Abstract

The advanced Automated Fiber Placement (AFP) technologies allow the fiber trajectories to be curvilinearly steered over the panel platform, which brings out a novel type of cylindrical panel structure, termed as Variable Angle Tow (VAT) composite cylindrical panel. So far, the thermal postbuckling problem of VAT composite cylindrical panels under temperature loadings remain unexplored. The aim of this article is to cover this lack by developing a methodology based on a generalized Rayleigh–Ritz formulation in the framework of the principle of thermoelastic complementary energy. The proposed panel model is based on Donnell’s shallow shell theory and accounts for von Kármán’s geometrical nonlinearity. With the aid of the Lagrange multiplier method and the introduction of Airy’s stress function, a mixed variational formula that governs the nonlinear thermoelastic problem of VAT composite cylindrical panels is derived from the principle of thermoelastic potential energy. The Rayleigh-Ritz formulation combined with the mixed variational formula is then applied to derive the simultaneous nonlinear thermoelastic equations, and the Crisfield’s arc-length method, which can cope well with snap-through or snap-back problems, is employed to trace the equilibrium path that characterizes the thermal postbuckling features. Two different modeling strategies, namely, semi-inverse method and Lagrangian multiplier method, are adopted to formulate the nonlinear thermoelastic problem of VAT composite cylindrical panels undergoing temperature change. The application of Lagrangian multiplier method overcomes some limitations inherent in semi-inverse method in terms of constructing Rayleigh-Ritz formulation, and thus provides generality to model general in-plane boundary constraint. The accuracy and robustness of the proposed Rayleigh-Ritz model are validated against finite element solutions and previously published results. Effects of geometric imperfection, curvature radius, aspect ratio and fiber orientation angle on thermal postbuckling responses of VAT cylindrical plates are discussed by several examples. The study presented here may be helpful for the preliminary design of VAT curved panels in thermal environments.

摘要

先进的自动纤维铺放 (AFP) 技术允许纤维轨迹在面板平台上曲线转向，从而产生了一种新型的圆柱形面板结构，称为可变角度丝束 (VAT) 复合圆柱形面板。到目前为止，VAT 复合圆柱板在温度载荷下的热后屈曲问题仍未得到探索。本文的目的是通过在热弹性互补能原理的框架内开发一种基于广义瑞利-里兹公式的方法来弥补这一不足。提议的面板模型基于 Donnell 的浅壳理论，并考虑了 von Kármán 的几何非线性。借助拉格朗日乘子法和艾里应力函数的引入，从热弹性势能原理推导出一个混合变分公式，用于控制 VAT 复合圆柱板的非线性热弹性问题。然后应用Rayleigh-Ritz公式结合混合变分公式推导出联立非线性热弹性方程，并采用Crisfield弧长法，可以很好地处理snap-through或snap-back问题，用于追踪平衡表征热后屈曲特征的路径。采用两种不同的建模策略，即半逆法和拉格朗日乘子法，来表述受温度变化的VAT复合圆柱板的非线性热弹性问题。拉格朗日乘子方法的应用克服了半逆方法在构造瑞利-里兹公式方面固有的一些局限性，从而为建模一般面内边界约束提供了通用性。所提出的 Rayleigh-Ritz 模型的准确性和稳健性已针对有限元解决方案和先前发布的结果进行了验证。通过几个例子讨论了几何缺陷、曲率半径、纵横比和纤维取向角对VAT圆柱板热后屈曲响应的影响。这里介绍的研究可能有助于热环境中增值税曲面面板的初步设计。所提出的 Rayleigh-Ritz 模型的准确性和稳健性已针对有限元解决方案和先前发布的结果进行了验证。通过几个例子讨论了几何缺陷、曲率半径、纵横比和纤维取向角对VAT圆柱板热后屈曲响应的影响。这里介绍的研究可能有助于热环境中增值税曲面面板的初步设计。所提出的 Rayleigh-Ritz 模型的准确性和稳健性已根据有限元解决方案和先前发布的结果进行了验证。通过几个例子讨论了几何缺陷、曲率半径、纵横比和纤维取向角对VAT圆柱板热后屈曲响应的影响。这里介绍的研究可能有助于热环境中增值税曲面面板的初步设计。