Purpose

The purpose of this paper is to attempt the buckling analysis of a laminated composite skew plate using the C₀ finite element (FE) model based on higher-order shear deformation theory (HSDT) in conjunction with minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS).

Design/methodology/approach

HSDT considers the third-order variation of in-plane displacements which eliminates the use of shear correction factor owing to realistic parabolic transverse shear stresses across the thickness coordinate. At the top and bottom of the plate, zero transverse shear stress condition is imposed. C₀ FE model based on HSDT is developed and coded in formula translation (FORTRAN). FE model is validated and found efficient to create new results. MPMR and MARS models are coded in MATLAB. Using skew angle (α), stacking sequence (Ai) and buckling strength (Y) as input parameters, a regression problem is formulated using MPMR and MARS to predict the buckling strength of laminated composite skew plates.

Findings

The results of the MPMR and MARS models are in good agreement with the FE model result. MPMR is a better tool than MARS to analyze the buckling problem.

Research limitations/implications

The present work considers the linear behavior of the laminated composite skew plate.

Originality/value

To the authors’ best of knowledge, there is no work in the literature on the buckling analysis of a laminated composite skew plate using C₀ FE formulation based on third-order shear deformation theory in conjunction with MPMR and MARS. These machine-learning techniques increase efficiency, reduce the computational time and reduce the cost of analysis. Further, an equation is generated with the MARS model via which the buckling strength of the laminated composite skew plate can be predicted with ease and simplicity.

中文翻译：

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有限元和机器学习方法对复合材料斜斜板的屈曲

目的

本文的目的是尝试使用基于高阶剪切变形理论（HSDT）的C ₀有限元（FE）模型，结合最小最大概率机器回归（MPMR）和多变量对层压复合材料斜板进行屈曲分析自适应回归样条（MARS）。

设计/方法/方法

HSDT考虑了平面位移的三阶变化，由于厚度坐标上存在实际的抛物线形横向剪切应力，因此消除了剪切校正因子的使用。在板的顶部和底部，施加了零横向剪切应力条件。开发了基于HSDT的C ₀ FE模型并将其编码为公式转换（FORTRAN）。有限元模型经过验证，可以有效地创建新结果。MPMR和MARS模型在MATLAB中编码。以偏斜角（α），堆垛顺序（Ai）和屈曲强度（Y）作为输入参数，利用MPMR和MARS提出了回归问题，以预测复合材料偏斜板的屈曲强度。

发现

MPMR和MARS模型的结果与FE模型的结果非常吻合。与MARS相比，MPMR是分析屈曲问题的更好工具。

研究局限/意义

本工作考虑了层压复合斜板的线性行为。

创意/价值

据作者所知，文献中没有进行基于C ₀ FE公式的叠层复合斜板屈曲分析的工作，该公式基于三阶剪切变形理论结合MPMR和MARS。这些机器学习技术可提高效率，减少计算时间并降低分析成本。此外，利用MARS模型生成方程式，通过该方程式可以容易且简单地预测层压复合斜板的屈曲强度。