Axisymmetric Pressures and Thermal Gradients in Conical Missile Tips

An iterative finite difference technique is presented for the analysis of axisymmetric conical shells with variable thickness. Temperature, surface pressure, and friction loadings due to supersonic flow are considered. The temperature loading is assumed to vary along the meridian and across the thickness of the shell. The variation of the material properties with temperature is taken into account. The applicability of classical thin shell theory is assumed in the analysis. The governing partial differential equation is presented in terms of the meridional and normal displacements. The proposed method of solution is applicable to short and long conical shells. Complete and truncated conical shells are treated, and results are presented and compared with those of existing solutions.     

Vibration of Open Cylindrical Shells with Stepped Thickness Variations

This paper presents the first-known exact solutions for vibration of open circular cylindrical shells with multiple stepwise thickness variations based on the Flügge thin shell theory. An open cylindrical shell is assumed to be simply supported along the two straight edges and the remaining two opposite curved edges may have any combination of edge support conditions. The shell is subdivided into segments at the locations of thickness variations. The state-space technique is adopted to derive the homogenous differential equations for a shell segment and the domain decomposition method is employed to impose the equilibrium and compatibility requirements along the interfaces of the shell segments. The correctness of the proposed method is checked against existing results in the open literature and results generated from finite element package ANSYS and excellent agreement is achieved. Several open shells with various combinations of end boundary conditions are studied by the proposed method.     

Buckling of Vertical Cylindrical Shells Under Combined End Pressure and Body Force

This paper is concerned with the elastic buckling of vertical cylindrical shells under combined end pressure and body force. Such buckling problems are encountered when cylindrical shells are used in a high-g environment such as the launching of rockets and missiles under high-propulsive power. The vertical shells may have any combination of free, simply supported, and clamped ends. Based on the Goldenveizer-Novozhilov thin shell theory, the total potential energy functional is presented and the buckling problem is solved using the Ritz method. Highlight in the formulation is the importance of the correct potential energy functional which includes the shell shortening due to the circumferential displacement. The omission of this contributing term leads to erroneous buckling solutions when the cylindrical shell is not of moderate length (length-to-radius ratio smaller than 0.7 or larger than 3). New solutions for body-force buckling parameters are presented for stubby cylindrical shells to long tube-like shells that approach the behavior of columns. The effects of the shell thickness and length on buckling parameter are also investigated.     

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compressive axial loads. The governing equations are based on Reddy’s higher-order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Nine-Node Resultant-Stress Shell Element for Free Vibration and Large Deflection of Composite Laminates

The newly constructed formulation of an element-based resultant-stress nine-node composite shell element is presented for the solution of free vibration and large deflection problems of isotropic and composite laminates. In this paper, the effectiveness of this new formulation is investigated in the static and free vibration analysis. The strain–displacement relationship of the shell could be explained from the point of the new element-based Lagrangian finite element formulation. The newly added terms between bending strain and displacement reflect the contributions of displacements to the curvature. Natural coordinate-based strains, stresses, and constitutive equations are used throughout the element-based Lagrangian formulation of the present shell element which offers significant implementation advantages compared with the traditional Lagrangian formulation. Using the assumed natural strain method the present shell element generates neither membrane nor shear locking behavior, and such an element performs very well as much as shells become thin. The arc-length control method is used to trace complex load–displacement paths and the Lanczos method is employed in the calculation of the eigenvalues of shells. A number of numerical analyses are presented and discussed in order to explore the capabilities of the present shell element. The test results showed very good agreement.     

Free Vibration of Open Circular Cylindrical Composite Shells with Point Supports

A variational full-field method is presented in this paper for the free vibration analysis of open circular cylindrical laminated shells supported at discrete points. A differential equation in matrix form is developed using the first-order shear deformable theory of shells, and rotary inertia is included. The displacement fields are defined by using very high-order interpolating polynomials and a large number of preselected nodal points on the reference surface of the shell. Each nodal point has 5 degrees of freedom, three displacement components, and two components of the rotation of the normal to the reference surface. The stiffness and mass matrices are obtained using the strain and kinetic energy functions. The numerical results are calculated for shallow and deep circular cylindrical panels with four-, six-, and eight-point supports along the two parallel straight edges. The values of the natural frequency obtained from the present method show good agreement with published data in the literature.     

