Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

Energy theorems for solving equations of deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano’s Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.     

Bending of thin circular rings

The basic equations for the bending of circular rings are deduced from a set of accurate equations for circular cylindrical shells. The advantages in using these differential equations as compared with the customary energy method are shown through examples. It turns out that solutions of these equations can be as easily obtained as solutions of the well-known differential equation for straight beams. It is also shown that the center line of the ring is essentially inextensible, which is assumed ab initio in the classical ring theory.     

On the formulation of contact problems of shells and plates

The equations of motion in terms of resultants and the constitutive equations in the theory of shells and plates are ordinarily derived from the three-dimensional equations relative to an interior surface, often taken to be the middle surface in the reference configuration of the shell-like body. This usual formulation is not, in general, applicable to contact problems of shells for which one of the major surfaces, e.g., the upper surface, is specified as the reference surface. The present paper is concerned with the transformation relations between the relevant variables (and hence also the response functions) of the traditional formulation and one which can be obtained relative to one of the major surfaces. Our derivations, carried out both from the three-dimensional equations and by a direct approach, utilize only the conservation laws and the field equations without recourse to constitutive equations. Hence, the results are applicable to any shell-like medium and their validity is not limited to elastic shells alone.     

Limit Analysis of Plates and Shells: Research over Two Decades

This paper summarizes results obtained by the author and his associates and students over the last two decades on limit analysis and optimal plastic design of plates and cylindrical shells. Circular metal plates are first considered, including minimum weight plastic design. Rectangular plates are then treated, both in metal and reinforced concrete. Limit analysis of cylindrical metal shells with reinforcing rings is the next subject, followed by optimal design of such shells. It is concluded that computer-aided analytical methods remain of value to complement purely numerical approaches.     

关于结构塑性动力失效若干问题的研究进展

重点分析常见工程结构元件（如梁、板、圆柱壳、圆环和夹层及复合材料结构）在强动短时载荷下塑性动力失效的研究方法、进展及尚待解决的问题，这些结构元件的失效模式及分析方法具有普遍意义，建议借用无量纲数──损伤数（ｄａｍａｇｅｎｕｍｂｅｒ）──来统一表征结构塑性动力失效的判据，最后以海洋平台和桁架为例简单介绍工程中复杂结构动力失效分析的情况。     

A new approach to the analysis of shells,plates and membranes with finite deflections

This paper presents a new perturbation method of analysis applicable to a class of geometrically non-linear problems of shells, plates, and membranes with translationally restrained edges. The perturbation parameter is a linear function of Poisson's ratio. The convergence of successive perturbations (i.e., approximations) is independent of the magnitudes of deflections. The method also offers a rational explanation of the efficacy of Berger's approximate equations, thus placing Berger's method on a firmer foundation while at the same time weakening his hypothesis of vanishing second membrane strain invariant in the strain energy integral. Several solutions and results are obtained for the purposes of illustration and discussion. Whenever possible, calculated values are compared with results obtained by other means.     

任意形状薄壳的弹性稳定性方程

本文用张量导出了任意形状薄壳的统一的弹性稳定性方程组,并且在正交曲线坐标系下化成了以张量的物理分量表示的方程,进而可以将正圆锥壳、球壳、圆柱壳、椭球壳、圆板、矩形板等形状的壳和板作为特例来研究。     

Geometrically nonlinear bending of thin-walled shells and plates under creep-damage conditions

Summary A phenomenological constitutive model for characterization of creep and damage processes in metals is applied to the simulation of mechanical behaviour of thin-walled shells and plates. Basic equations of the shell theory are formulated with geometrical nonlinearities at finite time-dependent deflections of shells and plates in moderate bending. Numerical solutions of initial/boundary-value problems have been obtained for rectangular thin plates (two-dimensional case) and axisymmetrically loaded shells of revolution (one-dimensional case). Based on the numerical examples for the two problems, the influence of geometrical nonlinearities on the creep deformation and damage evolution in shells and plates is discussed. Accepted for publication 30 October 1996     

On equations of the linear theory of shells with surface stresses taken into account

We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which are based on reducing the spatial elasticity relations with surface stresses taken into account to two-dimensional equations given on the shell median surface. We analyze the influence of surface elasticity moduli on the effective stiffness of plates and shells.     

强脉冲载荷作用下结构塑性大变形的最大挠度直接预测

经过多年的研究,由中国学者提出和研发的膜力因子法和饱和分析方法已被证明是分析和预测冲击、爆炸等强动载荷作用下梁、板等结构件的塑性大变形行为的有力工具.在这两套理论工具相结合所获得的一系列最新成果的基础上,文章提出一种对梁和板在强脉冲作用下的最大挠度的直接预测方法.考虑了膜力和弯矩相互作用的准确屈服条件,同时假定位移场近似地按照与准静态破损机构相似的模态发生变化,该方法直接从膜力因子的表达式出发,依据外载作的功与塑性耗散相等的能量条件,只需要求解初等方程就可以简单明晰地得到梁和板在矩形脉冲作用下的最大挠度,极大地简化了数学推导.与同时考虑准确屈服条件和瞬态响应阶段的完全解以及具有上下界的模态解相比,这一方法能够同样准确但更简单地计入膜力对结构大变形承载能力的效应,为工程设计提供比完全解更简明、比模态解更精准的梁和板最大塑性变形的估算公式;再同改进的脉冲等效技术相结合,这种直接预测方法有望进一步拓展到更复杂的结构件,获得广泛的工程应用.     

