Conventional Finite Element Procedure Research Articles

Coupled thermomechanical behavior of graphene using the spring-based finite element approach

The prediction of the thermomechanical behavior of graphene using a new coupled thermomechanical spring-based finite element approach is the aim of this work. Graphene sheets are modeled in nanoscale according to their atomistic structure. Based on molecular theory, the potential energy is defined as a function of temperature, describing the interatomic interactions in different temperature environments. The force field is approached by suitable straight spring finite elements. Springs simulate the interatomic interactions and interconnect nodes located at the atomic positions. Their stiffness matrix is expressed as a function of temperature. By using appropriate boundary conditions, various different graphene configurations are analyzed and their thermo-mechanical response is approached using conventional finite element procedures. A complete parametric study with respect to the geometric characteristics of graphene is performed, and the temperature dependency of the elastic material properties is finally predicted. Comparisons with available published works found in the literature demonstrate the accuracy of the proposed method.

Elastostatic Analysis of the Spatial FGM Structures

Abstract In this contribution, results of elastostatic analysis of spatial composite beam structures are presented using our new beam finite element of double symmetric cross-section made of a Functionally Graded Material (FGM). Material properties of the real beams vary continuously in the longitudinal direction while variation with respect to the transversal and lateral directions is assumed to be symmetric in a continuous or discontinuous manner. Continuously longitudinal varying spatial Winkler elastic foundations (except the torsional foundation) and the effect of axial and shear forces are considered as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by the multilayer method (MLM). For the homogenized beam finite element the local stiffness matrix is established by means of the transfer matrix method. By the conventional finite element procedure, the global element stiffness matrix and the global system of equation for the beam structure are established for calculation of the global displacement vector. The secondary variables (internal forces and moments) are then calculated by means of the transfer relations on the real beams. Further, the mechanical stress in the real beams are calculated. Finally, the numerical experiments are carried out concerning the elastic-static analysis of the single FGM beams and beam structures in order to show the possibilities of our approach.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

시공단계별 영향을 고려한 터널 전력구의 유한요소해석

In this paper structural analysis of underground electrical power cable structures which is excavated below the surface of the earth in the downtown area is carried out considering the effect of construction sequence. There are many various life-line facilities below the surface of the earth in the downtown area. MPDAP was used for finite element analysis of underground electrical power cable structures. Three typical sections are simulated by finite element models. Unbalanced equilibrium problems may be occurred when conventional finite element procedures were used for simulation of tunnel excavation. Therefore equilibrium perturbation concept was applied to solve these problems. The effects of time-dependent deformations in advancing tunnel excavation are considered in the stages of construction sequences as using the load distribution factor. It is shown that values of maximum displacement of both soil and rock surrounding underground electrical power cable structures obtained by our numerical studies are less than allowable values.

A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities

Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds. A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities. The one-quarter car model is used to represent the train as lumped masses connected by springs. The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency. The Fourier transform is applied in the direction of train’s movement to express the wave motion with a wave-number. The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface, including the irregularities on the track surface. Dynamic responses of the track and ground due to train’s moving loads are obtained in the wave-number domain by solving the governing equation, using a conventional finite element procedure. The amplitude and wavelength are identified as two major parameters describing track irregularities. The irregularity amplitude has a direct impact on the vertical response for low-speed trains, both for short wavelength and long wavelength irregularities. Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases. For low-speed case, vibrations induced by track irregularities dominate far field responses. For high-speed case, the wavelength of track irregularities has very little effect on ground vibration at distances far from track center, and train’s wheel axle weights becomes dominant.

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u i , electric displacement D i and volume fraction ρ I of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction ρ I of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction ρ I of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction ρ I of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Geometrically nonlinear analysis of planar circular arches based on rigid element concept — A structural approach

To overcome the difficulty involved in selecting proper shape functions for simulating the bending-tension coupling of a curved beam, a non-conventional “structural” approach is presented in this paper. For curved-beam elements with small subtended angles, the elastic stiffness matrix is derived as the composition of two chordwise straight beam elements used to represent the curved beam. In contrast, the geometrical stiffness matrix of the curved beam is derived by the rigid element concept, through transformation of the geometrical stiffness matrix of the rigid straight beam spanning the two ends of the curved bean from the rectangular to the curvilinear coordinates. Compared with the conventional finite element procedures relying strongly on numerical integrations, the present approach has the advantage of being simple in formulation, but also explicit in expressions. The numerical studies indicate that the derived curved beam element has good convergence characteristics upon mesh refinement for the linear problems studied, and is capable of solving the stability and nonlinear problems involving large-displacement postbuckling response.

