Free Vibration Analysis of Laminated Composite Plates Based on the Reconstructed Edge-Based Smoothing DSG Method
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摘要:
重构边界光滑离散剪切间隙（RES-DSG3）法，利用边界光滑技术将域积分转化为沿光滑域边界的边界积分，结合基于全局坐标系的非等参离散剪切间隙（DSG）法，避免了坐标映射和Jacobi矩阵的计算，同时克服了“剪切自锁”现象，提高了计算的精度。基于一阶剪切变形理论，采用该文给出的方法，从不同材料参数、边厚比、边界条件等几个方面对复合材料层合板自由振动固有频率进行了数值分析，通过典型算例的计算，验证了该方法的可行性和有效性。
Abstract:To avoid transverse shear locking and improve the accuracy, the RES-DSG3 method was proposed through the incorporation of the non-isoparametric DSG method with a novel edge-based smoothing technique based on global coordinates, and all the integration of smoothed matrices can be calculated along the boundary segments of smoothed cells without coordinate mapping. Based on the 1st-order shear theory, the RES-DSG3 method was used to analyze free vibration natural frequencies of laminated composite plates with different material parameters, edge-thickness ratios and boundary conditions. The free vibrations of the composite plates were analyzed numerically. The calculation of the example verifies the feasibility and effectiveness of the proposed method.
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图 2 三角形单元和基于边界的光滑域
Figure 2. Triangular elements and smoothing domains associated with edges
表 1 四层复合材料简支层合板的一阶无量纲固有频率
Table 1. The non-dimensional 1st fundamental frequency of the simply supported 4-layer laminated composite plate
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表 2 三层复合材料层合板的一阶无量纲固有频率
Table 2. The non-dimensional 1st fundamental frequency of the 3-layer laminated composite plate
a/h method SS SC CC a/h method SS SC CC 2 ref. [22] 5.211 5.217 5.263 10 ref. [22] 14.804 17.199 19.678 ref.[21] 5.205 5.211 5.257 ref. [21] 14.767 17.175 19.669 present 5.149 5.571 5.256 present 14.475 17.346 19.626 5 ref. [22] 10.207 10.658 11.274 100 ref. [22] 18.355 28.165 40.234 ref. [21] 10.290 10.646 11.266 ref. [21] 18.891 28.501 40.743 present 10.116 10.675 11.477 present 18.565 28.616 40.761
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表 3 三层复合材料层合板前三阶无量纲固有频率（a/h=10）
Table 3. The non-dimensional 1st 3 fundamental frequencies of the 3-layer laminated composite plate (a/h=10)
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