Multiple‐parameter reduced basis technique for bifurcation and post‐buckling analyses of composite plates
Multiple‐parameter reduced basis technique for bifurcation and post‐buckling analyses of composite plates
复制标题
复合材料板分叉和后屈曲分析的多参数简化基础技术
DOI：
10.1002/nme.1620191206
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发表时间：
1983
影响因子：
2.9
通讯作者：
J. Peters
中科院分区：
文献类型：
--
作者：
A. Noor;J. Peters
提出了一种多参数简化基础技术和问题自适应计算算法，用于复合载荷下复合板的分叉和后屈曲分析。计算算法可以方便地分为三个不同的阶段。第一阶段是确定稳定边界。通过使用位移有限元模型对板进行离散化，并通过利用板响应所表现出的特殊对称性来缩小分析区域。未知节点位移矢量表示为少量路径导数（节点位移相对于路径参数的导数）的线性组合，并使用瑞利-里兹技术通过小型代数方程组来近似有限元方程。简化的方程用于确定板的稳定性边界。
在第二阶段，通过使用分岔屈曲模式作为预测器获得稳定边界附近的非线性解，并生成一组简化方程。在第三阶段，简化的方程用于追踪与载荷参数的各种组合相对应的屈曲后路径。
讨论了所提出方法的潜力，并通过承受压缩和剪切载荷的层合复合板的数值示例证明了其有效性。
A multiple-parameter reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate.
In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post-buckling paths corresponding to various combinations of the load parameters.
The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings.