Abstract Variable Angle Tow (VAT) composites always exhibit in-plane variable stiffness property, which provides the designer with an extended freedom in stiffness tailoring to achieve higher structural performance for lightweight composite structures. In this paper, a methodology based on a generalised Rayleigh-Ritz formulation is developed to study the thermomechanical buckling response of symmetrical VAT composite plates with general in-plane boundary constraint. It is assumed that the material is of temperature-independent and the panel is exposed to an arbitrary in-plane temperature change. In the framework of thermoelastic theory, the principle of thermoelastic complementary energy in conjunction with Airy’s stress function formulation, for the first time, is applied to solve the in-plane thermoelastic problem of the tow-steered plate. The non-uniform distribution of in-plane force resultant over the entire plane is determined by utilizing the Rayleigh-Ritz formulation enhanced by Lagrangian multiplier method. The merit of the proposed modelling strategy lies in that the application of Lagrangian multiplier method removes the restrictions inherent in conventional Rayleigh-Ritz formulation and thus provides generality to model general in-plane boundary constraint against thermal expansion or contraction. During the buckling analysis, the governing equation of thermomechanical buckling problem of the tow-steered plate under a combination of both temperature change and general in-plane boundary constraint is derived based on the third-order shear deformation theory of Reddy’s type. The accuracy and robustness of the proposed Rayleigh-Ritz model is validated against finite element solutions and previously published results. Effects of boundary condition, fibre orientation angle and temperature change on the in-plane thermoelastic and thermomechanical buckling behaviours of VAT composite plates are studied by numerical examples. Finally, the mechanism of applying tow-steered technology to improve the thermomechanical buckling resistance of composite plates is explored.

中文翻译：

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Rayleigh-Ritz公式在具有一般面内边界约束的变角度丝束复合板热机械屈曲中的应用

摘要 可变角牵引 (VAT) 复合材料始终表现出面内可变刚度特性，这为设计人员提供了更大的刚度剪裁自由度，以实现轻质复合材料结构的更高结构性能。在本文中，开发了一种基于广义 Rayleigh-Ritz 公式的方法来研究具有一般面内边界约束的对称 VAT 复合板的热机械屈曲响应。假设材料与温度无关，并且面板暴露于任意的平面内温度变化。在热弹性理论框架内，首次将热弹性互补能原理结合艾里应力函数公式应用于解决牵引板的面内热弹性问题。平面内合力在整个平面上的非均匀分布是通过利用由拉格朗日乘子法增强的 Rayleigh-Ritz 公式确定的。所提出的建模策略的优点在于，拉格朗日乘子法的应用消除了传统瑞利-里兹公式中固有的限制，从而提供了对针对热膨胀或收缩的一般面内边界约束进行建模的通用性。在屈曲分析中，基于Reddy型三阶剪切变形理论推导出温度变化和一般面内边界约束相结合的牵引板热力屈曲问题的控制方程。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。通过数值算例研究了边界条件、纤维取向角和温度变化对VAT复合板面内热弹性和热机械屈曲行为的影响。最后，探讨了应用牵引转向技术提高复合板抗热机械屈曲性能的机理。