-order approximation of the exact solution as the slenderness ratio L/h goes to infinity.  相似文献   

18.
This is the first part of a two-part paper dedicated to a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff–Love theory (3 in-plane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called the Bending-Gradient plate theory is described in the present paper. It is an extension to arbitrarily layered plates of the Reissner–Mindlin plate theory which appears as a special case of the Bending-Gradient plate theory when the plate is homogeneous. However, we demonstrate also that, in the general case, the Bending-Gradient model cannot be reduced to a Reissner–Mindlin model. In part two (Lebée and Sab, 2011), the Bending-Gradient theory is applied to multilayered plates and its predictions are compared to those of the Reissner–Mindlin theory and to full 3D Pagano’s exact solutions. The main conclusion of the second part is that the Bending-Gradient gives good predictions of both deflection and shear stress distributions in any material configuration. Moreover, under some symmetry conditions, the Bending-Gradient model coincides with the second-order approximation of the exact solution as the slenderness ratio L/h goes to infinity.  相似文献   

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