共查询到20条相似文献,搜索用时 187 毫秒
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《数学的实践与认识》2013,(24)
将哈氏皮质骨看作纤维增强型复合材料,考虑了存在于哈氏皮质骨间质组织中的多条径向微裂纹问题.根据线弹性断裂理论,讨论了骨单位中骨密质和微裂纹群之间的相互影响.运用位错技术和奇异积分方程求解,得到了微裂纹尖端应力强度因子的数值结果.通过把此模型的数值结果与纤维陶瓷基底模型的结果比较,说明了哈氏管道的存在对微裂纹尖端应力强度因子的影响. 相似文献
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薛玉山 《数学物理学报(A辑)》2014,34(2):251-258
通过引入等谱和一阶非等谱Ablowitz-Kaup-Newell-Segur系统,得到了等谱KaupNewell(KN)谱问题和一阶非等谱KN谱问题的规范变换,并建立了等谱和一阶非等谱KN方程族之间的等价关系。 相似文献
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王东达 《数学的实践与认识》1985,(3)
<正> 文[1]讨论了在有限部分具有四个奇点二次系统(记作 E_2~4)的无穷远奇点.本文进而讨论在有限部分具有三个奇点二次系统(记作 E_2~3)的无穷远奇点.一般说来,二次系统(E_2)在有限部分奇点个数越少,无穷远奇点情况越复杂. 相似文献
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洪晓春 《纯粹数学与应用数学》2005,21(2):123-126,163
用定性分析和数值判定方法,对一类微分系统x=y,y=x(l-bx2) (α-cx2)y(其中l>0,b>0,c≠0)的极限环分布情况进行了研究,得出该系统有3个极限环,并且给出了该系统所有极限环的分布情况. 相似文献
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Schur不等式和H lder不等式是两个重要的不等式,本讲我们介绍Schur不等式和H lder不等式及其应用.Schur不等式:设x,y,z∈R ,则x(x-y)(x-z) y(y-z)(y-x) z(z-x)(z-y)≥0(1)简记为x(x-y)(x-z)≥0,下文均采用这一简记方法.一般地,Schur不等式为:设x,y,z≥0,r>0,则xr(x-y)(x-z)≥0.(2)证不妨设x≥y≥z,则左边≥xr(x-y)(x-z)-yr(x-y)(y-z)≥yr(x-y)(x-z)-yr(x-y)(y-z)=yr(x-y)2≥0.Schur不等式的如下两个形式在解题中非常有用:变形Ⅰx3-x2(y z) 3xy≥0.变形Ⅱ(x)3-4x yz 9xyz≥0.事实上,把(1)展开即得变形Ⅰ.对于变形Ⅱ,因为(x)3=x3 3x2(y z)… 相似文献
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Firstly,a vector loop algebra (~G)3 is constructed,by use of it multi-component KN hierarchy is obtained.Further,by taking advantage of the extending vector loop algebras (~G)6 and (~G)9 of (~G)3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively.Finally,Hamiltonian structures of obtained system are given by quadratic-form identity. 相似文献
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As candidates for tissue‐independent phase properties of cortical and trabecular bone we consider (i) hydroxyapatite, (ii) collagen, (iii) ultrastructural water and non‐collagenous proteins, and (iv) marrow (water) filling the Haversian canals and the intertrabecular space. From experiments reported in the literature, we assign stiffness properties to these phases (experimental set I). On the basis of these phase definitions, we develop, within the framework of continuum micromechanics, a two step homogenization procedure: (i) At a length scale of 100 – 200 nm, hydroxyapatite (HA) crystals build up a crystal foam ('polycrystal'), and water and non‐collagenous organic matter fill the intercrystalline space (homogenization step I); (ii) At the ultrastructural scale of mineralized tissues, i.e. 5 to 10 microns, collagen assemblies composed of collagen molecules are embedded into the crystal foam, acting mechanically as cylindrical templates. At an enlarged material scale of 5 to 10 mm, the second homogenization step also accommodates the micropore space as cylindrical pore inclusions (Haversian and Volkmann canals, inter‐trabecular space), that are suitable for both trabecular and cortical bone. The input of this micromechanical model are tissue‐specific volume fractions of HA, collagen, and of the micropore space. The output are tissue‐specific ultrastructural and microstructural (=macroscopic=apparent) elasticity tensors. A second independent experimental set (composition data and experimental stiffness values) is employed to validate the proposed model. We report a a good agreement between model predictions and experimentally determined macroscopic stiffness values. The validation suggests that hydroxyapatite, collagen, and water are tissue‐independent phases, which define, through their mechanical interaction, the elasticity of all bones, whether cortical or trabecular. 相似文献
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Tendon functions by transmitting tensile loads from muscle to bone. Morphologically, it can be described as a macromolecular multicomposite material, basically consisting of collagen fibrils held together by a soft, hydrated matrix material. Recently, tendon has been deformed beyond the "in vivo" elastic limit and by cyclical loading systematically damaged. Using high-resolution electron microscopy, decomposition of the collagen fibril into subfibrils (15 nm diameter) and microfibrils (3.5 nm diameter) has been noted. The interfacial adhesion between such units is strongly dependent on age, and is probably related with crosslinking phenomena observed by biochemical methods. In addition, tendon collagen contains a considerable amount of water throughout the entire structure which strongly affects its overall mechanical behavior. The various bound states of water have been identified using primarily dynamic mechanical spectroscopy coupled with more conventional methods of structural characterization.Published in Mekhanika Polimerov, No. 4, pp. 693–701, July–August, 1976. 相似文献
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根据电焓密度函数建立了压电材料静态损伤本构模型,详细讨论了横观各向同性力电损伤的一些特征,最后通过对四点弯曲PZT-PIC151梁跨中导电裂纹附近横观各向同性损伤的数值分析,研究了裂纹深度和外加力、电载荷对损伤分布的影响规律.结果表明:裂纹深度和力载荷对力电损伤都有非常明显相似的影响,随着裂纹深度和力载荷的增大,裂纹尖端的力电损伤明显增大,范围也相应扩大;电载荷对力损伤完全不同于对电损伤的影响,电载荷单调地改变裂纹尖端力损伤的大小,不改变力损伤的区域尺寸,但是对电损伤的影响则比较复杂. 相似文献
