Deformation Rigidity Analysis of Assumed Stress Modes in Hybrid Elements
-
摘要: 通过本征变形模式提出识别杂交元零能变形模式和假设应力场中零能应力模式的新方法，同时给出了在假设应力场中增加应力模式时杂交元变形刚度的计算公式．从而从理论上阐明了在假设应力场中增加零能应力模式不仅不能抑制单元零能变形模式而且可能增加非零能变形模式的刚度，因此不宜用来假设应力场；同时进一步指出寄生应力模式将使单元产生虚假应变能而使单元显得过刚，因此即使它能够抑制单元零能变形模式也不宜用来假设应力场，从而为假设应力场提供了合理的建议．数值算例说明了包含零能应力模式和寄生应力模式时单元的性能．Abstract: The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on That, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result in the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.
-
[1] Pian T H H.Derivation of element stiffness matrices[J].AIAA,1964,2(3)：576—577. doi: 10.2514/3.2372 [2] HUANG Qian.Modal analysis of deformable bodies with finite degree of deformation freedom-an approach to determination of natural stress modes in hybrid finite elements[A].In:CHIEN Wei-zang,FU Zi-zhi,Eds.Advances in Applied Mathematics & Mechanics in China[C].Beijing:IAP (International Academic Publishers),1991,3:283—303. [3] Han J,Hoa S V.A three-dimensional multilayer composite finite element for stress analysis of composite laminates[J].International Journal for Numerical Methods in Engineering,1993,36(22):3903—3914. doi: 10.1002/nme.1620362209 [4] FENG Wei,Hoa S V,HUANG Qian. Classification of stress modes in assumed stress fields of hybrid finite elements[J].International Journal for Numerical Methods in Engineering,1997，40(23):4313—4339. doi: 10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N [5] 吴长春,卞学.非协调数值分析与杂交元方法[M].北京:科学出版社,1997,128—174. [6] Pian T H H,Chen D P. On the suppression of zero energy deformation modes[J].International Journal for Numerical Methods in Engineering,1983,19(12):1741—1752. doi: 10.1002/nme.1620191202 [7] Cheung Y K,Wu C C.A study on the stability of 3-fild finite elements by theory of zero energy modes[J].International Journal of Solids & Structures,1992,29(2):215—229. [8] 张灿辉,冯伟,黄黔.杂交元本征应力模式和应力子空间的性质研究[J].力学季刊，2002,23(1)：9—14. [9] 张灿辉, 冯伟,黄黔.杂交应力元的应力子空间和柔度矩阵H对角化方法[J].应用数学和力学，2002,23(11)：1124—1132. -
计量
- 文章访问数: 2302
- HTML全文浏览量: 165
- PDF下载量: 722
- 被引次数: 0
下载:
渝公网安备50010802005915号