热弹性马氏体相变材料单晶体的细观力学统一本构模型

基于马氏体相变的晶体学理论和Hill Rice内变量本构理论 ,建立了热弹性马氏体相变材料单晶体的细观力学统一本构模型并对它进行了详细的讨论 .该本构模型能描述在复杂热力学加载条件下 ,热弹性马氏体相变材料微结构正向相变、反向相变以及重取向过程在单晶体中所表现出来的宏观本构特性 .理论预测与实验结果符合很好 .     

钱氏定理在有限变形极矩弹性力学广义变分原理的应用

应用Lagrange乘子法和钱伟长证明的两类广义变分原理的等价定理,在本文中导出有限变形极矩弹性力学的广义变分原理.文中采用了在拖带坐标系描述法建立的有限变形应变张量(称为Biot有限变形应变定义的准确形式)和应变速率定义与拖带系应力张量构成完整的数学描述.     

固体力学中的连续动态演化系统与Hamilton-Jacobi-Bellman方程

在许多固体力学所研究的前沿性领域中,如损伤力学、细观力学、粘塑性问题、蠕变问题等,其最突出的特点就是高度非线性、本构行为的时间相关性以及动态演化性.本文应用控制理论描述这一动态演化力学系统,并结合经典力学变分原理建立相应的用于固体力学的最优控制变分原理.首先,讨论它的连续形式,即相应的Hamilton-Jacobi-Bellman方程;然后,给出相应的数值解形式和算例.     

有限变形热粘弹性本构关系的内变量理论 *

基于非平衡态热力学理论 ,提出了一个新的有限变形热粘弹性本构关系 .在定容比热为常数的条件下 ,给出了热学效应和力学效应之间具有解耦形式的自由能表达式 .通过对固体高聚物细观变形机制的分析 ,引进了相应的内变量 ,并在此基础上建立了计及温度效应的有限变形粘弹性本构关系的内变量理论 .此外 ,还推导了参考构形中分子网络具有随机取向分布时本构关系的具体表达式 .讨论了温度变化对松弛时间的影响 .将自由能展开为内变量二次式的粘弹性本构理论仅仅是一种线性化近似 .     

饱和多孔介质的超粘弹性本构理论研究

为了建立能考虑固体材料、多孔固体与流体可逆和不可逆变形的饱和多孔介质超粘弹性理论,以多孔固相为参考构型,以有效应力、材料真实应力和流相真实孔压作为状态变量,结合混合物均匀化响应原理获得各项均符合热力学功共轭特征的饱和多孔介质能量平衡方程,根据非平衡热力学熵分解理论求得熵流和熵产.结果表明,超弹塑性理论是该理论的一个特例;多孔固体的总变形可分为固相间隙和材料变形两部分,间隙应变与Terzaghi有效应力构成功共轭对,材料应变与材料真实应力构成功共轭对.饱和多孔介质的自由能可分为固相和流相两部分.当固相间隙和材料变形解耦时,固相所含的自由能又可分为间隙和材料两部分.证明了Skempton有效应力不是饱和多孔介质的基本应力状态变量.     

抽象线性形变广义弹性理论

经典弹性力学已是一个完整的理论体系,但它的应用范围有局限性.本文利用凸分析方法,推广这个理论体系于一般的小变形广义非线性弹性力学模型.在用次微分描述的本构关系及边界条件下建立了静力学和动力学的一般的理论框架,给出了各种变分原理,证明了许多经典结论仍然成立,并从多个角度刻划了静(动)态解的性质.     

岩土力学的公理化理论体系*

本文以混合物理论为基础,融理性力学、不可逆过程热力学和土力学的精华于一体,提出了岩土力学的公理化理论体系。该理论体系包括5个基本定律和8个本构原理,它们在纯力学理论和工程实际的鸿沟之间架起了一道桥梁。     

中心引力场中刚-弹耦合系统平面运动的相对平衡点的稳定性

研究了中心力场中的刚-弹耦合系统的平面运动动力学, 综合考虑了系统轨道运动与姿态运动, 利用变分原理给出了系统的运动方程. 并以广义Hamilton力学的视点, 利用能量-动量方法给出了一类相对平衡点的稳定性条件.     

弹塑性有限变形力学的反逆渐近解法

最近几十年中,近代力学的非线性有限变形理论在概念与方法上有许多重要的进展([1],[2],[3]等).本文旨在说明自然拖带系描述法与Stokes-陈分解定理如何结合反过渐近解法于有效解答弹塑性有限变形力学问题应用至工程设计目的.文中举半平面冲压大变形为典型数值解例.     

热力学理论与空化现象

有关空化现象的理论研究大多建立在1917年由Rayleigh[1]开始的,后由Plesset等人发展起来的单个空泡运动理论的基础上.该理论仅从流体动力学的某些观点出发,考虑了力的作用,对诸如水下爆炸等问题的讨论,无疑是合适的.由于忽视了空泡生长或消失过程中气、液两相间的物质交换及能量转化,因此对空化现象的讨论则认为是不完备的. 本文主要从热力学观点.分析高速水流中的空化现象、空泡形成条件、空化数以及讨论空化模型实验的相似性问题.     

