Analysis of developable shells with special reference to the finite element method and circular cylinders

Cathodic protection (CP) anode bed grounding resistance calculating formulae, given by CP standards, are reviewed firstly. Underground assumptions and limitations of these grounding calculating formulae are analyzed, which means formula method may encounter problems when designing anode beds in high soil resistivity area. Based on finite element analysis (FEA) method, a new grounding resistance calculation method is suggested, which is can be treated as more suitable and flexible for anode bed grounding resistance calculation in high soil resistivity condition. The main steps of FEA method, geometric model building, meshing, boundary condition and solver setting, and grounding resistance calculating according to Ohmic law, are clearly presented. In order to introduce the FEA method in detail, a realistic anode bed design program for Northwestern China area, where soil resistivity is always very high, is demonstrated. Based field soil resistivity survey data by Wenner 4-pin method, the candidate anode bed site, named Station A, is regarded as optimal site, and Barnes’ soil layer analysis method is used to predict soil resistivity distribution in depth direction. Both formula method and FEA method are used to calculate grounding resistance. The following comparison results show that formulae from COR-GS-023, GB21448-2008, РД 153-39.4-039-99 standards and FEA method give out almost the same grounding resistance results under the assumption of uniform soil resistivity, which also, from another angle, verifies the correctness of FEA method. But for FEA method, designers can include realistic soil resistivity distribution function and any anode rod layout plan in calculation model. So, FEA method can be treated as a more flexible tool to calculate CP anode bed grounding resistance.

A nodeless variable element is combined with an adaptive meshing technique to improve solution accuracy of the finite element method for analyzing two-dimensional elasticity problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The fluxbased formulation is developed for the nodeless variable finite element to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The superconvergent patch recovery procedure is implemented to compute accurate stresses from the nodeless variable finite element solutions. The effectiveness of the combined procedure for providing higher solution convergence rate from the proposed formulation is evaluated by two well-known examples.

To gain a better insight into the deformation and failure of reinforced sand retaining walls subjected to the vertical load from the crest and their associated reinforcing mechanisms, the model experimental results from well-controlled fully-instrumented load tests of full-scale reinforced sand retaining wall with sand backfill are simulated by making use of a nonlinear elasto-plastic finite element model considering strain localization. In the finite element method (FEM) analysis, the effects of the following factors for the filled sandy soil are taken into account: (a) the non-linear pre-peak work-hardening and post-peak work-softening; (b) effects of stress history and stress path; (c) the confining pressure dependency and strength anisotropy; (d) the stress-dilatancy characteristics; and (e) strain localization into a shear band(s) with a width proportional to the particle size. The load-settlement relationship obtained from FEM analysis is generally in good agreement with the physical experimental result. It is also found that the progressive failure with a development of shear bands and the horizontal earth pressure on the back of facing and the tensile force in the reinforcement layers can be reasonably simulated by the proposed FEM analysis.

The finite element method (FEM) analysis of elastic-plastic deformation was applied to examine the effect of surface texture controlling of dies by means of hybrid-shot (double shot by two different kinds of particles) treatment on the galling property applied to high tensile strength steel sheets. The FEM analysis results showed that the apparent friction coefficient, which was calculated from pressing load and the drawing force, increased with each increase in the pressing load. The experimental results from the drawing tests with lubricant oil showed that the friction coefficient of the die after hybrid-shot treatment decreased slightly with the increase of the pressing load. On the other hand, the friction coefficient of the die without shot treatment, (i.e. nearly flat surface), slightly increased with the increase of the pressing load due to the digging effect. These findings reveal that the effect of surface texture of dies was caused not only by the elastic-plastic deformation but also by the oil lubrication condition. The FEM analysis was therefore performed by taking into account the digging effect as well as the micro-oil pool effect. The experimental result in the case of hybrid-shot dies corresponds well to the FEM result by adopting the virtual oil model where the oil segment was defined as an elastic solid body.

