今日更新：International Journal of Solids and Structures 2 篇，Journal of the Mechanics and Physics of Solids 1 篇，Mechanics of Materials 1 篇，Thin-Walled Structures 4 篇
International Journal of Solids and Structures
Serendipitous relationship between discrete distribution models representing random orientations of fillers in composite materials and the golden ratio
Hiroyuki Ono
doi:10.1016/j.ijsolstr.2024.112962
表示复合材料中填料随机方向的离散分布模型与黄金比例之间的偶然性关系
The purpose of this study is to establish simple discrete distribution models capable of expressing the two and three-dimensional random orientation states of fillers in composite materials. Initially, a new method is proposed to divide the elastic constants into isotropic and anisotropic parts. Employing this method, for the composite material containing ellipsoidal fillers with various orientations in the material, the macroscopic elastic constants and thermal expansion coefficients of the material are derived based on the Mori–Tanaka method. Subsequently, the analysis of the macroscopic properties is performed for fillers oriented two and three-dimensional discrete distributions. As a result, it is found that when both angular pitches of the azimuth angle and the rotational angle of the fillers in a plane are at most 72°, the macroscopic elastic constants and the thermal expansion coefficients of the material exhibit in-plane isotropy, leading to the realization of a two-dimensional random state. Furthermore, if the angular distribution of the zenith angle and azimuth angle corresponds to the vertices of the regular dodecahedron and icosahedron, and the angular pitch of the rotational angle of the fillers is at most 72°, the macroscopic properties of the material become isotropic, resulting in a three-dimensional random state. Notably, the angle of 72° and the orientation angles of the vertices of the regular dodecahedron and icosahedron are associated with the golden ratio. Therefore, this analysis suggests a serendipitous relationship between the golden ratio and the angular pitch that simplifies the random orientation distribution of fillers.
A contact model for the functionally graded coated elastic structures: Extension of the Hertz theory to the contact of beam structures
Chenxi Wei, Yin Zhang
doi:10.1016/j.ijsolstr.2024.112968
功能梯度涂覆弹性结构的接触模型:赫兹理论在梁结构接触中的推广
The Hertzian displacement assumption is widely used in analyzing the contact problems of non-uniform elastic bodies. It is essential to account for the support conditions of the elastic body as they significantly influence the contact stiffness and distribution of contact pressure. To address this, the deformation of beam structures is integrated into the Hertzian displacement assumption, which leads to the development of an extended contact mechanics model suitable for the elastic bodies of a beam structure which can be non-uniform and with functionally graded coatings. The problem is solved by using a numerical method based on the Gauss-Chebyshev quadrature for the singular integral equation of Cauchy type. In the contact problems of the doubly simply supported (SS-SS) and cantilever beams, the contact pressure and contact stiffness in conjunction with the interactions between the indentation and contact bodies are discussed. An in-depth study on the coupling effects between the structural deformation and functionally graded coatings is presented.
Effects of nonlinearities and geometric imperfections on multistability and deformation localization in wrinkling films on planar substrates
Jan Zavodnik, Miha Brojan
doi:10.1016/j.jmps.2024.105774
非线性和几何缺陷对平面基底起皱膜多稳定性和变形局部化的影响
Compressed elastic films on soft substrates release part of their strain energy by wrinkling, which represents a loss of symmetry, characterized by a pitchfork bifurcation. Its development is well understood at the onset of supercritical bifurcation, but not beyond, or in the case of subcritical bifurcation. This is mainly due to nonlinearities and the extreme imperfection sensitivity. In both types of bifurcations, the energy–displacement diagrams that can characterize an energy landscape are non-convex, which is notoriously difficult to determine numerically or experimentally, let alone analytically. To gain an elementary understanding of such potential energy landscapes, we take a thin beam theory suitable for analyzing large displacements under small strains and significantly reduce its complexity by reformulating it in terms of the tangent rotation angle. This enables a comprehensive analytical and numerical analysis of wrinkling elastic films on planar substrates, which are effective stiffening and/or softening due to either geometric or material nonlinearities. We also validate our findings experimentally. We explicitly show how effective stiffening nonlinear behavior (e.g., due to substrate or membrane deformations) leads to a supercritical post-bifurcation response, makes the energy landscape non-convex through energy barriers causing multistability, which is extremely problematic for numerical computation. Moreover, this type of nonlinearity promotes uni-modal, uniformly distributed, periodic deformation patterns. In contrast, nonlinear effective softening behavior leads to subcritical post-bifurcation behavior, similarly divides the energy landscape by energy barriers and conversely promotes localization of deformations. With our theoretical model we can thus explain an experimentally observed phenomenon that in structures with effective softening followed by an effective stiffening behavior, the symmetry is initially broken by localizing the deformation and later restored by forming periodic, distributed deformation patterns as the load is increased. Finally, we show that initial imperfections can significantly alter the local or global energy-minimizing deformation pattern and completely remove some energy barriers. We envision that this knowledge can be extrapolated and exploited to convexify extremely divergent energy landscapes of more sophisticated systems, such as wrinkling compressed films on curved substrates (e.g., on cylinders and spheres) and that it will enable elementary analysis and the development of specialized numerical tools.
