Thermal Stresses in Spherical Shells

This paper presents an iterative finite-difference technique for the analysis of axisymmetric spherical shells with variable wall thickness. The formulation is based on thin elastic shell theory. One-dimensional finite-difference points are used to discretize the shell into strips along the meridian, and an iterative technique is employed to determine the normal and meridional displacements. The stress resultants and bending stresses are then evaluated. Unlike existing analytical and finite-difference techniques, the proposed method is applicable with ease to any variation in rigidity along the meridian, to general loading conditions, and to steep and shallow shells. Results are presented and compared with those of the finite-element method.     

Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure

A mathematical approach based on the perturbation theory has been used for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. The equilibrium equations have been derived using the energy principle and considering the second-order shear deformation theory (SSDT), which includes shear deformation effects. This system of ordinary differential equations with variable coefficients has been solved analytically using the matched asymptotic expansion method of the perturbation theory. A comparison of the results with the finite-element method and the first-order shear deformation theory shows that the SSDT can predict the displacements and stresses of the shell for a wide range of thicknesses as well with less calculations than other analytical methods such as the Frobenius series method.     

Effect of Localized Bending at Through‐Flaws in Pressurized Composite Cylinders

An analytical and experimental investigation was conducted to determine the effect of localized bending at through‐flaws in pressurized composite cylinders. A finite‐difference solution was formulated to determine the stress, strain, and displacement fields in the vicinity of a slit. Tests were conducted on 305‐mm‐diameter cylinders made from graphite/epoxy fabric in a (0,?45)s configuration, with axial slits. Surface‐strain‐field measurements made in the vicinity of the slit showed a significant bending, which verified the finite‐difference solution. This significant bending near the slit tip results in a large magnification of the stresses there. An average stress criterion was employed to predict the failure response of these cylinders based on data obtained from coupon specimens. The finite‐difference solution provided correction factors to account for the localized bending. The prediction utilizing this methodology was excellent in all cases. A generalized methodology to assess damage tolerance of structural configurations with notches is proposed.     

铸轧辊辊套温度场及热辊型的数值模拟

介绍了求解铸轧辊辊套温度场所采用的有限差分法,即采用FTCS格式进行的二维轴对称坐标下的铸轧辊辊套瞬态导热分析;并在此基础上进行了相应热辊型的求解,所得结果对于优良板型的获得具有参考价值。     

Effects of Thermal Gradients and Rotational Flows on Grain Growth in 22 t Steel Ingots

Heavy ingots are widely used in many industrial fields.The coarse grains formed during the process of ingot solidification influence the properties and fracture behaviors of the final products.The coarse grain growth was simulated under different thermal gradients.A 30Cr_2Ni_4 MoV steel ingot was melted in a cubic crucible with dimensions of 15cm×10cm×23cm,and the cooling conditions on each side of the crucible were controlled by different thermal curves.The influences of thermal gradients and rotational flows on grain growth in heavy steel ingots were then investigated both numerically and experimentally.The results showed that when the amplitude of the rotation angle was 60°,the metal was solidified under a reciprocating horizontal rotational condition when the angular velocity was 10(°)/s or 20(°)/s.As the thermal gradient increased,the lengths of the primary columnar grains increased,and the diameters of equiaxed grains decreased.When the direction of flow rotation was perpendicular to the direction of grain growth,the columnar grain zone was nearly eliminated,and the average diameter of equiaxed grains was 0.5 mm.     

Liquefaction and Deformation Analyses Using a Total Stress Approach

Estimating deformations due to seismically induced liquefaction is often accomplished with a series of simplified uncoupled analyses. An alternative approach is presented in this paper that builds upon this common practice while making significant improvements to the modeling quality. A two-dimensional finite-difference analysis is performed in the time domain using a simple plasticity-based constitutive model. The triggering of liquefaction is assessed in each element by continuously weighting the cyclic shear stress history. Liquefaction is initially predicted in the most susceptible elements and then progressively spreads as the earthquake continues. The properties of liquefied elements are adjusted at the instant of liquefaction to reflect the anticipated loss of strength and stiffness. Dynamic equilibrium is always maintained so that computed deformations are rationally affected by the structural response, progressing liquefaction, and gravity forces. The method is demonstrated through application to the Upper San Fernando Dam and its response to the San Fernando earthquake of 1971. The objective of this approach is to achieve a practical balance between a rigorous numerical and theoretical analysis and currently accepted practice.     