The interlaminar properties of a bond joint of stacked layers in a carbon fibre-reinforced composite with a thermoplastic matrix were evaluated under static loading. The un-precracked tension specimen with an external reinforcing layer was analysed in detail in the area of a bond joint. A detailed finite element method (FEM) analysis was performed to evaluate the influence of the bond joint shape on the interlaminar cohesive forces, which are simulated using the cohesive zone model (CZM). Simple lap and tapered joints were analysed. Continuum and shell elements were utilized in the FEM analysis, and the delamination results obtained using both solutions were compared to each other; however, no significant influence of the bond joint shape on the delamination onset was observed. The FEM analysis was supported using an experimental test on an un-precracked specimen made from prepreg with a carbon fibre fabric and a polyphenylene sulphide (PPS) matrix.

This study intends to provide a simplified analytical model of the laterally confined concrete filled steel tube (CCFT) column system which adopts carbon-fiber-reinforced polymer (CFRP) jackets in order to make up for major defects of the traditional concrete filled steel tube (CFT) column system. This CCFT analytical model, by adding one additional parameter for CFRP confinement to the CFT column analytical solution, is greatly simplified and expedites the analytical processes to explain the stress-strain relationship of the CCFT column system. In the study, several types of the CCFT column systems with different parameters are analyzed by the proposed simplified analytical model and its associated numerical program (USC-CFT). To verify the accuracy of the analytical model, this study compares the load-strain relationship calculated by USC-CFT both to the experimental results conducted by the traditional method and to the results calculated by the computer-aided finite element method (FEM) analysis method. This study shows equilibrium conditions, deformation compatibilities, constitutive models, and an analysis procedure used in the proposed simplified analytical solution and presents finite element models and analysis procedure used in FEM analysis.

An assumed stress hybrid finite element method for an incompressible and near-incompressible material

In this study, a high strain rate test method of a steel plate under blast loading from high explosive was designed and was conducted by a combined experimental/numerical approach to facilitate the estimation process for the dynamic stress-strain curve under practical strain rate conditions. The steel plate was subjected to a blast load, which was generated by Composition C4 explosive and the dynamic deformation of the plate was observed with a high-speed video camera. Time-deformation relations were acquired by image analysis. A numerical simulation for the dynamic behaviors of the plate identical to the experimental condition was conducted using a coupling analysis of finite element method (FEM) and discrete particle method (DPM). Explosives were modeled by discrete particles and the steel plate and other materials were modeled by finite element. The blast load on the plate was described fluid-structure interaction (FSI) between DPM and FEM. As inverse analysis scheme to estimate dynamic stress-strain curve, an evaluation using a quasistatic data was conducted. In addition, two types of approximations for stress-strain curve were assumed and optimized by least square method. One is a 2-piece approximation, and was optimized by least squares method using a yield stress and a tangent modulus as parameters. The other is a continuous piecewise linear approximation, in which a stress-strain curve was divided into some segments based on experimental time-deformation relation, and was sequentially optimized using youngs modulus or yield stress as parameter. The results showed that the piecewise approximation can gives reasonably agreement with SS curve obtained from the experiment.

Natural stone-paved roads have been generally used to preserve historical regions due to its architectural aesthetic aspect and environmental impact. However, there are limitations of travelling speed and traffic volume owing to the defects caused by the increased traffic loading and volume. To deal with these hindrances, ultra-rapid-hardening cement for both jointing and laying course materials in rigid small element pavement was considered. The objective of the present study was to continuously evaluate and compare the long-term performance of the suggested bound stone pavement throughout the various test criteria such as skid resistance and Falling Weight Deflectometer tests. The skid resistance outcome was met to the requirement and the response of deflection was measured following by related test method. To compare rut depth, the Finite Element Method (FEM) analysis was performed by modelling with material properties and by creating the loading cycle for imitating the Accelerated Pavement Testing (APT). The maximum deflections of asphalt, concrete block, stone A and stone B were calculated to 17.7, 6.1, 6.3, and 3.6 mm, respectively. Compared to the final outcomes of APT and FEM analysis, there was a difference ranging from 2.1 to 2.3 mm in bound stone pavement B and A, respectively.