Probabilistic progressive damage modeling of hybrid composites
E. Polyzos, I.A. Rodrigues Lopes, P.P. Camanho, D. Van Hemelrijck, L. Pyl
doi:10.1016/j.mechmat.2024.105087
混杂复合材料的概率渐进损伤模型
A novel analytical probabilistic progressive damage model (PPDM) is introduced for multiphase composites to predict the damage behavior of hybrid composites. The PPDM is based on effective field methods and the stochastic nature of fiber damage is captured by including weakest link theory and Weibull statistics. Three additional models are developed to compare with the PPDM. A stochastic model analogous to the PPDM (called SPDM), and two finite element models, one stochastic (SFEM) and one probabilistic (PFEM). All models are developed in a thermodynamically consistent framework and are extended to include residual thermal stresses. Finally, the four models are compared with models from the open literature for an AS4-M50S hybrid carbon–carbon composite with different hybridization ratios of high to low elongation fibers. The comparison reveals a great agreement between all models and indicates that the stochastic nature of fiber damage is the most influential parameter leading to damage.
A scale-span method to characterize the mechanical property of BCF/PEEK considering uncertain structural characteristics
Yong Liu, Qiannan Li, Meng Zhu, Pan Sun, Honggen Zhou
doi:10.1016/j.tws.2024.112211
考虑不确定结构特性的BCF/PEEK力学性能标度跨度表征方法
The focus of this study is exploring a scale-span characterization method to predict the mechanical properties of Braided Carbon Fiber Reinforced Poly Ether Ether Ketone (BCF/PEEK) considering structural uncertainty. Firstly, a complicated micro-scale representative volume element (RVE) model that considers the random position and size of fiber was established via the developed Python script. Analogously, a mathematical expression adopted by the trust region algorithm was proposed to accurately describe the detailed cross-sectional shapes and fluctuation amplitude characteristics of BCF/PEEK for the sake of establishing the precision meso-scale RVE model. Then, the corresponding elastic properties that consider fiber volume fraction and fiber distribution location were characterized via the span-scale characterization method. Meanwhile, the influence of fiber bundle fluctuation amplitude and fiber volume fraction on the mechanical properties was investigated as well. In addition, the mechanical properties of BCF/PEEK with the change of the braid angle between warp and weft yarn were predicted via the established meso-scale RVE model. Finally, a series of experiments have been carried out. The maximum and minimum absolute prediction deviation of all elastic property parameters were only 4.07% and 1.41%, respectively, which verified the proposed scale-span characterization method can predict the mechanical properties of composites well.