Nonuniform and Unsteady Solute Transport in Furrow Irrigation. I: Model Development

A cross-section-averaged advection-dispersion equation (ADE) model was developed to simulate the transport of fertilizer in furrow irrigation. The advection and dispersion processes were solved separately at each time step by implementing a method of characteristics with cubic-spline interpolation and a time-weighted finite-difference scheme, respectively. The upstream boundary condition was a prescribed concentration. Downstream, a zero-flux boundary condition during advance and a concentration gradient following completion of advance were prescribed. Local pseudosteady state was assumed in order to apply Fischer’s longitudinal dispersion equation under nonuniform and unsteady furrow flow conditions. Statistical parameters were used to evaluate the ADE model performance.     

Ground Response in Lotung: Total Stress Analyses and Parametric Studies

Previous papers have reported on the performance of a recently developed nonlinear ground response analysis code, SPECTRA, with reference to the prediction of the free-field response at a Large-Scale Seismic Test site in Lotung, Taiwan during the M6.5 earthquake of May 20, 1986. Two more major earthquakes of different characteristics shook this test site later that same year, a M6.2 earthquake that occurred on July 30 and a M7.0 earthquake that occurred on November 15. The present article analyzes the free-field responses recorded by a downhole array from these latter two events using the code SPECTRA and a widely used equivalent linear analysis code SHAKE. The studies focus on the relative accuracy and sensitivity of the two codes with respect to the variations of the input material parameters, using time histories, acceleration response spectra, Fourier acceleration amplitude spectra, and Arias intensities as criteria for the comparison. The two codes captured the general wave form of the acceleration histories well, but there was a general tendency for both codes (particularly SHAKE) to underpredict the Arias intensities of the earthquakes.     

Simple, Robust, and Efficient Algorithm for Gradually Varied Subcritical Flow Simulation in General Channel Networks

This paper details the development of a method for subcritical flow modeling in channel networks by using the implicit finite-difference method. The method treats backwater effects at the junction points on the basis of junction-point water stage prediction and correction (JPWSPC). It is applicable to flows in both looped and nonlooped channel networks and has no requirement on the flow directions. The method is implemented in a numerical model, in which the Saint-Venant equations are discretized by using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved by using the Newton-Raphson method. With the help of JPWSPC, each branch is computed independently. This guarantees the simplicity, efficiency, and robustness of the numerical model. The model is applied to two hypothetic channel networks and a real-life river network in South China. All the networks contain both branched and looped structures. The simulated results compare well with the results from literature or the measurements.     

Interaction between Steel Stirrups and Shear-Strengthening FRP Strips in RC Beams

RC beams shear strengthened with either fiber-reinforced polymer (FRP) U-jackets/U-strips or side strips commonly fail due to debonding of the bonded FRP shear reinforcement. As such debonding occurs in a brittle manner at relatively small shear crack widths, some of the internal steel stirrups may not have reached yielding. Consequently, the yield strength of internal steel stirrups in such a strengthened RC beam cannot be fully used. In this paper, a computational model for shear interaction between FRP strips and steel stirrups is first presented, in which a general parabolic crack shape function is employed to represent the widening process of a single major shear crack in an RC beam. In addition, appropriate bond-slip relationships are adopted to accurately depict the bond behavior of FRP strips and steel stirrups. Numerical results obtained using this computational model show that a substantial adverse effect of shear interaction generally exists between steel stirrups and FRP strips for RC beams shear strengthened with FRP side strips. For RC beams shear strengthened with FRP U-strips, shear interaction can still have a significant adverse effect when FRP strips with a high axial stiffness are used. Therefore, for accurate evaluation of the shear resistance of RC beams shear strengthened with FRP strips, this adverse effect of shear interaction should be properly considered in design.