Strength of silicone breast implants

Rupture and leakage are recognized problems associated with silicone breast implants. Data are scarce about the durability of the silicone shell, and the life span of this device is unknown. The purpose of this study was to investigate the strength of silicone breast implants. Thirty implant shells were subjected to mechanical testing. Twenty-nine of the shells were tested after explanation, and one unused implant served as a control to validate the testing method. Implantation time varied from 4 months to 20 years, and all shells were tested, regardless of condition. Fourteen implant shells were intact, eight were leaking, and seven were ruptured. All ruptured implants had been in place for 10 years or longer. The breaking force of all excised shell specimens ranged from 2.6 to 22.4 N (0.6 to 5.0 lb.). Specimens from the control "high performance" shell required 15.5 to 25.6 N (3.5 to 5.8 lb) of force to fail. The weakest group was from thin-shelled implants between 10 and 16 years of age. More than half these specimens failed with less than 1 lb of force. The average breaking force of ruptured shell material was less than that of intact shells. A comparison of strength data in this study with manufacturers' data suggests that breaking force is dependent on implant type, shell thickness, and implantation time.     

Free Vibration Analysis of Laminated Stiffened Shells

The free vibration of the laminated composite anticlastic doubly curved stiffened shells is investigated using the finite element method. The stiffened shell element is obtained by appropriate combination of the nine-node doubly curved isoparametric thin shallow shell element with the three-node curved isoparametric beam element. The shell forms include the hyperbolic paraboloid, hypar, and conoidal shells. The accuracy of the formulation is validated by comparing the authors’ results of specific problems with those available in the literature. The additional problems are taken up for parametric studies to include the effects of fiber orientation and lamina stacking sequence of shells and stiffeners. Moreover, the effects of number, types, and orientations of stiffeners, and stiffener depth to shell thickness ratio on the fundamental frequency are also included in the present study. Further, mode shapes corresponding to the fundamental frequency for typical cases are obtained to verify the parametric trend of the results of the fundamental frequency.     

Two-Dimensional Nonlinear Analysis of Long Cables

A simple finite-difference iterative model is presented here for the nonlinear analysis of a long inclined cable due to its self-weight and other concentrated loads in between. The input requires the end coordinates, area of cross section, modulus of elasticity, and initial tension of the cable. If the ends of the cable are subjected to displacements, the tension in the cable varies nonlinearly and the new deformed shape is computed using an iterative procedure. Unlike finite-element methods, initial cable geometry is not required here, and the method automatically computes the initial geometry even with concentrated loads.     

Signs of surface torsion and torsional dioptric power

Although there is agreement in the literature over the magnitude of torsion and torsional dioptric power, there is ambiguity over the signs of those quantities. The purpose of this paper is to define terms in such a way that the ambiguity is removed. Explicit equations are presented for torsion and torsional power along a meridian of a surface. In keeping with common practice in other disciplines, right-handed torsion is chosen to be positive. The components of the dioptric power matrix of thin systems and of the reduced vergence matrix are reinterpreted in terms of curvital and torsional power. In this reinterpretation the off-diagonal components of the matrices remain the torsional power and the reduced torsion along the meridian orthogonal to the reference meridian. However, they become the negatives of those quantities along the reference meridian. In particular, the top-right component can be interpreted as the reduced torsion or the torsional power along the meridian orthogonal to the reference meridian and the bottom-left as the negative of those quantities along the reference meridian. Torsion and torsional power along a meridian, as well as curvature and curvital power, are invariant under change of reference meridian and under spherocylindrical transposition.     

Numerical Model for Local Scour under Offshore Pipelines

A numerical model, based on potential-flow theory is proposed for simulating the equilibrium scour hole formed by unidirectional flow underneath offshore pipelines. The model employs a finite-difference method to solve the Laplace equation in terms of velocity potential in a curvilinear coordinate system. A boundary adjustment technique based on the Newton-Raphson method is used to calculate the free boundary formed by the eroded seabed by means of the equilibrium of all forces acting on a sediment particle on a sloping bed. Because the solution of flow field and adjustment of the seabed topography are carried out in an iterative manner, the model takes into account the interactions between the flow, pipe, and the seabed. The comparison of the present model with empirical formulas on the prediction of the maximum scour depth indicates that the present model is useful for approximate estimation of scour depth at a pipeline on the seabed for the case of clear-water scour.     

凝固坯壳对高拉速板坯连铸结晶器钢水流动特征的影响

 采用全比例的水力学模型,利用刺激-响应法、波高传感器、流速仪研究了考虑凝固坯壳时高拉速板坯连铸结晶器内的钢水流动、液面特征与卷渣特征。结果表明：考虑凝固坯壳后钢液到达液面的时间缩短;在高拉速条件下(2.4 m/min), 有坯壳时结晶器液面最大平均波高与表面流速比没有坯壳时分别大31 % 和17.5 %,使卷渣更容易发生。其主要原因在于考虑坯壳后结晶器下部钢液的自由流动空间变小,下回流的钢液流动受到抑制,上回流的能量变大。所以在高拉速结晶器水模拟试验过程中,有必要考虑凝固坯壳的影响。     

Phase transformations and control of residual stresses in thick spray-formed steel shells