Nonaxisymmetric Vibrations of Discretely Reinforced Inhomogeneous Multilayer Cylindrical Shells under Nonstationary Loads

The equations of nonaxisymmetric vibrations of discretely reinforced multilayer cylindrical shells are analyzed. A refined Timoshenko model of shells and beams is used to analyze elements of an elastic structure. The vibration equations for an inhomogeneous elastic system are derived using the Reissner variational principle. The numerical solver of the dynamic equations is based on the integro-interpolation method used to construct finite-difference schemes for equations with discontinuous coefficients. The dynamic behavior of a five-layer cylindrical shell under distributed nonstationary loading is analyzed     

四边固定加劲板的非线性自由振动

针对工程中常用的加劲板, 研究了非线性振动的求解方法与振动特性. 将加劲板分为板与加劲肋两个部分考虑, 其中板视为考虑几何非线性的大挠度板, 加劲肋视为Euler梁. 假定加劲板的位移, 利用Lagrange方程结合系统能量和振型叠加推导了加劲板的动力平衡方程. 运用椭圆函数及摄动法计算加劲板非线性振动的单模态解, 多模态解则通过增量迭代法进行求解. 最后, 结合有限元软件ANSYS对一个四边固定且不可移动的加劲板进行分析, 讨论解的收敛性, 并分析两个方向设置不同数量加劲肋的情况下非线性自振频率与振幅的关系, 得到了一些加劲板非线性振动特性.      

Axisymmetric shells and plates on tensionless elastic foundations

This paper first describes a finite element method for the large deflection analysis of axisymmetric shells and plates on a nonlinear tensionless elastic foundation. Through the use of discrete data points, any form of nonlinear elastic foundation behaviour can be easily modelled. The analysis is then validated by comparison with existing results for circular plates and beams as the only existing results for shells on tensionless foundations are found to be in error. Following this verification, the analysis is applied to investigate the behaviour of shallow spherical shells subject to a central concentrated load on tensionless linear elastic foundations. A number of insightful conclusions regarding the behaviour of such structure-foundation systems are drawn. The numerical results for shells are believed to be the first correct results, which may be useful in benchmarking results from other sources in the future.     

局部损伤梁动力问题的近似计算方法

应用模态摄动法求解局部损伤梁动力特性。这一方法是在无损伤梁的模态子空间内实施,将含局部损伤梁的微分方程的求解转化为代数方程求解。通过算例,表明这一方法可有效的简化计算,同时计算结果具有较高的精度。     

AN ANALYTICAL SOLUTION TO LARGE DEFLECTION EQUATIONS OF SIMPLY－SUPPORTED RECTANGULAR HYPERBOLOIDAL SHALLOW SHELLS OF ORTHOTROPIC COMPOSITES

ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＴＯＬＡＲＧＥＤＥＦＬＥＣＴＩＯＮＥＱＵＡＴＩＯＮＳＯＦＳＩＭＰＬＹ－ＳＵＰＰＯＲＴＥＤＲＥＣＴＡＮＧＵＬＡＲＨＹＰＥＲＢＯＬＯＩＤＡＬＳＨＡＬＬＯＷＳＨＥＬＬＳＯＦＯＲＴＨＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＳＤ...     

Laminated shells with debonding between laminas in temperature field

A heat-conduction problem is formulated for laminated plates and shells with a heat-conducting layer and debonding between laminas. The approach consists in analyzing how the layer thickness changes in the process of debonding of laminas and deformation of plates and shells. The three-dimensional thermoelastic and heat-conduction equations are expanded into polynomial Legendre series in thickness. The first-order, Timoshenko’s, and Kirchhoff-Love equations are examined. A numerical example of laminated shells with a heat-conducting layer is considered Published in Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 135–141, July 2006.     

On stretching, bending, twisting and flexure of cylindrical shells

The first objective of this work is to use the differential equations of equilibrium of cylindrical shells in conjunction with the principle of minimum complementary energy for the derivation of constitutive equations for coupled stretching, bending and twisting of straight thin-walled open- and closed-cross section beams.The second objective is to use appropriate solutions of the cylindrical-shell differential equations, again in conjunction with the principle of minimum complementary energy, for the sake of deriving values for flexibility and stiffness coefficients of end-loaded, thin-walled cantilever beams, with applications to the problem of shear center and twist center location, including an analysis of the effect of shear lag on the location of these centers.     

Dynamic responses of functionally graded magneto-electro-elastic shells with closed-circuit surface conditions using the method of multiple scales

A three-dimensional (3D) free vibration analysis of simply supported, doubly curved functionally graded (FG) magneto-electro-elastic shells with closed-circuit surface conditions is presented using the method of perturbation. By means of the direct elimination, we firstly reduce the twenty-nine basic equations of 3D magneto-electro-elasticity to ten differential equations in terms of ten primary variables of magnetic, electric and elastic fields. The method of multiple scales is introduced to eliminate the secular terms in various order problems of the present formulation so that the present asymptotic expansion to the primary field variables leads to be uniform and feasible. Through the mathematical manipulation of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recurrent sets of governing equations for various order problems. The coupled classical shell theory (CST) is derived as a first-order approximation to the 3D magneto-electro-elasticity. Higher-order modifications can be further determined by considering the solvability and orthonormality conditions in a systematic and consistent way. Some benchmark solutions for the free vibration analysis of FG elastic and piezoelectric plates are used to validate the performance of the present asymptotic formulation. The influence of the material-property gradient index on the natural frequencies and corresponding modal field variables of the FG shells is mainly concerned.     

Green函数法在轴对称板壳理论中的应用

本文从轴对称板壳理论的基本方程出发,通过建立Green函数,导出了轴对称线载荷下解的一般表述式,由此可以求出任意轴对称载荷下的解,然后本文分别讨论了圆板和扁球壳受线载问题的解,文中的结果适用于各种边界条件。