弹性非保守压杆的大幅度动力分析

本文讨论弹性非保守压杆的大幅度动力问题。导出了在一般非保守力作用下杆的非线性运动微分方程,并给出与此相应的拟Hamilton变分表达式,具体地分析了悬臂杆在大挠度下的动力特性,当挠度很小其高次项可以略去时,本文所得结论都能近似地退化为线性理论的结果。     

弹性薄板的后屈曲特性

文章用三维弹性理论的非线性应变公式研究了弹性薄板的后屈曲特性，旨在探讨冯·卡门平板大挠度方程的可靠性范围。计算结果表明，当板中薄膜力较大时，用冯·卡门方程描述后屈曲问题会产生较大的误差。     

非线性弹性基础上矩形板热后屈曲分析

给出非线性弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下的后屈曲分析。采用摄动——Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。数值计算结果表明，非线性弹性基础上矩形板具有不稳定的热后屈曲平衡路径，且对初始几何缺陷是敏感的     

Postbuckling Behavior of Compressed Rods in an Elastic Medium

The postbuckling of rods loaded by a compressive force P in an elastic medium is considered. The resolving nonlinear equation is obtained, and a method for solving this equation is given. It is shown that, for large lengths, in contrast to the case without elastic medium, the deflection increases as the force P decreases after the loss of stability. Several simple finite-element models, namely, the problems of compression of multilink rods with links connected by springs, are considered to confirm this effect.     

The Dynamics of Finite-Dimensional Systems Under Nonconservative Position Forces

General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described     

Generalization of an Energetic Optimality Condition for Nonconservative Systems

ABSTRACT

An optimality condition based on strain energy densities, derived by earlier investigators, has been generalized. The generalized condition for an optimum structure is in bilinear form. The concept of the adjoint system is utilized. The resulting condition is applied to the minimization of the mass of a column loaded by a tangential follower force. Some results are presented.     

Thermomechanical Postbuckling of Imperfect Moderately Thick Plates on Nonlinear Elastic Foundations*

ABSTRACT

A postbuckling analysis is presented for a moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading, and resting on a softening nonlinear elastic foundation. The cases of (1) thermal postbuckling of initially compressed plates and (2) compressive post-buckling of initially heated plates are considered. The initial geometrical imperfections of the plates are taken into account. Formulations are based on Reissner-Mindlin plate theory, considering first-order shear deformation effects, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples include the performance of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. Typical results are presented in dimensionless graphical form.     

Complex Motion of Elastic Systems

This paper addresses issues of the theoretical dynamic analysis of elastic links making large relative translational and rotational motions. Mathematical models and analysis techniques for elastic vibrations of such systems are described. Examples of applied problems are adduced     

非完整非保守系统在相空间的Noether定理及其逆定理

本文根据动力学系统在相空间的作用积分在无穷小群变换下的变换性质，得到了非完整非保守系统在相空间的Ｎｏｅｔｈｅｒ定理和逆定理。并举例说明。     

Configuration Design Sensitivity Analysis of Nonlinear Structural Systems with Elastic Material*

ABSTRACT

A continuum-based design sensitivity analysis (DSA) method is presented for configuration design of nonlinear structural systems using Mindlin plate and Tim-oshenko beam theories. Both displacement and critical load performance measures are considered. Configuration design variables are characterized by shape and orientation changes of structural components. The material derivative that is used to develop the continuum-based shape DSA method is extended to account for effects of configuration design variation. The piecewise linear design velocity field, i.e., C⁰-regular, is used to support configuration design changes for a broad class of built-up structures with beams and plates. To allow use of the C⁰-design velocity field, mathematical models of beam and plate bending must be second-order partial differential equations, so that only first-order derivatives appear in the integrand of the energy equation and, thus, in the integrand of the configuration design sensitivity expression. Since the Mindlin plate and Timoshenko beam theories use displacement and rotation to describe structural response, mathematical models of beam and plate bending are reduced to second-order partial differential equations. The isoparametric finite element formulations are used for numerical evaluation of continuum design sensitivity expressions.     

Effect of Inertia of Elastic Waves in Elastic Systems with Axial Symmetry

We show that a standing wave excited in an elastic circular ring behaves like a material body: if the moment of external forces directed along the symmetry axis of the ring is applied to the ring, then not only the ring itself but also the initially standing wave excited in it will come to the accelerated rotation. In this motion, this “standing wave” does not change its shape and performs accelerated precession relative to the ring. In this case, the acceleration of the wave with respect to the ring constitutes a certain fraction of the acceleration of the ring relative to the inertial space. The moment of momentum of precessing and traveling waves is calculated.     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

层合析参固支边界条件下的不稳定后屈曲分析

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释,指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。     

Classical Thermodynamics of Elastic Solids as Open Systems

Herein we study the classical thermodynamics of multicomponent elastic solids as open systems. By writing down explicit expressions for the heat form and the work form, a simple derivation of the fundamental thermodynamic equations for elastic solids as open systems is presented. In particular a formula is obtained for the heats of mass transfer of the chemical components. This paper ends with a rebuttal to the contention that heat can not be unambiguously defined for open, classical reversible systems.     

