Matrix structural analysis using finite elements

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.

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.

The anti-scuffing bearing capacity of gears is a significant issue for their service lives, especially for the cases with heavy loads or high speeds. Generally, the anti-scuffing bearing capacity is evaluated according to the surface contact temperature that can be calculated with either analytical methods or finite element analysis (FEA) methods. The analytical methods usually apply the theory of Blok to efficiently obtain the results by simplifying some actual physical conditions, which are well considered in the FEA methods with accurate results but more computation time. Conversely, a new efficient and accurate analytical method is proposed by introducing the actual lubricant film thickness and continuous heat transfer for the theory of Blok. These two physical conditions are the key issues for the calculation of the two parts of surface contact temperature, flash temperature and bulk temperature, respectively. For the calculation of flash temperature, elastohydrodynamic lubrication (EHL) is introduced to consider the lubricant film thickness for the theory of Blok, and the result is obtained by solving the Reynolds equation efficiently with the finite difference method. For the bulk temperature, the result for a contacting point on the gear tooth surface is directly obtained according the theory of Blok, and the continuous heat transfer among the adjacent contacting points is considered with Gaussian heat morphology, which can accurately construct the bulk temperature field distribution in the contact region. The proposed method is validated as in good agreement with the FEA method and with less computation time.

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.

In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces. We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as the local approximation spaces of the GFEM, we have shown, in particular, that the energy norm of the GFEM approximation error of a smooth function is O(h l?+?k ). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation property of the PU.

PurposeThe purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.Design/methodology/approachAn existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.FindingsThe geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.Originality/valueThis study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

This paper presents an analysis of interacting cracks using a generalized finite element method (GFEM) enriched with so-called global-local functions. In this approach, solutions of local boundary value problems computed in a global-local analysis are used to enrich the global approximation space through the partition of unity framework used in the GFEM. This approach is related to the global-local procedure in the FEM, which is broadly used in industry to analyze fracture mechanics problems in complex three-dimensional geometries. In this paper, we compare the effectiveness of the global-local FEM with the GFEM with global-local enrichment functions. Numerical experiments demonstrate that the latter is much more robust than the former. In particular, the GFEM is less sensitive to the quality of boundary conditions applied to local problems than the global-local FEM. Stress intensity factors computed with the conventional global-local approach showed errors of up to one order of magnitude larger than in the case of the GFEM. The numerical experiments also demonstrate that the GFEM can account for interactions among cracks with different scale sizes, even when not all cracks are modeled in the global domain.

Viscoelastic model to describe mechanical response of compact heat exchangers with plate-foam structure

The Orthonormalized Generalized Finite Element Method–OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions

PurposeThis paper aims to present an adaptive approach of the generalized finite element method (GFEM) for transient dynamic analysis of bars and trusses. The adaptive GFEM, previously proposed for free vibration analysis, is used with the modal superposition method to obtain precise time-history responses.Design/methodology/approachThe adaptive GFEM is applied to the transient analysis of bars and trusses. To increase the precision of the results and computational efficiency, the modal matrix is responsible for the decoupling of the dynamic equilibrium equations in the modal superposition method, which is used with only the presence of the problem’s most preponderant modes of vibration. These modes of vibration are identified by a proposed coefficient capable of indicating the influence of each mode on the transient response.FindingsThe proposed approach leads to more accurate results of displacement, velocity and acceleration when compared to the traditional finite element method.Originality/valueIn this paper, the application of the adaptive GFEM to the transient analysis of bars and trusses is presented for the first time. A methodology of identification of the preponderant modes to be retained in the modal matrix is proposed to improve the quality of the solution. The examples showed that the method has a strong potential to solve dynamic analysis problems, as the approach had already proved to be efficient in the modal analysis of different framed structures. A simple way to performh-refinement of truss elements to obtain reference solutions for dynamic problems is also proposed.

The paper studies the magnetic field distribution of three degree-of-freedom (3-DOF) permanent magnet (PM) spherical motor adopting the 3-D magnetic equivalent circuits (MEC) method. Compared with the analytical method and finite element analysis (FEA) method, the MEC has such desirable attributes as moderate computational effort and reasonable accuracy. The model of PM spherical motor is evenly meshed into elements in spherical coordinates, and the expressions of reluctances and magnetomotive force (MMF) sources in the element have been deduced. Given that magnetic field of the PM spherical motor distributes in the whole space, to reduce the number of elements and increase the solving speed, an approximate equipotential surface is adopted based on the simplified magnetic circuit, and the different magnetic boundary conditions are represented by the corresponding states of nodes and branches of the elements. Finally, the MEC network, which represents half of the magnetic pole and the corresponding air region of the motor, is built. Flux density distribution is calculated by means of the proposed model and verified by the FEA method.

Strongly stable generalized finite element method: Application to interface problems

In this paper the general hybrid-mixed finite element methods are investigated systematically in a framework of multi-field variational equations. The commonly accepted concept “saddle point problem” is argued in this paper. The existence, uniqueness, convergence, and stability properties of the solutions are proved undertaking the assumptions of Ker*-ellipticity and nested BB-conditions. The relation between discrete BB-condition and smallest singular value, and a so-called singular value principle are proposed for the practical applications using hybrid-mixed finite element methods.

Premature failures of stator insulation account for a large percentage of repairs of marine generator systems. The failure mechanisms of such faults have been presented in many parts of the literature. Partial discharge activity, thermal degradation, thermal cycling, harmonics and transients are some examples of such failure mechanisms. Whilst there has been an insight into the failure mechanisms, there is still no definite answer to how these defects manifest in the first place. Most of the failures that have been identified within literature are on end windings, especially slot ends. Some failure mechanisms have also been linked with thermal cycling. Frequent and rigorous stop/start cycles stress coils by inducing mechanical forces between elements of the coil and housing owing to differential thermal expansion. This differential expansion is dependent on the rate of rise of temperature and also the different coefficients of thermal expansion of the materials. The present paper will evaluate the thermal degradation of insulation systems used on marine generators using Finite Element Analysis (FEA) methods. On board temperature measurements of stator coils during a high speed run are used as one of the parameters within the FEA simulations, to investigate if there is any risk of differential thermal expansions during such an operational cycle. Different ramp rates are also analyzed within the FEA simulations to understand the effect of uneven thermal expansions and the risk of material degradation of the insulation in coils on marine systems. A brief review of the standards available for thermal cycling and testing are also presented within the paper.

In this paper, the coupling factor between the primary and secondary windings of low profile planar transformer (LPPT) is studied with Finite Element Analysis (FEA) method, focusing on the coupling factor, the different planar structure is discussed. The electromagnetism simulation model is created in ANSOFT HFSS, and the coupling factor can reach 0.92976. Results of the simulation say agree with that of the prototype experimental test.