水动力-热动力学的极值定律

本文对水动力学和更普通性的连续介体动力学中以连续方程与运动方程所表达的现有诸经典守恒定律以外,提出另一最大能量消散率定律.这一定律的推论就是应用水力学中培纶格-波丝最小储存能学说. 凡在运动中消散了的机械能皆转化成为热能,储存在物体里.能量之消散当一定时刻一定温度都使产熵增加.所以,从最大能量消散率可引出热力学第二定律的一个新概念,即机械运动的产熵率也总是一个可能的最大值. 文中建议的这个连续介体极值定律,可从变分原理推导出来,重订热力学第二定律则可藉微观分析加以证明.两者合成水动力-热动力学极值定律     

On the paradoxical behavior of a cyclic device working with a non-Boltzmannian fluid

According to standard thermodynamics, the efficiency of a cyclic machine is strictly lower than one. Such a result is a straightforward consequence of the second principle of thermodynamics. Recent advances in the study of the thermodynamics of long-range interacting system report however on a rather intricate zoology of peculiar behaviors, which are occasionally in contrast with customarily accepted scenarios, dueling with intuition and common sense. In this paper, a thermodynamical cycle is assembled for an ideal device working with non-Boltzmanian long-range fluid and operating in contact with two thermal reservoirs. Assuming the microcanonical or canonical temperature to be the correct thermodynamic temperature, we obtain a paradoxical conclusion: the system is in fact analytically shown to violate the second principle of thermodynamics. This phenomenon ultimately relates to the existence of regions in the canonical ensemble where the energy decreases with the average kinetic temperature. We argue that the validity of the second principle of thermodynamics can be possibly regained, by revisiting the definition of canonical ensemble, as well as the Fourier law of heat transport, and consequently relaxing the constraint on the maximal efficiency as imposed by the Carnot theorem.     

Infinite dimensional model of a double flexible-link manipulator: The Port-Hamiltonian approach

This paper proposes a modular and control oriented model of a double flexible-link manipulator that stems from the modelling of a spatial flexible robot. The model consists of the power preserving interconnection between two infinite dimensional systems describing the beam’s motion and deformation with a finite dimensional nonlinear system describing the dynamics of the actuated rotating joints. To derive the model, Timoshenko’s assumptions are made for the flexible beams. Using Hamilton’s principle, the dynamic equations of the system are derived and then written in the Port-Hamiltonian (PH) framework through a proper choice of the state variables. These so called energy variables allow to write the total energy as a quadratic form with respect to a state dependent energy matrix. The resulting model is shown to be a passive system, a convenient property for control design purposes.     

A new sinusoidal shear deformation theory for bending,buckling, and vibration of functionally graded plates

A new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates.     

Maximum entropy principle closure for 14-moment system for a non-polytropic gas

In this paper, we consider a rarefied polyatomic gas with a non-polytropic equation of state. We use the variational procedure of maximum entropy principle (MEP) to obtain the closure of the binary hierarchy of 14 moments associated with the Boltzmann equation in which the distribution function depends also on the energy of internal modes. The closed partial differential system is symmetric hyperbolic and the Cauchy problem is well-posed. In the limiting case of polytropic gas in which the internal energy is a linear function of the temperature, we find, as a special case, the previous results of Pavić et al. (Physica A 392:1302–1317, 2013). This paper, therefore, completes the equivalence between the closure obtained in the phenomenological rational extended thermodynamics theory and the one obtained by the MEP for general non-polytropic gas.

     

Generalizations of the neumann system—a curve theoretical approach part III: Order n systems

The Neumann system is a well-known algebraically completely integrable Hamiltonian system. Its geometry has roots in hyperelliptic curve theory and the isospectral deformation theory of Hill's operator. In this paper generalizations of the Neumann system are found for n-sheeted Riemann surfaces and the isospectral deformation theory of operators of order n. Trace formulas, Lax pairs, and constants of motion are found. The new systems are shown to be algebraically completely integrable.     

地下结构变形速度在抗爆结构分析中的作用

在地下抗爆结构动力计算中,结构变形速度的作用是非常突出的.考虑结构变形速度的作用,所建立的结构体系运动微分方程可以真实地描述结构振动的实际情况.文中通过一维平面波理论,导出了作用在结构周边上的荷载表达式,给出了地下曲杆结构动力分析的广义变分原理,同时还进行了数值计算结构的对比分析.     

薄壳稳定的变分原理

本文按照易曲物体的形变理论来确定薄壳的内力和内矩,应变能以及外力的功。从而根据虚位移原理求得临载荷的能量准则,并导出稳定问题的平衡方程和边界条件。     

考虑横向剪切变形时圆截面悬臂梁的广义变分原理

本文通过二类变量广义变分原理导出了考虑横向剪切变形时圆截面等直悬臂梁的近似理论,给出了对应于该理论的具有两个广义位移的二类变量广义余能的算式.     

大位移Timoshenko转轴三维耦合动力学分析

对于高速柔性转轴,综合考虑滑移、弯曲、剪切变形、旋转惯性、陀螺效应和动不平衡等因素,运用Timoshenko旋转梁理论,给出弹性体空间运动的一般性描述,通过Hamilton原理建立弯曲-扭转-轴向三维耦合非线性动力学方程,应用参数摄动方法和假设振型方法进行化简,并用数值模拟分析了轴向刚性滑移、剪切变形、截面尺寸和转速等因素对转轴动力学响应的影响。