Finite Element Formulation For Analysis Research Articles

Simplified analysis of iron loss in three-phase transformer considering rotating loss

Purpose – A simplified method for calculating iron loss of three-phase transformer is proposed in this paper. The rotating iron loss measured from 2-D vector magnetic property measurement system of gain-oriented silicon steel sheet can be taken into account in this method. The paper aims to discuss these issues. Design/methodology/approach – The finite element analysis formulation is combined with the magnetic reluctivity model expressed by diagonal tensor for 2-D nonlinear and anisotropic magnetic problem, while the iron loss is computed in terms of the interpolation of rotational loss curves measured under various loci of controlled magnetic flux density B. Findings – The iron loss of three-phase transformer is obtained by the proposed method. And the calculating iron loss is verified with experimental results. Originality/value – The method presented in this paper enables the iron loss of three-phase transformer to be more accurately calculated and more easily applied, considering the rotational iron loss.

Finite element analysis in situ

We describe a significant extension of the finite element method (FEM) that allows finite element analysis (FEA) to be performed in situ, on a native geometric representation of a solid domain. The proposed method, called Scan&Solve, is a particular implementation of the solution structure method (SSM) that builds on the classical ideas of Kantorovich and Rvachev. It can be applied to any geometric model and used within any geometric modeling system that supports two fundamental queries: point membership testing and distance to boundary computation. The advantages of this approach include unmatched flexibility in handling geometric errors, small features, complex boundary conditions, and interfaces, while maintaining most of the benefits of classical FEA. This paper describes the technical background behind the proposed method, compares it to classical FEA formulation, details its implementation, and demonstrates its advantages.

Numerical analysis of a one‐dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method

AbstractA multiphase coupled elasto‐viscoplastic finite element analysis formulation, based on the theory of porous media, is used to describe the rainfall infiltration process into a one‐dimensional soil column. Using this framework, we have numerically analyzed the generation of pore water pressure and deformations when rainfall is applied to the soil. A parametric study, including rainfall intensity, soil–water characteristic curves, and permeability, is carried out to observe their influence on the changes in pore water pressure and volumetric strain. From the numerical results, it is shown that the generation of pore water pressure and volumetric strain is mainly controlled by material parameters α andn′ that describe the soil–water characteristic curve. A comparison with the laboratory results shows that the proposed method can describe very well the characteristics observed during the experiments of one‐dimensional water infiltration into a layered unsaturated soil column. Copyright © 2010 John Wiley & Sons, Ltd.

Thermal post-buckling analysis of uniform slender functionally graded material beams

Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams.

A method of analysis for end and transitional effects in anisotropic cylinders

We present a rigorous verification study and an extension to an existing semi-analytical finite element formulation for analysis of end and transition effects in prismatic cylinders. End and transition effects in stressed cylinders are phenomena associated with the difference between results that are predicted by the Saint–Venant solutions and the actual point-wise conditions. These differences manifest themselves as self-equilibrated stress states. Notwithstanding certain well-known exceptions (e.g., restrained torsion of open thin-walled sections), such effects in isotropic cylinders are usually confined to a very small neighborhood of a terminal boundary or transition zone, and are typically neglected. For anisotropy, as in the case of most smart/active and composite material systems, they can persist much further into the interior of the structure, and need to be quantified to design geometry transition zones and to fully understand the delamination effects. In the semi-analytical approach, we first discretize the governing equations within the cross-sectional plane of the cylinder. The end-solution fields satisfy the homogeneous form of the resulting semi-analytical system of ordinary differential equations. This leads to an algebraic eigenvalue problem, and an eigenfunction expansion of the stress and displacement fields due to end effects. Unique to the present study, we formulate a procedure to quantify the transitional effects for end-to-end connected cylinders for which the displacement and stress continuity along the transition interface need to be enforced. The semi-analytical approach has several distinct advantages: (i) It is computationally efficient, as only the cross-sectional geometry is discretized; (ii) it can be applied to arbitrary cross-sectional geometries and the most general form of anisotropy; and (iii) it yields direct measures for the decay lengths (or decay rates) of any end-or transition-solution field. Analytical solutions to end-effect problems are scarce. Those that exist are for simple geometry and material constitution. We use these analytical solutions, as well as solutions obtained using three-dimensional finite element models, to verify our approach and to assess its efficiency.

Finite Element Formulation for Analysis and Shape Regulating of Plates with Laminated Piezoelectric Material

This paper focuses on a refined modeling of the dynamics of thin plates formed by stacking layers of functionally graded material laminated with piezoelectric layers and studies its actuator capabilities. The purpose is to investigate the effectiveness of piezoelectric layers for plate shape regulating by using internal stresses. The influence of piezoelectric actuators and their positioning is considered. The optimal voltages for shape control are obtained for some predetermined locations of the piezo-actuators by using a genetic optimization procedure. A related damage identification problem is formulated and solved using static data and genetic optimization. Several numerical results are reported.

