一种适合于分析复合材料层板的三维杂交应力超单元研究

The Study of a Three-Dimensional HybridStress Isoparametric Super-Element for the Analysis of Composite Laminates

本文基于三维弹性理论和Hellinger-Reissner变分原理,推导了一种适合于分析复合材料层板的三维杂交应力超单元。该单元不同于常规的三维单元,它将复合材料层板沿厚度方向划分成一个或几个单元,每个单元中所包含的层数可视精度和计算费用的要求而定。在应用应力杂交模型导出三维超单元时,本文首次提出一种场变量假设方法,即在超单元内独立假设位移场,而应力场则分层独立假设,因而单元能较好地模拟层合板的力学性能。考虑横向剪切变形和局部扭曲变形的影响,保证了单元分析的精度。同时由于单元的自由度数不随层数的增加而增加,避免了常规三维单元在分析复合材料层板时自由度数随层数的增加而增加的弊端。通过对几个典型的复合材料层板的静、动力分析及与试验的比较。表明了单元能有效地用于各种层板的分析。

A three-dimensional hybrid stress isoparametric super-element is developed on the ba-sis of three dimensional elastic theory and Hellinger-Reissner variational principle for the analysis of composite laminates. Different from the conventional three-dimensional ele-ment,a super-element has a number of plies being chosen to minimize computational cost and yet to maximize numerical accuracy. In the derivation of super-element by appling hy-brid stress model,a new method of assuming field variaties is put forward.i. e. ,to assume displacement field within each super-element but to interpolate stress field independently within each layer of the element. Thus,the mechanical properties can be simulated finely. The transverse shear deformation as well as local warping effects are taken into considera-tion to ensure the accuracy of the element. In the meantime,the number of freedom degrees doesn't increase with the number of layers in the laminate as it does in the conventional case. The static and dynamic analyses of several typical composite laminates are compared with the test results,showing that the element can be used for the analysis of laminates ef-fectively.