今日更新:Journal of the Mechanics and Physics of Solids 1 篇,Mechanics of Materials 1 篇,Thin-Walled Structures 3 篇
Realization of planar and surface conformal mappings through stress-free growth of hyperelastic plates: Analytical formulas and numerical calculations
Jiong Wang, Zili Jin, Zhanfeng Li
doi:10.1016/j.jmps.2024.105727
通过超弹性板的无应力生长实现平面和表面共形映射:解析公式和数值计算
Conformal mapping is a well-known concept and has a long research history in mathematics. Accompanying the developments of computational science and 3D digital scanning technology, conformal mapping has also found wide applications in geometric modeling, computer graphics, medical imaging and other fields. In the virtual image or animation world, conformal mapping offers a convenient approach to achieve various shape changes of planar regions and 3D surfaces. In this work, we propose a promising approach, i.e., through the stress-free growth of hyperelastic plates, to realize arbitrary planar and surface conformal mappings in the physical world. The growth field in a hyperelastic plate can be represented by a symmetric tensor field. For any given planar or surface conformal mappings with explicit analytical expressions, the formulas of growth functions in the growth tensor are derived. In the case that the target surfaces of conformal mappings have no explicit analytical expressions, we further propose a numerical scheme to determine the growth data in the hyperelastic plates. The efficiency of the approach proposed in the current work is validated through several typical examples, where the 3D finite element simulations are conducted. The results demonstrate that, by incorporating the obtained growth functions or growth data, the target surfaces can be generated accurately through growth deformations of hyperelastic plates. As an application of the current work, we further propose an approach of shape-control for double-layer grid structures with plate forms. According to any given target shapes, the values of elongation or contraction of the bar elements are determined, then the desired deformations of the grid structures can be realized.
保角映射是一个众所周知的概念,在数学中有着悠久的研究历史。随着计算科学和三维数字扫描技术的发展,保角映射在几何建模、计算机图形学、医学成像等领域也得到了广泛的应用。在虚拟图像或动画世界中,保角映射为实现平面区域和三维曲面的各种形状变化提供了一种方便的方法。在这项工作中,我们提出了一种很有前途的方法,即通过超弹性板的无应力生长,实现物理世界中的任意平面和表面共形映射。超弹性板的生长场可以用对称张量场表示。对于任意给定平面或曲面的保角映射,导出了生长张量中生长函数的表达式。在保形映射的目标表面没有明确的解析表达式的情况下,我们进一步提出了一种确定超弹性板中生长数据的数值格式。通过几个典型实例进行了三维有限元仿真,验证了本文方法的有效性。结果表明,结合得到的生长函数或生长数据,可以通过超弹性板的生长变形精确地生成目标曲面。作为现有工作的应用,我们进一步提出了一种板型双层网架结构的形状控制方法。根据给定的目标形状,确定杆单元的伸长或收缩值,从而实现所需的网格结构变形。
Modeling the heterogeneous and anisotropic plastic deformation of lath martensite
J. Wijnen, S.A.O. Dreessen, V. Rezazadeh, R.H.J. Peerlings
doi:10.1016/j.mechmat.2024.105056
模拟板条马氏体的非均质和各向异性塑性变形
The plastic behavior of microscale lath martensite samples is highly anisotropic. Depending on the orientation, the deformation of such samples may be heterogeneous, with only a few localized slip traces while the remainder of the sample remains largely elastic. Although several continuum plasticity models that account for the anisotropy exist, they cannot reproduce the heterogeneous response observed in experiments. In this study, a model for lath martensite at the microscale is proposed which captures the orientation-dependent heterogeneous behavior observed in experiments. Before formulating the model we first study in detail two idealized cases, in which two different deformation mechanisms are activated. In both cases, the lath martensite is modeled using a discrete slip plane model. In the model, the activation stress of the individual slip systems varies randomly in space according to a distribution based on the underlying dislocation motion. The two configurations differ only in the orientation of the applied tensile load relative to that of the laths – either perpendicular or at 45 ° . In the latter case, slip along the so-called habit plane results in localized plastic deformation, while the former results in a more diffuse activation of plasticity. Insights obtained based on the idealized cases are used to formulate a three-dimensional constitutive model, which captures both deformation mechanisms. The model is applied to microtensile tests of single-packet lath martensite samples. It is shown that the orientation-dependent heterogeneity is accurately captured by the two deformation mechanisms accounted for by the model.