Integrated Optimization of Material Layout and Control Voltage for Piezoelectric Laminated Plates

Topology optimization techniques have recently been successfully applied to the design of piezoelectric smart structures. However, in previous formulations, the material layout is optimized under the condition of given electric actuation voltages. This imposes a restriction to the design problem and may consequently limit application of these approaches, particularly in complex shape control problems. The present article investigates the integrated optimization of structural topology and control voltage of piezoelectric laminated plates. The finite element analysis formulation of laminated plates with surface bonded piezoelectric layers is introduced first. The optimal design problem is then formulated based on an artificial material model with penalization for both mechanical and piezoelectric properties. In the formulated problem, the topologies of both host and actuation layers are optimized simultaneously with spatial distribution of control voltage. Several special cases of the proposed design problem are considered, and numerical techniques for sensitivity analysis and optimal solutions are proposed. Numerical examples are presented to demonstrate the validity and applicability of the proposed methods.

A unified formulation for finite element analysis of piezoelectric adaptive plates

This paper presents some finite elements for the dynamic analysis of laminated plates embedding piezoelectric layers based on the principle of virtual displacements (PVD) and an unified formulation. The description of the unknowns allows to keep the order of the expansion of the variables along the thickness direction as a parameter of the model and at the same time to perform both equivalent single layer (ESL) and layer-wise (LW) descriptions of the state mechanical variables. The full coupling between the electric and mechanical fields is considered; thus, the electric potential is taken as a state variable of the problem and is assumed LW with an order of the expansion that goes from 1 to 4 as the displacement field. In case of a ESL model the ZZ-function of Murakami has been introduced to recover the zig-zag form of the displacement field. Combining all the possible parameters, up to 12 different finite elements are addressed. Numerical results have been given for the free-vibrations frequencies of simply supported plates embedding piezoelectric layers. The lamination of the pure elastic layers has been limited to cross-ply in order to compare numerical results to analytical ones obtained by a Navier-type solution based on the same formulation.

Material forces as a simple criterion for the description of crack-turning problems

Crack-path prediction for crack-turning problems in stiffened structures is an important issue in modern aircraft design processes because the ability of modeling a crack-path correctly allows the engineer to predict lifecycles and maintenance cycles more appropriate. In this paper the method of material forces as a simple method to describe crack-turning problems is introduced. At first, simple problems are examined, in order to make sure that the computed numerical results are comparable to known analytical results. Thereafter a simple academic example of a stiffened structure is shown and the crack-path is predicted by means of an implementation of the material force method in a finite element analysis formulation. The results of these computations have been compared to the results achieved by several known methods for computing the stress intensity factors, the crack-path and the energy release rate. It can be seen that computations of the material force deliver all necessary information to describe a crack by linear elastic fracture mechanics.

Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches

We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The standard Eulerian formulation is described first. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the finite calculus (FIC) method. A simple extension of the fluid flow equations to an arbitrary Lagrangian–Eulerian (ALE) frame adequate for treating fluid–structure interaction problems is briefly presented. A fully Lagrangian formulation called the particle finite element method (PFEM) is also described. The PFEM is particularly attractive for fluid–structure interaction problems involving large motions of the free surface and breaking waves. Examples of application of the Eulerian, the ALE and the fully lagrangian PFEM formulations are presented.

Non‐linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory

AbstractThe well‐accepted triphasic theory for modelling the mechano‐electrochemical phenomena of charged hydrated soft tissue has been limited to infinitesimal deformation problems due to the difficulty of defining a common reference configuration for the whole tissue. In this paper, an imaginary reference configuration for soft tissue under large deformation is established based on the reference configuration of a solid matrix and a Piola transformation of the relative velocities of the fluid and ionic phases. A non‐linear finite element analysis formulation is proposed by applying a weighted residual method to the reformulated governing equations of triphasic theory reformulated in the imaginary reference configuration, with the displacement of the solid, fluid flows, ionic molar flows, hydrostatic pressure, and electrical potential as the unknown variables. After verifying the proposed finite‐element formulation by comparing the results of a linear‐confined compression problem with those obtained by the finite difference method, the numerical analysis of a three‐dimensional free‐swelling problem of articular cartilage with large deformation, and a strong non‐linearity in the material properties is carried out to reproduce the curling behaviour of articular cartilage strips in vitro when submerged in solution baths of various concentrations. The results obtained by finite element analysis are in agreement with those measured experimentally. Copyright © 2005 John Wiley & Sons, Ltd.

A vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation

An energy finite element analysis (EFEA) formulation for high frequency vibration analysis of stiffened plates under heavy fluid loading is presented. The added mass effect and the radiation dampin...

