Multiparameter Optimal Design of Plates and Shells

For global behavioral constraints, the problem of optimal design of plates and shells is formulated by assuming the design to be dependent upon a set of design parameters. Global minimum theorems are proved for some constraints, whereas for others only local extremum conditions are derived. A possibility of constructing some numerical algorithms by using the optima-lity condition and proper variational principle is discussed. The following behavioral constraints are considered: prescribed mean compliance measurer1 as the work of surface tractions, prescribed local deflection of linearly or nonlincarly elastic structure, given set of several free frequencies, prescribed safety factor for limit load of a plastic structure, any global constraint ex pressed as a surface integral with integrand depending on generalized stresses or strains.     

The Stress State of Multilayered Physically Nonlinear Plates

A theory of and a solution to stationary and nonstationary problems for multilayered unsoldered plates are constructed. They are shown to converge within the framework of the kinematic Kirchhoff model with physical nonlinearity allowed for. The methods of variational iterations and finite differences are used for stress–strain analysis of a two-layered unsoldered plate of constant thickness with allowance for structural and physical nonlinearities. A wide class of problems is considered. In addition, the complex vibrations of two-layered plates are studied for arbitrary boundary conditions and for different gaps between layers     

Guided Waves in the Multilayered One-Dimensional Hexagonal Quasi-crystal Plates

Guided waves in the multilayered one-dimensional quasi-crystal plates are,respectively,investigated in the context of the Bak and elasto-hydrodynamic models.Dispersion curves and phonon and phason displacements are calculated using the Legendre polynomial method.Wave characteristics in the context of these two models are analyzed in detail.Results show that the phonon-phason coupling effects on the first two layers are the same at low frequencies;but,they are more significant on the first layer than those on the second layer at high frequencies.These obtained results lay the theoretical basis of guided-wave nondestructive test on multilayered quasi-crystal plates.     

Evolution of the Theory of Laminated Plates and Shells

The theory of laminated plates and shells is considered. Three-dimensional models of layered systems and methods of reducing them to two-dimensional models are elucidated. An analysis is made of how two-dimensional models are constructed by the method of hypotheses. Two basic approaches to the construction are presented: one leads to the discrete structural theory of laminated systems and the other to continuous structural theory. Attention is drawn to transverse shear and reduction in nonclassical theories of high approximation. The finite-element implementation of the theory is described. Examples of analysis by various models are given. Results of an applicability analysis of various theories and experimental data supporting them are presented. New research areas for the theory of laminated structures are pointed out.     

正交各向异性板壳的弹塑性分析

用最小二乘配点法对正交各项异性薄板和双曲扁壳的弹性问题进行了分析.文中采用Huber—Mises屈服函数在各向异性问题中的推广形式,把材料的塑性变形作为等效塑性荷载处理,并取双五次样条函数为位移试函数,推出了迭代公式.算例证明,该法精度高、收敛快,所需计算机内存少,是简单、精确、高效的.     

压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状,着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法;（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发,不引进任何变形假设,因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。     

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.     

A Set of Strain-Displacement Relations in Nonlinear Theories of Rods and Shells

The direct approach of Reissner and of Simmonds and Danielson is used to derive polynomial approximations to the strain-displacement relations in nonlinear theories of rods and shells via the representation of the finite rotational displacement matrix in terms of the exponential of an antisymmetric matrix.     

Allowing for Rotations about the Normal in Nonlinear Theories of Shells

Consideration is given to three versions of nonlinear strain–displacement relations in the case of small strains and moderately small angles of rotation: (i) relations that neglect rotations about the normal in conformity with the hypotheses of the Donnel–Mushtary–Vlasov theory; (ii) relations, derived from the elasticity equations using Novozhilov's tensor, that exactly allow for rotations; and (iii) relations, proposed by Sanders, that allow for rotations but neglect shear strains. These versions are compared by comparing the solutions of the stability problem for a corrugated cylindrical shell. It is established that the critical loads are close when rotations are allowed for exactly and when Sanders' technique is used     

Approximate Methods for the Linear and Nonlinear Analysis of Plates and Shallow Shells

Abstract

Berger's equations for the large amplitude deformation of membranes are used to produce a simple approximate expression for the large amplitude deflection of plates. The deformation of shallow shells is also considered and two approximate methods are outlined. Several important problems are discussed, the obtained solution being in good agreement with both experimental data and other approximate results. The main advantage of this technique is its ease of application, as it requires comparatively little computational work. A simple approximate formula for computing the fundamental frequency of a vibrating shallow shell is also presented and is shown to yield very accurate values in the case of a shallow dome and a rectangular panel.     