Large, thick steel shells for tooling applications have been produced using a robot manipulated electric arc spraying technique with steady-state temperatures ranging from 170 °C to 450 °C. Critical to these experiments has been the use of a real-time feedback control system for surface temperature based on infrared thermal imaging. There was a reproducible trend in net residual shell distortion as a function of temperature with residual tensile stresses in the shell for temperatures ≤210 °C and ≥390 °C, and net compressive stresses at intermediate temperatures. In-situ linear displacement sensor experiments have been used to investigate the dynamic distortion of sprayed steel shells on steel substrates, over the same range of surface temperatures. Residual and in-situ distortion measurements confirmed two manufacturing temperatures at which stresses in the steel shells were either minimized or eliminated. A numerical model has been developed to relate shell quench and transformations stresses to the shell dynamic distortion behavior. It is proposed that tensile quench stresses are balanced by the time- and temperature-dependent expansive austenite-to-bainite phase transformation.     

Three-Dimensional Vibration Analysis of Thick Shells of Revolution

A 3D method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight-line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components u;gf, uz, and u;gu in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ? and z directions. Potential (strain) and kinetic energies of the entire body are formulated, and upper-bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations and completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.     

Research on the integral hydrobulge forming technology of spheroidal shells

In the present paper an altemative novel process of manufacturing oblate spheroidal vessels is proposed: the integral hydro-bulge forming (IHBF) technology of oblate spheroidal shells. A few mild steel and stainless steel oblate spheroidal shells for industrial use were manufactured using this new technology with one of the major diameters as high as 3 m. There is a critical value of the ratio between the vertical diameter and the horizontal diameter of the shell before forming, which can determine whether the shell will be wrinkled during hydro-bulging. The processes were analysed afterwards, using the explicit finite element code LS-DYNA3D. The numerical results are discussed and compared with the practical processes. Based on the numerical results a few proposals for the improvement of the IHBF technology of the spheroidal shells are presented.     

高炉中间段炉壳拆除更换技术

文章介绍了一种大型高炉炉壳快速拆除更换的安装技术,此更换安装技术既节约了临时支撑的材料用量,同时也节约了制作、安装费用,为今后高炉炉壳检修施工提供了宝贵经验。     

Closed-Form Solution of Axisymmetric Slender Elastic Toroidal Shells

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper.     

Posttensioned FRP Composite Shells for Concrete Confinement

Experiments have shown that externally bonded fiber-reinforced polymer (FRP) jackets for square and rectangular columns are not as effective as they are for circular columns. The results of experiments on shape-modified concrete columns using posttensioned FRP shells are presented. Posttensioning was achieved by radially straining the precured FRP shell outwards to a substantial strain level, using expansive cement concrete, over a period of 60?days. The prefabricated FRP shell was also used as a stay-in-place formwork. The effectiveness of shape modification using posttensioned FRP shells is compared to FRP-confined original square and rectangular columns, as well as shape-modified columns with nonshrink grout and externally bonded FRP jackets. It is shown that shape modification with posttensioning of FRP shells, using expansive cement concrete, can change the confinement from passive to active and improve significantly the axial strength and ultimate compressive axial strain capacity of square and rectangular columns.     

Nonlinear Transient Response of Laminated Composite Shells

This paper first compares the writers’ results of static and dynamic analyses of plates, cylindrical and spherical shells employing four-, eight-, and nine-noded elements with different integration rules with those of earlier investigators and including some of the recent composite theories. Thereafter, the nonlinear transient responses of laminated composite cylindrical and spherical shell panels with cutouts are investigated taking up additional examples that are yet to appear in the published literature. For these, the finite-element model is employed using eight-noded C0 continuity, an isoparametric quadrilateral element considering von Karman large deflection assumptions. In the time integration, the Newmark average acceleration method is used in conjunction with a modified Newton–Raphson iteration scheme. Important conclusions with respect to nonlinear transient responses are summarized for cylindrical and spherical shells with and without cutouts.     

Inclusion of Some Aspects of Chemical Behavior of Unsaturated Soil in Thermo/Hydro/Chemical/Mechanical Models. I: Model Development

This paper presents an investigation of the inclusion of some aspects of chemical behavior within a model of coupled thermo/hydro/chemical/mechanical behavior of unsaturated soils. In particular, multicomponent reactive chemical transport behavior is addressed. The chemical transport model is based on the advection/dispersion/reaction equation, while geochemical reactions are considered via coupling with an established geochemical speciation model. A numerical solution of the governing differential equations is achieved by the use of the Galerkin-weighted residual method for spatial discretization and an implicit backward Eulerian finite-difference method for temporal discretization. The solution of the geochemical reactions is achieved externally to the main solution procedure. Coupling between the chemical transport and geochemical models is achieved via the implementation of both sequential iterative and sequential noniterative techniques. Three application problems are then presented to demonstrate the capability of the coupled model.