A finite element formulation for analysis of functionally graded plates and shells

A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constituent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a scalar variable and a constant matrix through the thickness. The nonlinear heat-transfer equation is solved for thermal distribution through the thickness by the Rayleigh–Ritz method. According to the results, the formulation accounts for the nonlinear variation in the stress components through the thickness especially for regions with a variation in martial properties near the free surfaces.

A finite element formulation for analysis of functionally graded plates and shells

A finite element formulation for analysis of functionally graded plates and shells

A vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation

An energy finite element analysis (EFEA) formulation for high frequency vibration analysis of stiffened plates under heavy fluid loading is presented. The added mass effect and the radiation damping effect due to the fluid loading are incorporated in the derivation of the EFEA governing differential equations. In addition, the fluid loading effect and the presence of a stiffener are accounted when computing the power transfer coefficients through plate/stiffener junctions. The effect of the fluid on power transfer coefficients of a plate/stiffener junction is analyzed and discussed. The new formulation is validated by comparing EFEA results to solutions by very dense finite element models for several plate/stiffener assemblies, which include two coplanar plates connected by a stiffener, two plates connected at a 45° angle by a stiffener, and a section of a typical naval structure. All plates are considered in contact with dense fluid from one side. The energy ratios between the receiving sections of the plates and the excited sections of the plates are computed and good correlations are observed between the EFEA and the very dense FEA results.

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.

An accurate laminated element for piezoelectric smart beams including peel stress

This paper presents a laminated element for piezoelectric (PZT) smart beams in taking into account peel stresses. In the finite element analysis (FEA) formulation, a coupled electrical and mechanical beam element is used to model PZT patches, and a conventional structural element is used to model a host beam. A continuous adhesive element with shear and peel stiffness is derived to form a PZT laminated element. For a smart beam with a partially bonded PZT patch or distributed PZTs, the laminated element is applied to an area of the host beam with PZTs and the conventional element is used in the host beam where no PZT is bonded. A novel PZT laminated element is firstly derived based on the Timoshenko beam theory, in which the FEA formulation based on the Euler-Bernoulli beam theory can be considered as its special case. FEA numerical results of static and dynamic analyses based on the Euler-Bernoulli beam theory are compared with the exact static and dynamic solutions to validate the present FEA formulation. The present FEA framework based on the Timoshenko beam theory is then used to investigate the effects of PZT debondings on static behaviors and dynamic responses, and an original and effective procedure for detecting debondings in PZT actuators or sensors is proposed.

A basic hybrid finite element formulation for mid-frequency analysis of beams connected at an arbitrary angle

When beams are connected at an arbitrary angle and subjected to an external excitation, both longitudinal and bending waves are generated in the system. Since longitudinal wavelengths are considerably longer than bending wavelengths in the mid-frequency region, the number of bending wavelengths in the beams is considerably larger than the number of longitudinal wavelengths. In this paper, plannar beams connected at arbitrary angles are considered. The energy finite element analysis (EFEA) is employed for modelling the bending behavior of the beams and the conventional finite element analysis (FEA) is utilized for modelling the longitudinal vibration in the beams. Thus, a basic hybrid FEA formulation is presented for mid-frequency analysis of systems that contain two types of energy. The bending vibration is associated with the long members in the system and the longitudinal vibration is associated with the short members. The long members are considered to have high modal overlap and to contain several wavelengths within their dimension, and uncertainty effects are present. The short members contain a small number of wavelengths, and exhibit a low modal overlap. Due to the low modal overlap the resonant frequencies are spaced far apart in the frequency domain, therefore the short members exhibit resonant or non-resonant behavior depending on the frequency of the excitation. In this work, the bending and the longitudinal vibration within the same beam member are treated as a long and as a short member, respectively. A hybrid joint formulation is developed between long and short members. Power reflection and transmission coefficients are derived for each joint. The distribution of the energy throughout the system demonstrates a strong dependency on the power transfer coefficients. Several systems are analyzed by the hybrid FEA and by analytical solutions, and good correlation between them is observed.

Three-field formulation of finite element analysis of compressible viscoplastic powders

Three-field formulation of finite element analysis of compressible viscoplastic powders

Finite-Element Formulation for Analysis of Laminated Composites

This paper presents a multilayered/multidirector and shear-deformable finite-element formulation of shells for the analysis of composite laminates. The displacement field is assumed continuous across the finite-element layers through the composite thickness. The rotation field is, however, layerwise continuous and is assumed discontinuous across these layers. This kinematic hypothesis results in independent shear deformation of the director associated with each individual layer and thus allows the warping of the composite cross section. The resulting through-thickness strain field is therefore discontinuous across the different material sets. Numerical results are presented to show the performance of the method.