On the Decay Rates of Porous Elastic Systems

In this paper we analyze the porous elastic system. We show that viscoelasticity is not strong enough to make the solutions decay in an exponential way, independently of any relationship between the coefficients of wave propagation speed. However, it decays polynomially with optimal rate. When the porous damping is coupled with microtemperatures, we give an explicit characterization on the decay rate that can be exponential or polynomial type, depending on the relation between the coefficients of wave propagation speed. Numerical experiments using finite differences are given to confirm our analytical results. It is worth noting that the result obtained here is different from all existing in the literature for porous elastic materials, where the sum of the two slow decay processes determine a process that decay exponentially.     

Damping of Free Elastic Vibrations in Linear Systems

The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 110–117, February 2005.     

The Effect of Multiple Buckling Modes on the Postbuckling Behavior of Plane Elastic Frames. Part I. Symmetric Frames

The postbuckling behavior of a one-bay, two-storey frame with built-in edges and symmetric with respect to midspan is analyzed. Columns are assumed to be inextensible and shear-undeformable, and beams are rigid. Then two buckling modes are possible, that is, sidesway of the lower floor with rigid horizontal displacement of the top floor and sidesway of the top floor with the lower floor undergoing no displacement. Obviously, the two buckling modes occur simultaneously if the ratios EI/h⁷ (EI being the bending stiffness of a column and h its length) are properly selected. Within the framework of a Koiter-type energy approach a suitable perturbation formulation is derived from a “hybrid” functional which is obtained by adding to the potential energy certain extra terms which account for the nonlinear energy associated with the internal forces applied to the beam at the joints. Results show that the postbuckling behavior of a single buckling mode can be stable or unstable according to the value of the ratio h/l, where l is the frame span. In the case of simultaneous buckling modes the structural behavior in the postbuckling range never improves, but no severe changes are noticed in comparison with the preceding case.     

三维编织复合材料圆柱壳的扭转后屈曲分析

随着三维编织复合材料应用的日益广泛,且由于三维编织复合材料的优异性能是与细观结构密切相关的,深入研究其细观结构显得尤为重要.本文通过研究三维圆型编织中所形成的空间纱线交织结构的特征,给出改进的三胞结构单胞模型,通过单胞的组装和变换,得到编织预制件的整体力学性能模型.基于Reddy高阶剪切变形理论导得广义Krmn型大挠度方程,计及边界层效应,采用奇异摄动法,考虑非线性前屈曲、大挠度和初始几何缺陷的影响,给出三维四向编织复合材料圆柱壳在扭转载荷作用下的严格满足边界条件的大挠度渐近解,讨论了纤维体积含量、编织角和几何参数等因素对圆柱壳屈曲和后屈曲行为的影响.     

The Effect of Multiple Buckling Modes on the Postbuckling Behavior of Plane Elastic Frames. Part II. Asymmetric Frames

The postbuckling behavior of an asymmetric one-bay, two-storey frame with clamped edges is analyzed. Columns have different bending stiffnesses and are pairwise of the same length. By assuming columns to be inextensible and shear undeformable, and beams to be rigid, two buckling modes are possible which are described by the sidesway of the lower floor with a rigid horizontal displacement of the upper floor and a sidesway of the upper floor, the lower floor undergoing no displacement. By properly selecting the ratios EI/h² (EI being the bending stiffness of a column and h its length) the two buckling modes may occur simultaneously. A third buckling mode is also possible which is characterized by no displacement of the horizontal beams and local deflection of one or more columns in the shape of a beam with fixed edges. This third case will not be considered in this paper. The Koiter general nonlinear theory of elastic stability recast in a form convenient for the development of finite elment models along lines similar to the recent presentation by Budiansky has been employed in the analysis. Nonlinear constraints on the field variable φ (φ being the cross-section rotation) are accounted for by means of Lagrangian multipliers. Results show that the postbuckling behavior of a single buckling mode is always asymmetric unstable and depends both on the degree of asymmetry of the structure and on the ratio h/l, l being the frame span. The occurrence of simultaneous buckling modes exacerbates the imperfection sensitivity of the structure.