Punching shear is a type of failure of reinforced concrete slabs subjected to localized forces. This failure has been examined by many researchers experimentally, analytically or numerically. Empirical equations based on tests observations are nowadays the basis of the existing design codes. The work described herein presents 3D Finite elements method (FEM) analysis of three slab-column connections also tested experimentally to investigate the three fundamental geometries: central, side and corner column. The sensitivity of the FEM response to input parameters such as material constitutive laws is studied. Concrete constitutive models are described in detail, including their effects on the accuracy of FEM analysis. The comparison between FEM results, experimental tests, code provisions and a new model for punching based on the compression chord capacity model is presented. As a conclusion, an estimation of the model uncertainties related to FEM analyses of punching failures without shear reinforcement is discussed.

Donnell’s thin shell theory and basic equations based on the wave propagation method discussed in detail here, is used to investigate the natural frequencies of thin finite length circular cylindrical shells under various boundary conditions. Mode shapes are drawn to explain the circumferential mode numbern and axial mode numberm, and the natural frequencies are calculated numerically and compared with those of FEM (finite element method) to confirm the reliability of the analytical solution. The effects of relevant parameters on natural frequencies are discussed thoroughly. It is shown that for long thin shells the method is simple, accurate and effective.

Objectives: This paper proposes a general formula for computation of the stiffness matrix of three-dimensional linearelastic bodies by the method of Moment Schema of Finite Elements (MSFE). Methods: Numerical methods based on Lagrange variational principle, such as Finite Element Method (FEM) and the method of Moment Schema of Finite Elements (MSFE). The paper focuses on the problem of obtaining the stiffness matrices of Finite Elements (FE), which ensure effectiveness of the developed version of FEM. Variational principle for calculation of energy functional of rectangular three-dimensional finite element is used. Results: Analyses of various problems of mechanics of deformable solids shows slow convergence of traditional FEM, especially for rigid bodies and surfaces of complex curved shapes. This paper proposes a scheme for inference for FEM ratios, which takes into account the basic properties of rigid displacements for isoparametric and curvilinear FE. The presented version of FEM allows us to obtain the stiffness matrix of FE, taking into account the effect of a false shift and low compressibility of elastomers. Conclusion/Application: The general method to find the potential energy of three-dimensional linear-elastic bodies is proposed, which allows us to solve the problems of mechanics of complex structures with higher accuracy.

The three phase flux reversal machine (FRM) is a doubly salient permanent magnet machine with concentrated windings. This study proposes the distributed winding for this machine. This winding (i.e. full pitch winding) offers high-power density and improves the efficiency. The permanent magnet (PM) flux linking the stator winding has effectively two or four pole flux pattern, which depends on the number of stator poles and independent of number of rotor poles. Finite element method (FEM) analysis is performed on the concentrated stator pole winding FRM (CSPFRM) and proposed full pitch winding FRM (FPFRM) to obtain induced EMF, flux linkages and inductance of the winding. The inductance of both machines is also obtained using winding function approach and compared with FEM results. The effect of armature reaction is compensated by capacitive series compensation to improve the voltage regulation. FEM analysis is also carried out on both the compensated generators to evaluate the power density. Speed of the flux pattern and that of the rotor is different in FRM. The ratio of these two speeds is termed as fictitious 'electrical gear'. FRM and permanent magnet synchronous machine (PMSM) have sinusoidal terminal voltage and surface mounted PMs. The power density of both machines is compared using the concept of fictitious 'electrical gear'. To verify the above analysis, a 6/14 pole FRM with distributed and concentrated winding is designed and fabricated. The experimental results are in close agreement with simulated results.

This research was carried out to investigate the strain hardening in an aluminum alloy worksheet caused by punch/die shearing by means of microhardness measurement and finite element method (FEM) analysis. To examine the strain-hardened zone at the sheared edge of a worksheet, a 0.36 mm thick AA4047 aluminum alloy cut by punch/die shearing was subjected to microhardness measurements. In addition, a two-dimensional FEM model was developed and used to simulate the shear cutting of the aluminum alloy worksheet. The fundamental shear cutting parameters, punch/die clearance, cutting tool wear, and friction at the worksheet/tool interfaces were numerically varied and simulated. From the investigation results, the strain-hardened zone was observed by hardness measurement. The size of the zone significantly varied under different cutting parameters. From the simulated stresses at the sheared zone, the variation of the width of the strain-hardened zone with respect to cutting parameters was determined by the maximum principal stress on the worksheet being sheared.

Chapter 8 - Guided-wave excitation in aerospace composites