今日更新:Computer Methods in Applied Mechanics and Engineering 1 篇,Thin-Walled Structures 2 篇
A low-rank isogeometric solver based on Tucker tensors
Montardini M., Sangalli G., Tani M.
doi:10.1016/j.cma.2023.116472
基于塔克张量的低阶等距求解器
We propose an isogeometric solver for Poisson problems that combines (i) low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, (ii) a Truncated Preconditioned Conjugate Gradient solver to keep the rank of the iterates low, and (iii) a novel low-rank preconditioner, based on the Fast Diagonalization method where the eigenvector multiplication is approximated by the Fast Fourier Transform. Although the proposed strategy is written in arbitrary dimension, we focus on the three-dimensional case and adopt the Tucker format for low-rank tensor representation, which is well suited in low dimension. We show by numerical tests that this choice guarantees significant memory saving compared to the full tensor representation. We also extend and test the proposed strategy to linear elasticity problems.
我们针对泊松问题提出了一种等几何求解器,该求解器结合了:(i) 低阶张量技术,将未知解和系统矩阵近似为具有克朗克积结构的几个项的总和;(ii) 截断预处理共轭梯度求解器,以保持较低的迭代秩;(iii) 基于快速对角化方法的新型低阶预处理器,其中 特征向量乘法近似于快速傅立叶变换。虽然所提出的策略可以在任意维度下编写,但我们将重点放在三维情况下,并采用塔克格式来表示低秩张量,这种格式非常适合低维度。我们通过数值测试表明,与完整的张量表示法相比,这种选择能显著节省内存。我们还将提出的策略扩展到线性弹性问题并进行了测试。
A Unified Dynamic Model and Vibration Suppression for Moving Corrugated Sandwich Panels with General Boundaries
Zhou Kai, You Taiwen, Gong Dao, Zhou Jinsong
doi:10.1016/j.tws.2023.111248
带一般边界的移动波纹夹芯板的统一动态模型与振动抑制
The sandwich plate structures with corrugated cores are extensively utilized in engineering cases, such as the panels in railway vehicles, aerospace flight vehicles and so on. These sandwich plates in service can be simplified as the axially moving panel structures in the dynamic modeling. To research the dynamic behaviors of moving corrugated sandwich (CS) panels, an equivalent model is utilized. The energy method combined with penalty factor approach is applied to deduce the energy functions of the panel structure, and the corresponding formulations are further deduced based on the Hamilton's principle. Based on the proposed model, the examples with classical and elastic edge boundaries can be considered. Several computational examples are implemented to verify the present formulations, and satisfactory consistency can be observed. Meanwhile, impacts of several structural parameters on the dynamic and stability properties of the CS panel are investigated. To suppress the vibration of CS panels, the negative capacitance piezoelectric shunt damping circuit (PSDC) is further adopted. The impacts of the velocity parameter on the optimal values of the PSDC are discussed and calculated results demonstrate that dynamic responses of moving CS panels are satisfactorily attenuated by the proposed control strategy.
带波纹芯材的夹层板结构在工程案例中得到广泛应用,如铁路车辆、航空飞行器等的面板。在动态建模中,这些服役中的夹芯板可简化为轴向移动的面板结构。为了研究移动波纹夹层板(CS)的动态行为,我们采用了等效模型。采用能量法结合惩罚因子法来推导板结构的能量函数,并根据汉密尔顿原理进一步推导出相应的公式。根据提出的模型,可以考虑经典和弹性边缘边界的示例。通过几个计算实例验证了本公式,并观察到了令人满意的一致性。同时,研究了几个结构参数对 CS 面板动态和稳定性能的影响。为了抑制 CS 面板的振动,进一步采用了负电容压电并联阻尼电路(PSDC)。讨论了速度参数对 PSDC 最佳值的影响,计算结果表明,采用所提出的控制策略后,移动 CS 面板的动态响应得到了令人满意的抑制。
A star-shaped tubular structure with multiple-directional auxetic effect
Lang Jian Ping, Han Dong, Zhang Xue Gang, Jiang Wei, Zhang Yi, Ni Xi hai, Hao Jian, Teng Xing Chi, Ren Xin
doi:10.1016/j.tws.2023.111247
具有多向辅助效应的星形管状结构
A majority of tubular structures have been widely studied due to their superior mechanical performance. Existing works on star-shaped tubular structures have focused on improving their stability and energy absorption performance. This paper proposes a novel star-shaped tubular lattice structure (STL), which not only possesses excellent mechanical properties but also exhibits exceptional auxetic effect. In addition, such structures exhibited two distinct deformation modes under different loading directions. Numerical and experimental studies of the mechanical behavior of the star-shaped tubular structure demonstrated low peak stresses under lateral loading and superior bearing capacity and stability under axial compression. Most importantly, the structure embodied a significant auxetic effect under the direction of both loads. The mechanical performance of the star-shaped tubular structures was investigated by changing wall thickness and angles, which can realize the optimal design. This study enriches the research on star-shaped tubular structures and provides a new perspective and reference for the design of auxetic tubular metamaterials in the future. Furthermore, the star-shaped tubular structure with auxetic behavior has considerable potential for applications in civil engineering and protective fields.
大多数管状结构因其卓越的机械性能而被广泛研究。现有关于星形管状结构的研究主要集中在提高其稳定性和能量吸收性能上。本文提出了一种新型星形管状晶格结构(STL),这种结构不仅具有优异的机械性能,还表现出卓越的辅助效应。此外,这种结构在不同加载方向下表现出两种截然不同的变形模式。对星形管状结构力学行为的数值和实验研究表明,该结构在横向加载下具有较低的峰值应力,在轴向压缩下具有出色的承载能力和稳定性。最重要的是,该结构在两种载荷方向上都体现了显著的辅助效应。通过改变壁厚和角度,研究了星形管状结构的力学性能,从而实现了优化设计。这项研究丰富了星形管状结构的研究内容,为今后设计辅助管状超材料提供了新的视角和参考。此外,具有辅助行为的星形管状结构在土木工程和防护领域的应用具有相当大的潜力。