The Solution for Axisymmetrical Shells with Abrupt Curvature Change(Corrugated Shells)by the Finite Element Method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct.     

Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

ABSTRACT

The semi-analytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied in this paper. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semi-analytical method. It characterizes the difference in errors between a general finite difference method and the semi-analytical method. A method for improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.     

Study of the Elastoplastic Axisymmetric Stress–Strain State of Irradiated Laminated Shells with a Loading History

A technique is proposed to determine the axisymmetric state of laminated shells under thermoradiation loading. The deformation is assumed simple. The axisymmetric elastoplastic stress–strain state of a two-layered continuous plate under a distributed load and a neutron flux incident on one of the plate surfaces is studied within the framework of the Kirchhoff–Love hypothesis for a layer stack. The results obtained with and without regard for the loading history are presented. An important role of the loading history in a stress analysis is confirmed     

Effect of the Asymmetry of Cylindrical Sandwich Shells on their Stress–Strain State under Non-Stationary Loading*

International Applied Mechanics - The stress–strain state of asymmetric three-layer cylindrical shells under nonstationary loads is considered. The sandwich structure is asymmetric due to the...     

Impact of the Buoyancy–Viscous Force Balance on Two-Phase Flow in Layered Porous Media

Motivated by geological carbon storage and hydrocarbon recovery, the effect of buoyancy and viscous forces on the displacement of one fluid by a second immiscible fluid, along parallel and dipping layers of contrasting permeability, is characterized using five independent dimensionless numbers and a dimensionless storage or recovery efficiency. Application of simple dimensionless models shows that increased longitudinal buoyancy effects increase storage efficiency by reducing the distance between the leading edges of the injected phase in each layer and decreasing the residual displaced phase saturation behind the leading edge of the displacing phase. Increased transverse buoyancy crossflow increases storage efficiency if it competes with permeability layering effects, but reduces storage efficiency otherwise. When both longitudinal and transverse buoyancy effects are varied simultaneously, a purely geometrical dip angle group defines whether changes in storage efficiency are dominated by changes in the longitudinal or transverse buoyancy effects. In the limit of buoyancy-segregated flow, we report an equivalent, unidimensional flow model which allows rapid prediction of storage efficiency. The model presented accounts for both dip and layering, thereby generalizing earlier work which accounted for each of these but not both together. We suggest that the predicted storage efficiency can be used to compare and rank geostatistical realizations, and complements earlier heterogeneity measures which are applicable in the viscous limit.     

Development of the Spectral Sturm–Liouville Method for the Solution of a Boundary-Value Problem for the Biharmonic Equation

We generalize the spectral Sturm–Liouville method for the solution of the biharmonic equation. The characteristic equation for the determination of eigenvalues is investigated and eigenfunctions are constructed. We determine the stress-strain state for a rectangular plate loaded by arbitrary forces on its sides. For an arbitrary external load, we obtain a relation for the stress-strain state in the form of a series in eigenfunctions. A method of integral moments for the determination of the coefficients of the series is proposed. The Saint-Venant principle is verified.     

Calculation of Ionization and Radiative Characteristics of Air in the Shock Layer on the Basis of Various Models of Vibration–Dissociation Interaction

Models of vibrationdissociation interaction are verified on the basis of results of numerical simulation of nonequilibrium air flow in the shock layer near vehicles flying in the atmosphere and data of inflight and windtunnel experiments on measurement of ionization and radiative characteristics of the shock layer.     

The Thermoviscoelastoplastic Axisymmetric Stress–Strain State of Laminated Flexible Orthotropic Shells

A technique is proposed to determine the thermoviscoelastoplastic axisymmetric stress–strain state of laminated shells made of isotropic and orthotropic materials. The paper deals with processes of shell loading such that both instantaneous elastoplastic and creep strains occur in isotropic materials and elastic and creep strains in orthotropic materials. The technique is developed within the framework of the Kirchhoff–Love hypotheses for a stack of layers with the use of the equations of the geometrically nonlinear theory of shells in a quadratic approximation. The deformation of isotropic materials is described by the equations of the theory of deformation along slightly curved trajectories, while the deformation of orthotropic materials is described by Hooke's law with additional terms allowing for creep. A numerical example is given     

Revisiting the Drainage Relative Permeability Measurement by Centrifuge Method Using a Forward–backward Modeling Scheme

Measurement of drainage relative permeability by the centrifuge method was first introduced by Hagoort (SPE J. 29(3):139–150, 1980). It has been shown that capillary end effects can cause error in the measurement of relative permeability if a minimum rotational speed is not honoured. To determine the minimum rotational speed that makes the capillary end effect negligible, ω _min, we propose that the value of capillary-gravity number, N _cg, should be of the order of 10⁻² or smaller. This conclusion is based on the use a Forward–backward scheme consisting of a forward numerical simulator developed for centrifuge experiments and applying Hagoort’s method as a backward model. The article presents the use of this Forward–backward scheme as a powerful tool for error analysis such as determining the impact of capillary end effects. By using this loop, we first determine ω _min for specific core and fluid properties. Later, we generalize the ω _min calculations by using the definition of N _cg as a “rule of thumb” for designing relative permeability experiments by centrifuge method. We also demonstrate another use of this loop for controlling the quality of the experimental data.     

Inverse determination of liquid viscosity by means of the Bleustein–Gulyaev wave

The Bleustein–Gulyaev (B–G) wave in piezoelectric materials of orthorhombic mm2 crystal class is reported to be a promising candidate for application to liquid sensing. In this work we present a rigorous quantitative investigation of the propagation of B–G wave in mm2 crystals in contact with a viscous liquid. An inversion algorithm is formulated to determine the liquid viscosity from the wave speed and attenuation data. Numerical results and discussions are given for potassium niobate (KNbO₃). The inversion results demonstrate that the liquid viscosity can be successfully determined from wave propagation characteristics.     

Approximation of a Solution to the Euler Equation by Solutions of the Navier–Stokes Equation

We show that a smooth solution u ⁰ of the Euler boundary value problem on a time interval (0, T ₀) can be approximated by a family of solutions of the Navier–Stokes problem in a topology of weak or strong solutions on the same time interval (0, T ₀). The solutions of the Navier–Stokes problem satisfy Navier’s boundary condition, which must be “naturally inhomogeneous” if we deal with the strong solutions. We provide information on the rate of convergence of the solutions of the Navier–Stokes problem to the solution of the Euler problem for ν → 0. We also discuss possibilities when Navier’s boundary condition becomes homogeneous.     

On the Ellipticity of the Middle Surface of a Shell and its Application to the Asymptotic Analysis of ‘Membrane’ Shells

We consider a surface S = (), where ² is a bounded, connected, open set with a smooth boundary and : ³ is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H¹() × H¹() × L²(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = .     

General Solutions of Axial Symmetrical Ring Shells

This paper gives the general solutions of axial symmetrical ring shells for all values of slender-ness ratio.This solution is newly brought out,and can be used to solve various practical nroblems,including corrugated tubes,thermal expansion joints,Borden tubes,etc.     

Investigation of the Stability Problems of Elastic Bodies Using the Method of Mathematical Theory of Elasticity

In this paper,using the equilibrium equations and boundary conditionsof elastic stability problem of Новожилов and the method of mathematicaltheory of elasticity,we solve some elastic stability problems,which werestudied byищлинскииandвоицеховская,and obtained more reason-able results than theirs.     

The Calculation of Semi-circular Corrugated Tube-An Application of the General Solution of Ring Shell

In this paper,the deformation and stress distribution in semi-circularcorrugated tube under axial force are calculated by means of the generalsolutions of circular ring shell given in previous paper[1].