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91.
有限变形弹性动力学的非传统Gurtin型变分原理 总被引:5,自引:2,他引:5
根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出的一条简单而统一的途径,系统地建立了有限变形弹性动力学的各类非传统Gurtin型变分原理,给出一个以卷积表示的重要关系式,可以认为,该式是有限变形动力学的广义虚功原理的表式。从该式出发,不仅能得到有限变形动力学的虚功原理,而且通过给出的一系列广义Legendre变换,还能系统地成对导出5类变量,3类变量,2类变量和1类变量非传统Gurtin型变分原理的互补泛函。通过这条途径还能清楚地阐明这些原理之间的内在联系。 相似文献
92.
Sérgio H. Faria 《Continuum Mechanics and Thermodynamics》2003,15(2):147-159
Recently, there appeared in this journal a short review article by Müller ((2002), 14: 227–229), in which it was argued that
the internal energy of a reacting mixture of liquid crystals should not be an objective quantity (i.e., a quantity independent
of the referential frame). Such a paradoxical conclusion has revealed the urging necessity for a better comprehension of the
interactions taking place in structured mixtures, specially when referred to non-inertial observers. This work shows that
Müller's paradox is avoided when all inertial effects are carefully accounted for. Further, it predicts interesting phenomena
without analogue in reacting mixtures of structureless fluids: internal inertial effects, produced by a combination of mass exchanges (e.g. by chemical reactions or phase changes) with the extra degrees of freedom
posed by the microstructure. Such effects clarify the reasons why inertial forces and couples acting on a mixture do not always
coincide with the sum of the inertial forces and couples exerted upon its individual constituents. The present conclusions
establish a reinterpretation of some fundamental concepts of continuum mechanics and thermodynamics, including a deeper understanding
of the manner in which total energy and momenta are conserved in complex media.
Received: July 25, 2002 / Published online: February 17, 2003
Communicated by Kolumban Hutter, Darmstadt
e-mail: faria@mechanik.tu-darmstadt.de 相似文献
93.
变分原理通常应用于箱形截面梁剪力滞效应弹性分析,本文基于换算截面法,运用变分原理推导了预应力混凝土简支箱梁均布荷载作用、钢筋混凝土简支箱梁集中荷载作用的剪力滞系数计算公式,考虑了混凝土开裂对箱梁剪力滞效应的影响,并与试验结果和规范方法进行了对比分析。变分原理分析开裂混凝土箱梁剪力滞效应方法力学概念明确,是其弹性分析适用范围的拓展,亦可推广应用到混凝土连续箱梁开裂后的剪力滞效应分析,具有广阔的应用前景。 相似文献
94.
Peter Takáč 《Journal of Dynamics and Differential Equations》2006,18(3):693-765
We are concerned with the existence of a weak solution
to the degenerate quasi-linear Dirichlet boundary value problem
It is assumed that 1 < p < ∞, p ≠ 2, Ω is a bounded domain in
is a given function, and λ stands for the (real) spectral parameter near the first (smallest) eigenvalue λ1 of the positive p-Laplacian − Δ
p
, where
. Eigenvalue λ1 being simple, let φ1 denote the eigenfunction associated with it. We show the existence of a solution for problem (P) when f “nearly” satisfies the orthogonality condition ∫Ω
f φ1 dx = 0 and λ ≤ λ1 + δ (with δ > 0 small enough). Moreover, we obtain at least three distinct solutions if either p < 2 and λ1 − δ ≤ λ < λ1, or else p > 2 and λ1 < λ ≤ λ1 + δ. The proofs use a minimax principle for the corresponding energy functional performed in the orthogonal decomposition
induced by the inner product in L
2(Ω). First, the global minimum is taken over
, and then either a local minimum or a local maximum over lin {φ1}. If the latter is a local minimum, the local minimizer in
thus obtained provides a solution to problem (P). On the other hand, if it is a local maximum, one gets only a pair of sub- and supersolutions to problem (P), which is then used to obtain a solution by a topological degree argument. 相似文献
95.
This paper is concerned with a new improved formulation of the theoretical model previously developed by Benamar et al. based on Hamilton's principle and spectral analysis, for the geometrically non-linear vibrations of thin structures. The problem is reduced to a non-linear algebraic system, the solution of which leads to determination of the amplitude-dependent fundamental non-linear mode shapes, the frequency parameters, and the non-linear stress distributions. The cases of C-S-C-S and C-S-S-S rectangular plates are examined, and the results obtained are in a good qualitative and quantitative agreement with the previous available works, based on various methods. In order to obtain explicit analytical solutions for the first non-linear mode shapes of C-S-C-S RP2 and C-S-S-S RP, which are expected to be very useful in engineering applications and in further analytical developments, the improved version of the semi-analytical model developed by El Kadiri et al. For beams and fully clamped rectangular plates, has been slightly modified, and adapted to the above cases, leading to explicit expressions for the higher basic function contributions, which are shown to be in a good agreement with the iterative solutions, for maximum non-dimensional vibration amplitude values up to 0.75 and 0.6 for the first non-linear mode shapes of C-S-C-S RP and C-S-S-S RP, respectively. 相似文献
96.
付宝连 《应用数学和力学(英文版)》1996,17(1):38-44
FuBaolian(付宝连)(ReceivedNov.22,1993;CommunicatedbyChienWeizang)COUPLEDVARIATIONALPRINCIPLESANDGENERALIZEDCOUPLEDVARIATIONALPRI... 相似文献
97.
对具有初速的有限长弹性杆与文克勒地基上弹性薄板的冲击问题进行了研究,用伽辽金原理求出了冲击力及薄板位移响应的近似公式,并对计算结果作了分析讨论 相似文献
98.
本文首先对国家自然科学基金在1986-1991年间资助摩擦学基础研究的情况进行了简洁的分析,接着就其资助办法作了介绍,最后着重对如何利用科学基金促进摩擦学的发展问题作了讨论,指出应当把坚持应用摩擦学学科发展战略的研究成果、鼓励和支持创新性研究、积极支持交叉学科研究和注意扶植新的学科生长点、加强摩擦学研究与实际应用相结合和促进优秀青年摩擦学研究人才的迅速成长等作为国家自然科学基金资助摩擦学基础研究的 相似文献
99.
Chung Fang Yongqi Wang Kolumban Hutter 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,76(3-4):119-131
In the present study a variational principle is proposed for the revised Goodman–Cowin theory with internal length for cohesionless granular materials (Fang et al. in Continuum Mech Thermodyn in press). The balance equations of the internal variables employed in the theory in equilibrium states, the equilibrium expressions of the constitutive variables and the corresponding natural boundary conditions are derived by use of the proposed variational principle for both cases of compressible and incompressible grains. It is demonstrated that the derived results coincide with those obtained by use of the thermodynamic analysis. The current work serves as a supplementary variational verification of the constitutive theory proposed in Fang et al. (in Continuum Mech Thermodyn in press). 相似文献
100.
V. I. Kushch 《International Applied Mechanics》2004,40(8):893-899
An elastic-equilibrium problem is rigorously solved for a transversely isotropic body containing a finite number of arbitrarily arranged and oriented transversely isotropic spherical inclusions or an infinite periodic array of such inclusions. The solution is found based on the superposition principle for general solutions of single-particle problems and the addition theorems for partial vector solutions of the elastic equilibrium equations. The numerical results presented allow assessing the influence of matrix anisotropy on the stress concentration between inclusions 相似文献