Duality in algebra and topology

We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.     

The Domany-Kinzel cellular automaton phase diagram

The boundaries between the three phases of the Domany-Kinzel probabilistic cellular automaton are determined with high accuracy via the gradient method. The difficulties the extrapolation to the thermodynamic limit are circumvented and the critical exponents are also presented.     

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions北大核心CSCD

Based on the von Kármán geometric nonlinear plate theory, the displacement⁃type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2⁃point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer⁃thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness⁃radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

涉及肌肉作用影响的髓内钉屈曲分析

在骨折的修复过程中，常发生髓内钉断骨内的情况。其主要原因是涉及肌肉影响后，髓内钉不是单钝的受压杆件，而是多种组合变形的屈曲问题。文中利用有限元法对目前较新结构的髓内钉在骨折治疗中涉及肌肉作用影响进行多方面的压、弯曲与扭转组合变形屈曲分析。得出了三叶瓣型髓内钉在涉及肌肉影响时的屈曲临界压力比单纯受压时髓内钉的屈曲临界压力小51％。并得出髓内钉只能额外承受15Nm左右的外来扭力。这些结果可供髓内钉进一步发展及临床应用参考。通过有限元的分析还可以对髓内钉受力状态的薄弱环节有一个全面的认识，为髓内钉合理设计、材料的选择等进行优化设计提供依据。     

ELASTIC PULSE BUCKLING OF CYLINDRICAL SHELLS UNDER RADIAL IMPULSIVE LOADING

ＥＬＡＳＴＩＣＰＵＬＳＥＢＵＣＫＬＩＮＧＯＦＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＵＮＤＥＲＲＡＤＩＡＬＩＭＰＵＬＳＩＶＥＬＯＡＤＩＮＧＨｕａｎｇＣｈｅｎｇｙｉ（黄承义）ＬｉｕＴｕｇｕａｎｇ（刘土光）ＺｈｅｎｇＪｉｊｉａ（郑际嘉）（Ｄｅｐａｒｔｍｅｎｔｏ...     

板壳塑性屈曲中的佯谬及其研究进展

本文详细论述了板壳塑性屈曲中的佯谬及其研究进展。并对现有的各种观点作了分析讨论。     

Experiments on snap buckling, hysteresis and loop formation in twisted rods

We give the results of large deflection experiments involving the bending and twisting of 1 mm diameter nickel-titanium alloy rods, up to 2 m in length. These results are compared to calculations based on the Cosserat theory of rods. We present details of this theory, formulated as a boundary value problem. The mathematical boundary conditions model the experimental setup. The rods are clamped in aligned chucks and the experiments are carried out under rigid loading conditions. An experiment proceeds by either twisting the ends of the rod by a certain amount and then adjusting the slack, or fixing the slack and varying the amount of twist. In this way, commonly encountered phenomena are investigated, such as snap buckling, the formation of loops, and buckling into and out of planar configurations. The effect of gravity is discussed.     

中厚板屈曲的加权残值方法

用加权残值方法分析了矩形中厚板的屈曲问题。试函数和权函数依据短梁函数进行构造。结果良好。     

环形板的非轴对称屈曲分析

本文利用打靶法研究了内外边界固支且在外边界受均匀径向压力作用下的极正交各向异性环形板的非轴对称屈曲和过屈曲,计算了临界载荷,讨论了分支解的存在性,得到了分支解的渐近表达式,分析了环形板的屈曲性态。     

On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.