Free vibrations of rectangular orthotropic shallow shells with varying thickness

The paper proposes a numerical-analytic approach to studying the free vibrations of orthotropic shallow shells with double curvature and rectangular planform. The approach is based on the spline-approximation of unknown functions. Calculations are carried out for different types of boundary conditions. The influence of the mid-surface curvature and variable thickness on the behavior of dynamic characteristics is studied __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 102–115, June 2007.     

Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation

The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.     

Elastoplastic bending of a sandwich bar on an elastic foundation

The elastoplastic bending of a sandwich bar with a stiff compressible core on an elastic foundation is studied. The kinematics of the bar, which is asymmetric across the thickness, is described adopting Bernoulli’s hypotheses for the face layers. The displacements of the core are assumed to vary linearly across the thickness. The foundation is described by the Winkler model. A system of equilibrium equations for displacements is derived and solved. Numerical results for a metal-polymer sandwich bar are presented __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 110–120, April 2007.     

Solution describing the natural vibrations of rectangular shallow shells with varying thickness

Natural vibrations of shallow cylindrical shells with rectangular plan and varying thickness are studied using a spline-approximation method developed previously. Computation is carried out for different types of boundary conditions. The effect of the curvature of the midsurface on the natural frequencies is examined. The natural frequencies of shells with constant and varying thickness are compared __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 89–98, April 2007.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

Stress-strain analysis of closed nonthin orthotropic conical shells of varying thickness

The approach developed to solve two-dimensional static problems for nonthin conical shells of varying thickness is used to examine the effect of the geometrical parameters on the stress-strain state of shells. The approach is based on spline-approximation and a stable numerical method of solving one-dimensional problems __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 46–58, June 2008.     

Identification of several impulsive loads on a plate

The paper presents a method to identify a system of several nonstationary independent transverse loads on a rectangular plate of medium thickness. The input data for solving the inverse problem are time-dependence of displacements or strains given at some points of the plate. Examples of numerical calculations to identify two or three loads are presented. The deformation of plates is modeled using a refined Timoshenko theory. Tikhonov’s regularizing algorithm is used to solve the Volterra equations for the unknown loads __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 90–97, July 2007.     

Natural vibrations of thin conical panels of variable thickness

A numerical analytical approach is proposed to study the natural vibrations of thin isotropic conical shells with varying thickness. The approach is based on the spline-approximation of unknown functions. Open shells (panels) with different boundary conditions are considered. The effect of variable thickness on the dynamic characteristics is analyzed     

Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads

We present a generalized shear deformation theory in combination with isogeometric (IGA) approach for nonlinear transient analysis of smart piezoelectric functionally graded material (FGM) plates. The nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Kármán strains, which includes thermo-piezoelectric effects, and solved by Newmark time integration scheme. The electric potential through the thickness of each piezoelectric layer is assumed to be linear. The material properties vary through the thickness of FGM according to the rule of mixture and the Mori–Tanaka schemes. Various numerical examples are presented to demonstrate the effectiveness of the proposed method.     

啮入冲击对直齿轮弹流润滑的影响

考虑齿轮啮入冲击载荷,曲率半径、卷吸速度沿啮合线随时间的变化以及温度场的影响,用非牛顿流体的Ree-Erying润滑模型,利用多重网格法模拟了轮齿从啮入到啮出整个时间历程中油膜压力、膜厚和温度分布的变化,对比分析了啮入冲击载荷与平稳载荷对渐开线直齿轮时变非牛顿热弹流润滑结果的影响.数值结果表明,啮入冲击载荷只对啮入初始阶段的油膜压力、膜厚、温度有很大影响,最小膜厚和最大压力都发生在冲击载荷的最大峰值载荷时刻,所以齿轮的啮入冲击对齿轮保持良好的润滑状态是不利的.     