微尺度板条马氏体试样的塑性行为具有高度的各向异性。根据取向的不同,这些样品的变形可能是不均匀的,只有少数局部滑移痕迹,而样品的其余部分仍然具有很大的弹性。虽然存在几种解释各向异性的连续介质塑性模型,但它们不能再现实验中观察到的非均质响应。本文提出了板条马氏体的微观模型,该模型捕捉了实验中观察到的与取向相关的非均相行为。在建立模型之前,我们首先详细研究了两种理想情况,其中两种不同的变形机制被激活。在这两种情况下,板条马氏体采用离散滑移面模型建模。在该模型中,单个滑移系统的激活应力在空间上随机变化,其分布基于位错运动。这两种结构的不同之处在于施加的拉伸载荷相对于板条的方向——垂直或45°。在后一种情况下,沿着所谓的习惯面滑动导致局部塑性变形,而前者导致更广泛的塑性激活。根据理想情况获得的见解用于制定三维本构模型,该模型捕获了两种变形机制。将该模型应用于单包板条马氏体试样的微拉伸试验。结果表明,该模型所考虑的两种变形机制准确地反映了取向相关的非均质性。
Dynamic analysis with point-masses of perforated pallet rack structural members by means of the Generalized Beam Theory
Ignasi López, Jordi Bonada, Oriol Bové, Miquel Casafont
doi:10.1016/j.tws.2024.112090
基于广义梁理论的开孔托盘架结构点质量动力分析
This paper presents two different formulations for introducing point-masses into a dynamic problem using the Generalized Beam Theory (GBT) method. The first one implies placing a point-mass at a beam-node (with or without eccentricities) while the other implies placing a point-mass at a cross-section node. In order to evaluate the accuracy of such formulations, different modal analyses of members have been performed using GBT beam elements, shell elements and classical beam elements. The values of natural modal frequencies obtained through different models have been successfully compared. The results of various harmonic analyses are also presented. Some of the studied structural members include perforations. Finally, the influence of GBT modes and perforations when using point-masses is discussed.
本文用广义梁理论(GBT)方法给出了两种不同的将点质量引入动力问题的公式。第一种方法意味着在光束节点(有或没有偏心)放置一个点质量,而另一种方法意味着在截面节点放置一个点质量。为了评估这些公式的准确性,分别用GBT梁单元、壳单元和经典梁单元对构件进行了不同的模态分析。对不同模型得到的固有模态频率进行了比较。文中还介绍了各种谐波分析的结果。研究的一些结构构件包括孔洞。最后,讨论了采用点质量时GBT模式和穿孔的影响。
Low-Cycle Fatigue Behaviour of Stainless-Clad Bimetallic Steel Welded Connections
Xiaofeng Yang, Huiyong Ban, Yongjiu Shi, Kwok-Fai Chung, Yi-Fei Hu
doi:10.1016/j.tws.2024.112104
不锈钢包层双金属钢焊接接头的低周疲劳行为
The stainless-clad (SC) bimetallic steel is the most widely used laminated high-performance steel in construction, which often offers a variety of prominent structural performance and competitive advantages. Welding with electrodes of suitable mechanical properties and corrosion resistance is vital for SC bimetallic steel structures to ensure a complete corrosion-resistant surface. However, the research on welded connections under cyclic actions is very limited. Many recommendation designs and current standards for SC bimetallic steel are primarily developed for precision equipment, and they are not suitable for structural engineering. To this end, this paper aims to investigate the low-cycle fatigue behaviour of butt welded connections with different welding configurations for the SC bimetallic steel. Failure modes, cyclic characteristics and Masing behaviour of typical welded connections were analysed, and the low-cyclic fatigue behaviour was validated using the Basquin-Coffin-Manson model. A new proposed strain energy-based model was also proposed to describe. Differences in the low-cycle fatigue behaviour between the welded connections and the base bimetal were demonstrated, as well as that for various welding configurations. It was found that the low-cycle fatigue life of the welded connections with a transition weld zone is similar to that of these welded connections without a transition weld zone, both being about 60% to 80% of the base bimetal's fatigue life. However, the fatigue life of the welded connection with a single filler material is much shorter than that of the previous two, being only 15% to 30% of that of the base bimetal. It should be noted that both the adapted Basquin-Coffin-Manson model and the newly proposed strain energy-based model may predict well the low-cycle fatigue life of the three welded connections. Finally, the transition weld zone in these welded connections is recommended to be eliminated in order to simplify the welding procedures, and hence to improve welding efficiency.
