EI、Scopus 收录
中文核心期刊
申志强, 夏军, 宋殿义, 程盼. 基于高阶剪切变形理论的四边形求积元板单元及其应用[J]. 力学学报, 2018, 50(5): 1093-1103. DOI: 10.6052/0459-1879-18-225
引用本文: 申志强, 夏军, 宋殿义, 程盼. 基于高阶剪切变形理论的四边形求积元板单元及其应用[J]. 力学学报, 2018, 50(5): 1093-1103. DOI: 10.6052/0459-1879-18-225
Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan. A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1093-1103. DOI: 10.6052/0459-1879-18-225
Citation: Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan. A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1093-1103. DOI: 10.6052/0459-1879-18-225

基于高阶剪切变形理论的四边形求积元板单元及其应用

A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION

  • 摘要: 近年来由各类新型复合材料或功能梯度材料构成的板结构在工程领域得到了广泛应用,其显著特点是材料性能沿板厚变化.为合理考虑横向剪切应变,许多学者基于Reddy高阶剪切变形理论,构建了不同的有限元单元对该类板结构进行分析,但其中满足C^1连续条件的单元相对较少.本文基于Reddy高阶剪切变形理论,采用求积元方法,建立了C^1连续的四边形板单元.利用该单元对均质材料、复合材料、功能梯度材料构成的等厚度矩形板、变厚度矩形板及等厚度斜板的线弹性弯曲和自由振动问题进行了计算分析,并与现有文献中的相应计算结果进行了对比.研究表明:基于高阶剪切变形理论的四边形求积元板单元具有较高的计算效率和良好的适应性,文中各类材料构成的等变厚度矩形板及等厚度斜板均只需1个单元即可得到理想的计算结果.对于等/变厚度矩形板,可仅使用9\times9个积分点,而对于等厚度斜板,随着斜角的增大,所需积分点的数目逐渐增多至15\times 15.该四边形求积元板单元可进一步用于新型复合材料板的非线性分析.

     

    Abstract: Plate structures made of advanced composite materials or functionally graded materials have been widely used in engineering practice recently, which is characterized by the variation of material properties along the plate thickness. Several plate elements have been presented utilizing the finite element formulation based on Reddy's higher-order shear deformation theory which yields more accurate transverse shear strain distributions of these structures. However, the C^1 continuous plate elements is very limited. Based on Reddy's higher-order shear deformation theory, a C^1 continuous quadrilateral plate element is established using the weak form quadrature element method in this work. The element presented here is then used for linear flexural and free vibrational analyses of the rectangular and skew plates made of homogenous or composite materials with constant thickness as well as the homogenous rectangular plates with variable thickness. The numerical results of quadrature element formulation are compared with those of other numerical method from the open literatures in order to validate the correctness and efficiency of the presented quadrature plate element. It is shown that only one quadrature element is fully competent for linear analysis of a quadrilateral plate regardless of its thickness variation and component materials. As for rectangular plates with constant or variable thickness, one quadrature element with only 9\times 9 numerical integration points is needed. And for skew plates, the number of numerical integration points required for acceptable accuracy gradually increases to 15\times 15 with the skew angle enlargement. As a completive numerical formulation, the quadrilateral quadrature plate element can be further applied in nonlinear and transient analyses of composite material plate structures.

     

/

返回文章
返回