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A novel post-processing method for predicting the interlaminar shear stresses of laminated plates

DOI：10.7511/jslx20201205003

 作者 单位 E-mail 杨胜奇 大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 116024 刘书田 大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 116024 stliu@dlut.edu.cn

层合板是航空航天领域典型的承力构件，过大的层间应力是导致其分层失效的主要原因。准确的层间应力预测往往依赖于三维平衡方程后处理方法（TPM）。然而，该方法需要计算面内应力的一阶导，使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力。本文在三维平衡方程后处理方法的基础上，提出了一种新后处理方法（NPM）。新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导。基于提出的新后处理方法和C0型板理论，仅需使用线性单元就可以预测层合板的横向剪应力。为了验证所提方法的有效性，本文基于修正锯齿理论（RZT）和所提方法构造了一种C0连续的三节点三角形线性板单元。数值算例表明，所提方法和三维平衡方程后处理方法具有相同的计算精度，提出的板单元能够准确高效地预测层合板的横向剪应力。此外，所提方法便于结合现有的有限元商用软件使用，基于商用软件中板壳单元获得的节点位移，使用新后处理方法极易获得准确的层间剪应力。

Laminated plates are typical bearing members in the aerospace industry.Excessive interlaminar shear stresses are the main cause of delamination failure.The accurate prediction of the interlaminar shear stresses often depends on the post-processing method (TPM) for three-dimensional equilibrium equations.However,this method needs to calculate the first derivative of the in-plane stresses,so that simple linear element based on the C0 plate theories cannot use TPM to calculate the transverse shear stresses.Based on the TPM,a novel post-processing method (NPM) is proposed in this paper.The NPT eliminates the high-order derivative of displacement parameters generated in the TPM through the Virtual Work Equivalent Method (VWEM).So,accurate transverse shear stresses can be obtained by linear elements using the NPT and C0 plate theories.To verify the effectiveness of the NPT,an efficient C0-continuous three-node triangular plate element is formulated based on the refined zigzag theory (RZT) and the NPM.Numerical examples show that the proposed NPM have the same calculation accuracy as the TPM,and the proposed plate element can accurately and efficiently predict the transverse shear stresses of laminates.In addition,the NPM is very easy to use in combination with existing commercial finite element software.Based on the nodal displacements obtained by the plate and shell elements in commercial software,the NPM can easily obtain accurate interlaminar shear stresses.