Recent advancements in fibre placement technologies have expanded the potential applications of variable stiffness curved composite beams in industries such as aerospace, automotive, and naval engineering. Accurate solution techniques for examining these beams, especially those composed of advanced composite materials, are indispensable. In view of this demand, this study proposes a new high-order computational tool that combines the higher-order accuracy of the emerging inverse differential quadrature method (iDQM) and the simple kinematics of the Timoshenko beam theory for efficient and accurate prediction of the static behaviour of both constant stiffness and variable stiffness curved beam structures. This novel application of iDQM to curved beam analysis is leveraged upon its excellent potential to mitigate differentiation-induced errors by using the so-called indirect approximation strategy. Simple procedures for implementing different orders of iDQM models are presented to analyse curved beam problems, and are independently benchmarked against closed-form Navier's solutions, as well as numerical solutions obtained through the differential quadrature method (DQM) and finite element method (FEM), demonstrating excellent spectral accuracy. Furthermore, the iDQM scheme offers outstanding potential in recovering transverse shear stress, achieving superior accuracy over lower-order FEM in approximating higher-order derivatives. Remarkably, iDQM predictions for variable stiffness curved beams exhibit satisfactory agreement with the Strong Unified Formulation, achieving over 98% computational efficiency. Finally, convergence analysis of iDQM solutions reveal up to three orders of improved accuracy and faster convergence rates compared to the DQM, constituting a new benchmark for curved beam analysis.

中文翻译：

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基于反微分求积的变刚度组合曲梁静态行为模型

纤维铺放技术的最新进展扩大了变刚度弯曲复合材料梁在航空航天、汽车和船舶工程等行业的潜在应用。用于检查这些梁（尤其是由先进复合材料组成的梁）的精确解决方案技术是必不可少的。鉴于这一需求，本研究提出了一种新的高阶计算工具，该工具结合了新兴的反微分求积法（iDQM）的高阶精度和Timoshenko梁理论的简单运动学，用于高效、准确地预测静力恒刚度和变刚度曲梁结构的行为。 iDQM 在曲梁分析中的这种新颖应用利用了其通过使用所谓的间接逼近策略来减轻微分引起的误差的巨大潜力。提出了实现不同阶 iDQM 模型的简单程序来分析曲梁问题，并独立地针对封闭式纳维解以及通过微分求积法 (DQM) 和有限元法 (FEM) 获得的数值解进行基准测试，表现出出色的光谱精度。此外，iDQM 方案在恢复横向剪切应力方面具有出色的潜力，在逼近高阶导数方面比低阶 FEM 具有更高的精度。值得注意的是，iDQM 对变刚度曲梁的预测与强统一公式表现出令人满意的一致性，实现了超过 98% 的计算效率。最后，iDQM 解决方案的收敛分析表明，与 DQM 相比，精度提高了三个数量级，收敛速度更快，构成了曲梁分析的新基准。