Interactive buckling behaviour of Q420–Q960 steel welded thin-walled H-section long column
Jie Wang, Jin Di, Yuanlin Zheng, Fengjiang Qin, Yi Su
doi:10.1016/j.tws.2024.112219
Q420-Q960型钢焊接薄壁h型长柱的相互作用屈曲行为
Considering the broad application prospect of high-strength steel (HSS) in engineering structure, and the limitations present in existing studies on interactive buckling of HSS welded thin-walled box-section long column, both test and finite element analysis were employed to investigate the interactive buckling behaviour exhibited by 12 specimens fabricated from Q420–Q960 steels. The detailed analysis considered various aspects, including the failure mode, axial deformation, interaction of local and overall buckling deformation, and the ultimate bearing capacity. Observations revealed that the utilization rate of steel strength diminished with an escalation in both the plate width–thickness ratio and steel strength. An increase in the plate width–thickness ratio correlated with an earlier onset of local buckling, and the influence of steel strength was found to be negligible. More importantly, the limit of the plate width–thickness ratio for columns undergoing interactive buckling increased with a rise in column slenderness and decreased with an increase in steel strength. Taking into account the influence of column slenderness and steel strength, a novel calculation formula for determining the limit of the plate width–thickness ratio was derived. It is noteworthy that Eurocode 3 and JGJ/T 483-2020 were found too conservative for calculating the ultimate bearing capacity, while ANSI/AISC 360-22 was found suitable. Additionally, a calculation method for the ultimate bearing capacity of Q420–Q960 steel welded thin-walled H-section long column was proposed based on the direct strength method.
Vibration behaviours of composite conical–cylindrical shells with damping coating: Theory and experiment
Jinan Li, Hui Li, Yao Yang, Yanhong Fang, Haijun Wang, Xiangping Wang, Haiyang Zhang, Haizhou Wang, Hang Cao, Junxue Hou, Guowei Sun, Dongxu Du, Xiaofeng Liu, Zhuo Xu, Wei Sun, Zhong Luo, Qingkai Han
doi:10.1016/j.tws.2024.112218
有阻尼涂层的锥形圆柱复合壳的振动特性:理论与实验
This study presents the theoretical and experimental investigations on vibration behaviours of carbon fiber/ resin composite conical-cylindrical shells (or C-C shells) with damping coating. First, an analytical model of such a combined shell with coating material considers the effects of base harmonic excitation load under arbitrary boundary conditions is proposed using the first-order shear deformation theory, virtual artificial spring technique, modal superposition approach, the Rayleigh-Ritz method, etc. Subsequently, the solutions of fundamental frequencies, mode shapes, and vibration displacements in the frequency domain are acquired by deriving the corresponding energy expressions and motion equations. Convergence analysis is utilized to determine the virtual spring stiffness value and the appropriate truncation numbers. Both literature and experimental results are conducted to give an adequate validation of the current model, in which the continuous 3D printing technology is adapted to fabricate two C-C shell specimens with one of the outside surfaces being sprayed by coating material using an atomization deposition approach. Finally, the effects of the coating thickness ratio, Young's modulus ratio of the coating and the substrate shell, the semi-vertex angle, and the fiber laying angle on the free vibration and forced vibrations of the coated structure are discussed, with some practical recommendations being provided to improve the vibration suppression of such a coated structure.
Effect of solid blocking on lateral bracing requirements for cold-formed steel wall studs
Linbo Zhang, Lei Xu, Ronald D. Ziemian, Constance Ziemian
doi:10.1016/j.tws.2024.112208
固体阻塞对冷弯型钢壁钉横向支撑要求的影响
The effectiveness of horizontal bracing in increasing the strength of cold-formed steel (CFS) load-bearing walls has been widely acknowledged. However, while significant research has been conducted regarding the bracing requirements for CFS bearing walls, the effect of solid blocking, which prevents columns (studs) within the wall from rotating, has not been fully explored. In this study, we propose an analytical method to quantitatively assess the effect of solid blocking on bracing requirements for CFS load-bearing walls. This method is comprehensive as it can be applied to systems with different bracing patterns, load patterns, or non-identical columns (studs), and it accounts for the columns’ initial curvature and semi-rigid end connections. It has been verified that considering the solid blocking always decrease the bracing requirements because the existence of solid blocking increases the system’s stiffness and subsequently decreases the additional displacement as well as the brace force, as expected. An example consisting of 23 CFS studs is presented to illustrate how the effect of solid blocking on bracing requirements is influenced by the location and interval of solid blocking, the stiffness of column end connections, and the characteristics of tie bracing. The results indicate that the effect of solid blocking on bracing requirements increases when the location of solid blocking is closer to the anchor and the solid blocking interval is smaller. Moreover, a modification to the equation in AISI S100 is proposed to account for the effect of solid blocking on the strength requirement of tie bracing. Overall, this research contributes to a better understanding of the role of solid blocking in CFS load-bearing walls and provides insights for optimizing bracing design in practice.