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Large deflections of a cantilever beam subjected to a tip-concentrated load whose inclination to the deformed axis of the beam is assumed as constant. The mathematical formulation yields a non-linear two-point boundary value problem amenable to numerical integration. A relation is obtained between the load and the tip-angle of the beam when the tip-concentrated load is normal to the deformed axis of the beam. Many possible loads are found for a specified tip-angle. For the specified load, the tip-angle is found to be unique. However, there is a change in the deformation pattern of the beam having a specified tip-angle with the corresponding multiple loads. This confirms the uniqueness of the solution for the governing non-linear differential equations of a cantilever beam under a tip-concentrated load whose inclination is normal to its deformed axis. 相似文献
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Analytical solutions to the thermoelastic problem of equal-stressed reinforcement for homogeneously deformed axisymmetric momentless shells containing families of fibers of constant cross section are obtained. Based on these solutions, a possibility of controlling such structures is demonstrated, which allows one to further reduce (up to several times) the consumption of reinforcement. The effect of the thermal action and thermosensitivity of phase materials on the load-carrying capacity of equal-stress-reinforced momentless shells and on the required amount of reinforcement is investigated. With the example of a boron-magnesium shell, it is shown that its load-carrying capacity can be greatly increased or the total consumption of reinforcement decreased even in the case of a considerable drop in the strength characteristics of the binder upon heating. Several necessary conditions of thermal-force loading of a momentless shell for ensuring its homogeneous deformed state are formulated. 相似文献
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Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981. 相似文献
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Xing Lü Mingshu Peng 《Communications in Nonlinear Science & Numerical Simulation》2013,18(9):2304-2312
Conservation law plays a vital role in the study of nonlinear evolution equations, particularly with regard to integrability, linearization and constants of motion. In the present paper, it is shown that infinitely many conservation laws for certain nonlinear evolution equations are systematically constructed with symbolic computation in a simple way from the Riccati form of the Lax pair. Note that the Lax pairs investigated here are associated with different linear systems, including the generalized Kaup–Newell (KN) spectral problem, the generalized Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem, the generalized AKNS–KN spectral problem and a recently proposed integrable system. Therefore, the power and efficiency of this systematic method is well understood, and we expect it may be useful for other nonlinear evolution models, even higher-order and variable-coefficient ones. 相似文献
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Validation of a Structural Optimization Algorithm Transforming Dynamic Loads into Equivalent Static Loads 总被引:4,自引:0,他引:4
Generally, structural optimization is carried out based on external static loads. However, all forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is almost impossible in a large-scale problem. Therefore, in engineering practice, dynamic loads are often transformed into static loads via dynamic factors, design codes, and so on. Recently, a systematic transformation of dynamic loads into equivalent static loads has been proposed in Refs. 1–3. Equivalent static loads are made to generate at each time step the same displacement field as the one generated by the dynamic loads. In this research, it is verified that the solution obtained via the algorithm of Refs. 1–3 satisfies the Karush–Kuhn–Tucker necessary conditions. Application of the algorithm is discussed. 相似文献
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Jayabal Kaliappan Andreas Menzel Arockiarajan Arunachalakasi Sivakumar M Srinivasan 《PAMM》2010,10(1):299-300
Piezoelectric materials are one of the most prominent smart materials due to their strong electromechanical coupling behaviour. Ferroelectric ceramics behave like piezoelectric materials under low electrical and mechanical loads, but exhibit pronounced nonlinear response at higher loads due to microscopic domain switching. Modern smart devices consist of complex geometries that may force the ferroelectrics employed within them to experience higher fields than they were originally designed for, so that the material responds within its nonlinear region. Hence, models predicting the nonlinear effects of ferroelectrics under complex loading cases are important from the design point of view. Within standard finite element models dealing with electromechanical problems, each grain may be subdiscretized by several finite elements. This problem can be approximated or rather overcome by a polygonal finite element method, where each grain is modelled by solely one single finite element. In this contribution, a micromechanically motivated switching model for ferroelectric ceramics, as based on volume fraction concepts, is combined with polygonal finite element approach. Related representative numerical examples allow to further study and understand the nonlinear response of this material under complex loading cases. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献