共查询到16条相似文献,搜索用时 546 毫秒
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本文提出了微极原弹性物质体的定义并利用虚功率原理导出了该类物质体的变分原理.利用上述同样思想和这里给出的微极原势的定义很自然地导出了非局部微极弹性介质的本构方程. 相似文献
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关于变分学中逆问题的研究 总被引:19,自引:1,他引:18
本文研究了变分学中的逆问题.通过变积概念的引入,给出了系统地研究变分学中逆问题的一种新途径.将这种方法应用于线弹性动力学和粘性流体力学中,建立了各自的变分原理和广义变分原理. 相似文献
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广义连续统场论中新的增率型功率和能率原理 总被引:2,自引:1,他引:1
目的是建立广义连续统场论的增率型功率和能率原理.通过组合具有交叉项的增率型虚速度和虚角度原理以及虚应力和虚偶应力原理提出了微极连续统场论中具有交叉项的增率型功率和能率原理,并借助广义Piola定理同时而且无需其它附加要求地推导出微极和非局部微极连续统场论的所有增率型运动方程和边界条件以及能率方程.类似地可以推导出微态连续统的相应结果.文中给出的结果是新的,并可作为建立广义连续统力学相关的增率型有限元方法的理论基础. 相似文献
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“非局部微极线性弹性介质理论中的各种互易定理和变分原理”,戴天民,本刊第1卷第1期(1980),89-106页. 相似文献
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本文基于拖带坐标描述和S-R分解定理,建立了包含速度梯度、动量、速度、应力和应变率等五类独立场变量的非线性弹性动力学率型广义变分原理和广义子域混合杂交变分原理. 相似文献
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本文把A.C.Eringen建立的非局部微极连续统的本构理论推广到包括具有隐含的和多重相互作用的非局部性的微极连续统的情形.这里以隐含的和多重相互作用的非局部微极热弹性固体为例说明建立各自本构理论的过程并给出两个相应的有关本构理论的定理. 相似文献
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C. E. Athanasiadis D. Natroshvili V. Sevroglou I. G. Stratis 《Mathematical Methods in the Applied Sciences》2015,38(15):3264-3294
Direct scattering problems for partially coated piecewise homogenous and inhomogeneous layered obstacles in linear elasticity lead to mixed impedance transmission problems for the steady‐state elastic oscillation equations. For a piecewise homogenous isotropic composite body, we employ the potential method and reduce the mixed impedance transmission problem to an equivalent system of boundary pseudodifferential equations. We give a detailed analysis of the corresponding pseudodifferential operators, which live on the interface between the layers and on a proper submanifold of the boundary of the composite elastic body, and establish uniqueness and existence results for the original mixed impedance transmission problem for arbitrary values of the oscillation frequency parameter; this is crucial in the study of inverse elastic scattering problems for partially coated layered obstacles. We also investigate regularity properties of solutions near the collision curves, where the different boundary conditions collide, and establish almost best Hölder smoothness results. Further, we analyze the asymptotic behavior of the stress vector near the collision curve and derive explicit formulas for the stress singularity exponents. The case of Lipschitz surfaces is briefly treated separately. In the case of a composite body containing homogeneous or inhomogeneous finite anisotropic inclusions, we develop an alternative hybrid method based on the so‐called nonlocal approach and reduce the mixed transmission problem to an equivalent functional‐variational equation with a sesquilinear form that ‘lives’ on a bounded part of the layered composite body and its boundary. We show that this sesquilinear form is coercive and that the corresponding variational equation is uniquely solvable. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(4):955-981
In this paper we address nonlocal vector variational principles obtained by substitution of the classical gradient by the Riesz fractional gradient. We show the existence of minimizers in Bessel fractional spaces under the main assumption of polyconvexity of the energy density, and, as a consequence, the existence of solutions to the associated Euler–Lagrange system of nonlinear fractional PDE. The main ingredient is the fractional Piola identity, which establishes that the fractional divergence of the cofactor matrix of the fractional gradient vanishes. This identity implies the weak convergence of the determinant of the fractional gradient, and, in turn, the existence of minimizers of the nonlocal energy. Contrary to local problems in nonlinear elasticity, this existence result is compatible with solutions presenting discontinuities at points and along hypersurfaces. 相似文献
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Dorothee Knees 《Annali di Matematica Pura ed Applicata》2008,187(1):157-184
We derive a global regularity theorem for stress fields which correspond to minimizers of convex and some special nonconvex
variational problems with mixed boundary conditions on admissible domains. These are Lipschitz domains satisfying additional
geometric conditions near those points, where the type of the boundary conditions changes. In the first part it is assumed
that the energy densities defining the variational problem are convex but not necessarily strictly convex and satisfy a convexity
inequality. The regularity result for this case is derived with a difference quotient technique. In the second part the regularity
results are carried over from the convex case to special nonconvex variational problems taking advantage of the relation between
nonconvex variational problems and the corresponding (quasi-) convexified problems. The results are applied amongst others
to the variational problems for linear elasticity, the p-Laplace operator, Hencky elasto-plasticity with linear hardening and for scalar and vectorial two-well potentials (compatible
case).
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In this paper, we study the stabilization problem of vibration of linearized three-dimensional nonlocal micropolar elasticity. For this purpose, we need to demonstrate the well-posedness of the system of equations governing the vibration of three-dimensional nonlocal micropolar media for both forced (i.e. with boundary feedback) and unforced cases. We assume the non-homogeneous system of equations for the unforced (uncontrolled) case to establish the well-posedness. It should be pointed out that the well-posedness of the evolution equations in micropolar case has been studied by many authors; but, the well-posedness in the nonlocal micropolar is an open problem. Our tools in well-posedness analysis are the semigroup techniques. Afterwards, we pursue the stabilization problem and show that the vibration of the nonlocal micropolar elastic media will be eventually dissipated under boundary feedback actions consisting of stress and couple stress feedback laws. These control laws are simple, linear and can be easily implemented in practical applications. The stabilization proof is accomplished using Lyapunov stability and LaSalle’s invariant set theorems. 相似文献
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In this paper, we consider vector variational inequalities with set-valued mappings over countable product sets in a real Banach space setting. By employing concepts of relative pseudomonotonicity, we establish several existence results for generalized vector variational inequalities and for systems of generalized vector variational inequalities. These results strengthen previous existence results which were based on the usual monotonicity type assumptions 相似文献