Influence of variable thickness on stability of rectangular plate under compression

This paper analyzes the stability of the elastic rectangular thin plates with sinusoidal changes in the plate thickness. The buckling load is defined in a weighted residual approach for different boundary conditions. The influence of the plate thickness variation and the edge ratio on the critical loads is investigated. The results are compared to the case of uniform thickness.     

A combined experimental-analytical approach in the fluid-induced vibration analysis of the reactor core barrel

A combined experimental-analytical approach in the fluid-induced vibration analysis of the reactor core barrel is proposed. Some theoretical problems of the approach are discussed. The applicability of the approach in a real engineering case is studied and discussed Published in Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 121–128, November 2007.     

Stress state of nonthin orthotropic shells with varying thickness and rectangular planform

The stress-strain state of a shallow orthotropic shell with rectangular planform and thickness varying in two coordinate directions is studied. A refined problem formulation is used. Different boundary conditions are considered. A numerical analytic approach based on the spline approximation and discrete orthogonalization is developed. The stress-strain state of shallow orthotropic shells whose thickness is varied keeping its mass constant is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 91–102, August 2008.     

The influence of radiation on the temperature profile of an induced discharge in argon at atmospheric pressure

This study presents a quantitative evaluation of the influence of radiation upon the parameters of a long induced discharge in argon at atmospheric pressure. Radiation heat transfer in the optically transparent tin plasma layers with thickness of the order of several centimeters) and reabsorption spectral intervals is examined. Experimental error produced by inaccurate knowledge of the transfer and optical characteristics of the plasma is evaluated. The effect of convection on radial temperature profile is evaluated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiztki, No. 6, pp. 35–43, November–December, 1971.     

The in-plane stiffnesses of a honeycomb core including the thickness effect

Summary The subject of the consideration is the contribution of a regular honeycomb core to the effective in-plane stiffnesses of a sandwich structure. Due to the coupling of the core displacements with those of the sandwich face sheets, the stiffness contribution of the core is not proportional to its total thickness, as could be expected. The corresponding thickness effect is investigated by means of an appropriate closed-form approach. In doing so, the total elastic core strain energy is calculated based on an adequately chosen displacement representation. Further on, the resultant effective stiffnesses are derived as a function of the total core thickness. A comparative computation of the effective stiffnesses by finite element analysis gives good agreement. Received 5 August 1997; accepted for publication 23 October 1997     

Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles

In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions.     

Design of corrugated cylindrical shells under different end conditions

An approach to the solution of problems of statics for corrugated cylindrical shells with varying thickness is proposed. The solution is based on spline approximations along the generatrix and on the stable numerical method of discrete orthogonalization along the directrix. Problems on the stress-strain state of corrugated shells whose thickness varies along the directrix with different amplitudes and frequencies under different boundary conditions are solved. The effect of the boundary conditions, the type of end fixity, and the law of thickness variation on the parameters of the stress-strain state is analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 38–46, September, 1999.     

Plastic size effect analysis of lamellar composites using a discrete dislocation plasticity approach

Plastic size effect analysis of lamellar composites consisting of elastic and elastic-plastic layers is performed using a discrete dislocation plasticity approach, which is based on applying periodic homogenization to the superposition method for discrete dislocation plasticity. In this approach, the decomposition of displacements into macro and perturbed components circumvents the calculation of superposing displacement fields induced by dislocations in an infinitely homogeneous medium, resulting in two periodic boundary value problems specialized for the analysis of representative volume elements. The present approach is verified by analyzing a model lamellar composite that includes edge dislocations fixed at interfaces. The plastic size effects due to dislocation pile-ups at interfaces are also analyzed. The analysis shows that, strain hardening in elastic-plastic layers arises depending on two factors, namely the thickness and stiffness of elastic layers; and the gap between slip planes in adjacent elastic-plastic layers. In the case where the thickness of elastic layers is several dozen nm, strain hardening in elastic-plastic layers is restrained as the gap of the slip planes decreases. This particular effect is attributed to the long range stress due to pile-ups in adjacent elastic-plastic layers.