不锈钢包层(SC)双金属钢是建筑中应用最广泛的层压高性能钢,通常具有多种突出的结构性能和竞争优势。焊接具有合适的机械性能和耐腐蚀性的电极是确保SC双金属钢结构具有完全耐腐蚀表面的关键。然而,对循环作用下焊接连接的研究非常有限。SC双金属钢的许多推荐设计和现行标准主要是为精密设备而制定的,并不适用于结构工程。为此,本文旨在研究SC双金属钢不同焊接形式对接焊接连接的低周疲劳行为。分析了典型焊接接头的破坏模式、循环特性和振动行为,并采用Basquin-Coffin-Manson模型验证了接头的低周疲劳行为。提出了一种新的基于应变能的模型来描述。结果表明,焊接接头和基体双金属之间的低周疲劳性能存在差异,不同的焊接结构也存在差异。结果表明,带过渡焊区的焊接接头的低周疲劳寿命与不带过渡焊区的焊接接头相似,均为母材疲劳寿命的60% ~ 80%。但单填料焊接接头的疲劳寿命比前两种材料短得多,仅为母材双金属的15% ~ 30%。值得注意的是,无论是修正后的Basquin-Coffin-Manson模型,还是新提出的基于应变能的模型,都能较好地预测三种焊接接头的低周疲劳寿命。最后,建议消除这些焊接连接中的过渡焊区,以简化焊接程序,从而提高焊接效率。
Exact Solutions for the Elastic-plastic Response of Functionally Graded Pipe under External Pressure
Shitang Cui, Jingsong Cheng, Yongliang Zhang
doi:10.1016/j.tws.2024.112106
外压作用下功能梯度管弹塑性响应的精确解
This study investigates the influence of material gradient on the elastoplastic response of functionally graded (FG) thick-walled pipes subjected to external pressure. Closed-form solutions are derived for radial and circumferential stresses across various stages: purely elastic, partially plastic, and post-unloading from plastic regimes. Both the elastic modulus and yield stress exhibit radial variation defined by power-law functions, while Poisson's ratio remains constant. The stress distribution within the pipe depends not only on the external pressure but also on the material gradient index and the geometric dimensions of the pipe. A method is presented to accurately determine the first yielding position in a thin-walled tube based on the material gradient index by employing Tresca's yield criterion. Plastic zones nucleate at one or both surfaces as external pressure increases. The propagation of elastoplastic interfaces and stress distributions within each zone are examined in detail. Notably, following plastic deformation and complete unloading, FG thick-walled pipes may exhibit re-emergence of plastic deformation, depending on the pre-unloading stress state and the gradient of the elastic modulus. The conclusions of this work expected to aid in the design of FG pressure vessels and improve their load-carrying capacity and safety.
研究了材料梯度对功能梯度厚壁管外压弹塑性响应的影响。推导了不同阶段径向和周向应力的封闭解:纯弹性、部分塑性和从塑性状态卸载后。弹性模量和屈服应力均呈现幂律函数定义的径向变化,泊松比保持不变。管道内的应力分布不仅与外部压力有关,还与材料梯度指数和管道的几何尺寸有关。提出了一种基于材料梯度指数,利用Tresca屈服准则精确确定薄壁管首屈服位置的方法。当外部压力增加时,在一个或两个表面形成塑性区。详细研究了弹塑性界面的传播和各区域内的应力分布。值得注意的是,在塑性变形和完全卸载后,FG厚壁管可能会再次出现塑性变形,这取决于卸载前的应力状态和弹性模量的梯度。本研究的结论将有助于FG压力容器的设计,提高其承载能力和安全性。