板壳结构弹塑性稳定性的有限元分析

构造了20参数圆柱壳拟协调单元,同时采用分层模型的弹塑性稳定性分析.根据塑性屈曲的Stowell形变理论,用基于切线刚度矩阵的增量法和修正的Newton-Raphson方法,计算屈曲前的弹塑性内力分布,并用逆幂迭代法求解弹塑性屈曲荷载.     

Refined Stress Analysis of Flexible Multilayered Shells of Revolution with Orthotropic Layers of Variable Thickness

A refined theory of flexible layered shells with orthotropic layers of variable thickness is considered. The theory assumes that each layer has a local rotation angle due to lateral shear. This makes it possible to derive equations whose order does not depend on the number of layers. The basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading     

Static Response of Composite Circular Cylindrical Shells Studied by Different Theories

A detailed study, on the static response of cross-ply laminated composite circular cylindrical shell of revolution and shell panel with various support conditions, has been made using Levy type of solution and the classical shell theories of FlSanders, Love and Donnell in an unified form. It has been shown that while developing a Levy type of solution using aforementioned theories, certain difficulty is encountered for determining the particular integral in respect of Fl Sanders and Love theories. This difficulty has been overcome by making use of the membrane solution as a particular integral. A comparative study has been carried out using the above shell theories for different geometrical parameters, lamination schemes and support conditions. It has been shown that Donnell theory predicts inaccurate results for certain lamination schemes, support conditions and geometrical parameters of the shell. It is suggested that, for developing shear deformation shell theories, it would be better to use a more accurate shell theory like Flügge Sommario. La risposta statica di gusci cilindrici circolari di materiale composito laminato, a strati incrociati, e di pannelli con varie condizioni di supporto viene analizzata utilizzando in una forma unificata soluzioni tipo Levy e le classiche teorie dei gusci di Flügge Sanders, Love e Donnell. Si mostra che nello sviluppare una soluzione di tipo Levy si incontra una certa difficoltà nel determinare l'integrale particolare rispetto alle teorie di Flügge, Sanders e Love. Tale difficoltà viene superata usando la soluzione di membrana come integrale particolare. Viene sviluppato uno studio comparativo facendo uso delle suddette teorie dei gusci per differenti parametri geometrici, schemi di laminazione e condizioni di vincolo. Si mostra che la teoria di Donnell fornisce risultati non accurati per certi schemi di laminazione, condizioni di supporto e parametri geometrici del guscio. Si suggerisce che per sviluppare teorie dei gusci che tengano conto delle deformazioni di scorrimento sarebbe più opportuno l'uso di una teoria dei gusci più accurata come ad esempio quella di Flügge.     

Infinitesimal Isometries on Developable Surfaces and Asymptotic Theories for Thin Developable Shells

We perform a detailed analysis of first order Sobolev-regular infinitesimal isometries on developable surfaces without affine regions. We prove that given enough regularity of the surface, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. We discuss the implications of this result for the elasticity of thin developable shells.     

A Note on the Iterative Solution of Stress Problems for Plates and Shallow Shells

A technique based on a refined iterative theory and the numerical method of local variations is developed and used to determine the stress–strain state of transversely isotropic shallow shells and plates. All the components of the stress–strain state and boundary-layer effects are taken into account. The solutions are analyzed for accuracy and convergence.     

加筋板弹性大挠度的冲击响应分析

用半解析的方法分析了横向冲击载荷下加筋板的非线性瞬态响应。考虑膜力的存在 ,忽略筋截面上的剪切应力 ,引入板的应力函数 ,采用离散加筋板模型 ,运用能量原理建立加筋板的动响应控制方程。假设挠度为双级数形式 ,运用迦辽金法 ,将加筋板的动响应方程转化为一个多自由度的动力系统 ,采用数值方法来求解。最后给出了几个模型的计算结果。