Plane Collision Problem for Two Identical Elastic Parabolic Bodies—Direct Central Impact

A direct central collision of two identical infinite cylindrical bodies is studied. A nonstationary plane elastic problem is solved. The variable boundary of the contact area is determined. A mixed boundary problem is formulated. Its solution is represented by Fourier series. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying boundary conditions. The basic characteristics of the collision process are determined numerically depending on the curvature of the frontal surface of the bodies     

On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities

Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance ( _n ) and subharmonic resonance of order one-half ( 2 _n ), where is the excitation frequency and _n is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches.     

万有引力场中挠性联结双体系统的稳定性与分岔

本文讨论受万有引力矩作用沿圆轨道运动的挠性联结双体系统的平面天平动。讨论其相对轨道坐标系的可能平衡状态。利用Ｌｉａｐｕｎｏｖ直接法分析各平衡状态的稳定性。分析表明，当刚度系数足够小时，平衡状态呆产生分岔和稳定性突变。利用参数空间对系统的全局运动性态作出定性的描述。     

多体系统动力学设计灵敏度分析直接微分法

针对受完整约束的多体系统动力学微分／代数方程数学模型动态最优化设计问题，建立了通用的目标函数和约束方程，并以此为基础，用直接微分方法系统地推导出了计算设计灵敏度的通用公式，最后通过平面机械臂模型对理论结果和相应算法进行了验证．     

Subharmonic transition to turbulence in channel flow

A direct numerical simulation of subharmonic transition to turbulence in channel flow has been performed. The stages of primary and secondary instability have been identified in the results leading to a staggered pattern of A-shaped vortices. The associated staggered symmetry has been found to persist up to rather late stages of the breakdown process. This symmetry rapidly disappears in the final stage of transition and a developed turbulent flow is attained. A pronounced difference in the development between the two channel halves is observed which is consistent with the predictions of secondary instability theory.     

Correct Solutions of Plane Elastic Problems for a Half-Plane

Continuous and integrable solutions and one-to-one relationships between boundary forces and displacements are found through the direct integration of the differential equations of the plane elastic problem for a half-plane with boundary conditions for either forces or displacements or with mixed boundary conditions. The necessary equilibrium conditions for forces and the compatibility conditions for displacements that ensure the correctness of the solutions are formulated     

Fluorinated Porous Poly(spirobifluorene) Via Direct C‒H Arylation: Characterization,Porosity, and Gas Uptake

Considering intrinsic properties of conjugated polyfluorenes and special functions of porous polymers, synthesis of fluorinated porous poly(spirobifluorene) via direct C?H arylation polycondensation is explored. Owing to the contorted structure and cross-linking nature, the obtained polymer FPSBF shows permanent porosities with Brunauer–Emmett–Teller specific surface area up to 700 m² g^?1 and exhibits a narrow pore size distribution with the dominant pore size at about 0.63 nm, which is more suitable for adsorption of small gas molecules. Based on the measured gas physisorption isotherms with pressure up to 1.13 bar, the obtained polymer shows good uptaking capacities for hydrogen (1.30 wt% at 1.0 bar and 77 K) and methane (4.80 wt% 1.0 bar and 273 K). Moreover, FPSBF has significant adsorption selectivity for CH₄ against N₂ and the estimated ideal adsorption selectivity ratio is up to 30/1 at 1.0 bar and 273 K, which makes the material possess potential application in gas separation.     

THE DETERMINATION OF THE COMPUTATIONAL DEGREES OF FREEDOM OF BAR SYSTEMS1)

为了简化和统一结构力学教材中杆件体系计算自由度$W$的算法,本文提出了“直接法”。该方法以相邻节点间的杆件和结点为分析对象,对于含$m$根杆件、$g$ 个单刚结点和$h$个单铰结点的平面杆件体系,直接法给出计算自由度公式$W=3m-(3g+2h$)。相比于已有方法,直接法研究对象清晰,数学运算统一,适合于编程计算,便于初学者准确而快速计算复杂体系的$W$;也为结构超静定次数的确定提供了一种简单有效的数值算法。     

Advanced Polymer Designs for Direct-Ink-Write 3D Printing

The rapid development of additive manufacturing techniques, also known as three-dimensional (3D) printing, is driving innovations in polymer chemistry, materials science, and engineering. Among current 3D printing techniques, direct ink writing (DIW) employs viscoelastic materials as inks, which are capable of constructing sophisticated 3D architectures at ambient conditions. In this perspective, polymer designs that meet the rheological requirements for direct ink writing are outlined and successful examples are summarized, which include the development of polymer micelles, co-assembled hydrogels, supramolecularly cross-linked systems, polymer liquids with microcrystalline domains, and hydrogels with dynamic covalent cross-links. Furthermore, advanced polymer designs that reinforce the mechanical properties of these 3D printing materials, as well as the integration of functional moieties to these materials are discussed to inspire new polymer designs for direct ink writing and broadly 3D printing.