有限元方法研究修正偶应力Mindlin层合板的尺寸效应

Study on the scale effect of Mindlin laminated plate based on modified couple stress theory by finite element method

修正偶应力层合板的模型已由作者提出。受边界条件和板形状限制,只能够研究承受双正弦载荷四边简支板的尺寸效应。基于修正偶应力理论,提出了一种新的板单元,用于分析具有复杂边界条件的复合材料Mindlin层合板的尺寸效应。该单元是四边形单元,并能够同时满足C0连续条件和C1弱连续条件。为了验证该单元的性能和精度,给出了具有不同边界条件和载荷的算例。数值结果表明,提出的单元不仅能够捕捉到尺寸效应,而且结果与已发表论文中的解析解吻合,具有较高的精度。

Models of composite laminated plates based on modified couple stress theory have been proposed by authors, but the investigation of the scale effect is limited to a simply supported rectangular plate subject to bending loads of fw = q0 sin （ πx/a ） sin （ πy/a ）. In this paper, a novel plate element based on modified couple stress theory is presented to further the study of the scale effects for more complex boundary conditions and load cases on composite Mindlin laminated plate. The present element is a refined quadrilateral one in which the C1 weak-continuity condition and C0 continuity condition can be satisfied simultaneously. To verify the applicability and accuracy of the present element, examples with various boundary conditions and loads are examined. The numerical results based on the current element can not only capture the scale effects of microstructure, but also coincide with analytical results in the pre-existing literatures with high calculating precision.