Linear and higher order displacement theories for adhesively bonded lap joints

This work presents an adhesive model for stress analysis of bonded lap joints, which can be applied to model thin and thick adhesive layers. In this theory, linear variations of displacement components along the adhesive thickness are firstly assumed, and the longitudinal strain and the Poisson's effect of the adhesive are modeled. A differential form of the equilibrium equations for the adherends is analytically solved by means of compatible relations of the adhesive deformation. The derived shear and peel stresses are compared with the classical adhesive model of continuous springs with constant shear and peel stresses, and validated with two-dimensional finite element results of the geometrically nonlinear analysis using a commercial package. The numerical results show that the present linear displacement theory can be applied to both thin and moderately thick adhesive layers. The present formulation of the linear displacement theory is then extended to the higher order displacement theory for stress analysis of a thick adhesive, whose numerical results are also compared with those of the finite element computation.     

Subspace variational principle of rods and shells

This paper builds the general forms of subspace variational principles of rods andshells which are taken as the controlled equations of the constitutive theories developedfrom the three-dimensional (non-polar) continuum mechanics. And the constitutiveequations of rods and shells using the principles are satisfactory.     

基于高阶位移模式的压电层合板动力有限元模型

建立了含压电片层合板的有限元动力学模型。以位于压电层上下表面处的电场强度和层间电压为未知量,给出了三次函数的电势分布模式,采用Reddy的高阶剪切理论描述板的位移场,假设板厚度方向的正应力为零给出了减缩的本构方程,采用有限元方法,基于Hamilton原理导出结构的动力学方程,然后用静态缩聚的方法压缩掉电场自由度和次要的位移自由度。最后用四边形矩形单元求解了一对称铺层和非对称铺层悬臂板的固有频率,并与ANSYS结果对比验证了本文模型的精确性。     

Asymptotic theories of elastic beams and rods

Summary Through the asymptotic approach to elastic theory of beam-like structural elements, various categories of problems are distinguished with different first approximation formulations, showing different degrees of non-linearity.

---

Sommario Per la teoria elastica di elementi strutturali tipo trave, il metodo asintotico porta a individuare varie categorie di problemi, retti da diverse formulazioni con diversi gradi di non-linearità, qui considerate in forma di prima approssimazione. Il metodo, oltre a fornire giustificazione di formulazioni classiche, offre la possibilità di approfondimenti sistematici.

     

Stability theory of rods,plates, and shells made of composite material

S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 10, pp. 94–100, October, 1993.     

Some comments on the original Kaluza-Klein theory

In this note the basis of the Kaluza-Klein theory is examined critically and it is pointed out that the five-dimensional version can’t work in the way that was originally intended. The reason why the problem was not noted originally is elucidated.     

On the lower-order theories of continua with application to incremental motions,stability and vibrations of rods

The relative merit of lower-order theories, which have been deduced from the three-dimensional theories of continua, is evaluated with respect to the quantified and un-quantified errors in mathematically modeling the physical response of structural elements. Then, the one-dimensional theories are derived with high accuracy, internal consistency and flexibility from the three-dimensional theory of elasticity in order to govern the nonlinear and incremental motions and stability of a functionally graded rod. First, a kinematic-based method of separation of variables is introduced as a method of reduction, which may lead to the lower-order theories with the same order of errors of the three-dimensional theories, and the nonlinear theories of the rod are derived under Leibnitz’s postulate of structural elements by use of Hamilton’s principle. A theorem of uniqueness is proved in solutions of the linear equations of the rod by means of the logarithmic convexity argument. Next, the kinematic basis is expressed by the power series expansion in the cross-sectional coordinates using Weierstrass’s theorem. Mindlin’s method is used so as to derive the equations in an invariant and fully variational form for the small motions superposed on a static finite deformation, the stability analysis and the high-frequency vibrations of the rod. Moreover, the free vibrations of the rod are considered, the basic properties of eigenvalues are examined, and Rayleigh’s quotient is obtained. The invariant equations of the rod, which are expressible in any system of orthogonal coordinates, may provide simultaneous approximations on all the field variables in a direct method of solutions. The equations are indicated to contain some of earlier equations of rods, as special cases, and also, the numerical elasticity solution of a sample application is presented.     

从牛顿铭文汉译说起

“道法自然,久藏玄冥;天降牛顿,万物生明．”这是Alexander Pope为牛顿所写铭文的汉译(大意),原文是:“Nature and Nature's laws lay hid in night, God said,‘Let Newton be',and all was light．”1984年,我在参与《中国大百科全书·力学》(1985)的编辑时,对傅裕寿所写“牛顿”条目原稿中语体文译文改为上面16个字的形式．1987年我在《牛顿〈原理〉三百年祭》(力学与实践1987年第5期)文中再次用了这个译法．最近注意到,这个翻译已被一些作者认可．《启蒙运动百科全书》(Reill和Wilson著,刘北成,王皖强编译,上海人民出版社,2004)序中采用了16字的译文,并在括号中加上直译:     

Some remarks on the theory of shallow spherical shells

Conclusions It is shown that Vlasov's explicit solutions for shallow spherical shells correspond to a very special boundary condition which does not usually occur in practice.A shell loaded by a normal loading p is fully discussed and it is shown that the discrepancy between these results and those obtained by Vlasov may be considerable. An asymptotic solution of the same problem is also given.Finally it is indicated how Geckeler's approximate equations can be derived from a suitable transformation of the linearized Marguerre equations.This paper was prepared under the support of the Argentine Council for Scientific and Technological Research.     

Forced vibrations and vibroheating of shallow viscoelastic laminated shells with the piezoelectric effect

The vibrations and dissipative heating of a hinged shallow shell made of viscoelastic piezoelectric material and subject to harmonic electric loading are considered. The basic relations are obtained by using the Kirchhoff-Love mechanical hypotheses supplemented with the respective hypotheses for electric quantities. Analytical solutions of both electromechanical and thermal problems are derived for the case where the temperature is constant along the shell thickness. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 78–87, June, 2000.