Formulation method for solid-to-beam transition finite elements

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can be used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (l) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

Generation of exact stiffness matrix for a conical shell element

The present paper describes a method of generating an exact stiffness matrix for elastic stress analysis of a uniform thin circular conical shell frustum subject to bending and in-plane loads. The method is based upon an exact solution of the equations of elasticity governing mechanical behavior of a thin cone under prescribed loads. Stiffness coefficients are obtained computationally. Advantages of the use of the proposed element are reduction of CPU time owing to far fewer elements than are necessary in the conventional finite element procedure and achievement of higher solution accuracy. The paper also presents results of the application of the proposed method to some selected problems.

Generation of an exact stiffness matrix for a cylindrical shell element

The present paper describes a novel method of generating a stiffness matrix for the elastic stress analysis of a uniform thin circular cylinder subject to bending and inplane loads. The method is based upon an exact solution of the equations of elasticity governing mechanical behaviour of a thin cylinder under prescribed loads. Stiffness coefficients are obtained computationally. Advantages of the proposed method are reduction of CPU time owing to far fewer elements than are necessary in the conventional finite element procedure and achievement of higher solution accuracy. The paper also presents results of application of the proposed method to some selected problems.

A spline wavelets element method for frame structures vibration

A spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis. Instead of exploring orthogonal wavelets for specific differential operators, the spline wavelets are applied directly in finite element implementation for general differential operators. Although lacking orthogonality, the “two-scale relations” of spline functions and its corresponding wavelets from multiresolution analysis are employed to facilitate the elemental matrices manipulation by constructing two transform matrices under the constraint of finite domain of elements. In the actual formulation, the segmental approach for spline functions is provided to simplify the computation, much as conventional finite element procedure does. The assembled system matrices at any resolution level are reusable for the furthur finer resolution improvement. The local approximation and hiararchy merits make the approach competitive especially for higher mode vibration analysis. Some examples are studied as verification and demonstration of the approach.

A PHYSICAL APPROACH TO FINITE-ELEMENT MODELING OF COUPLED CONDUCTION AND CONVECTION

Abstract Finite-element formulations for coupled conduction and convection problems are obtained by a direct approach based on energy balances, at both element and node levels. This way, clear physical interpretations are provided for all the essential steps of conventional finite-element procedures of the Galerkin type. In the examples, the finite-element formulation is validated first by comparison with the analytical solution of a typical benchmark problem. Then the capabilities of the finite-element method are demonstrated by the analysis of coupled conduction and convection problems of practical interest

J-Integral Estimation Procedures

This paper presents efficient procedures for estimating the J-integral, a parameter for characterizing stable crack growth under inelastic conditions. Two different formulations are shown. The basis of the first approximate J-integral formula is the familiar extension of the elastic strain energy release rate computation for elastic-plastic loads. This extension is particularly suited for contained plasticity. With continued yielding, when the global load-deflection curve exhibits nonlinear behavior (i.e., net section yielding commences), this first J-approximation formula deviates from the actual J-integral. A second approximate formula derived here can be used at this point which is based on the definition that J-integral can be interpreted as the potential energy difference between two identically loaded specimens having crack sizes that differ infinitesimally. This latter formula is exact for linear loading and rigid-plastic material response, and is shown to predict J accurately in the elastic-plastic range of loading. Several standard cracked geometries for which documented J-integral solutions exist were applied to test the estimation procedures. This technique is very general and can be applied to virtually any structure or continuum. And no special assumption of material hardening, such as Ramberg Osgood, is necessary. These estimation techniques are significantly easier and more economical to use than a conventional finite element procedure, which models details of a cracked geometry.

A Simplified Method for Elastic-Plastic Analysis of Plate Structure by the Finite Element Method (The 1 st Report)

The present paper proposes a methed for the elastic-plastic analysis of plate bending problems using the finite element method. In the present method plastic deformations are idealized according to the concept of plastic hinge lines, while the conventional finite element procedure is employed before yielding occurs. Morley's plate bending element is used herein because of its simplicity. Plastic analysis is based on the assumption that plastic bending deformations are concentrated in plastic hinges along the element boundaries. In order to decrease dependancy of calculated results on mesh idealization, simple automatic mesh re-subdivision is implemented in the procedure.This method overcomes the following two difficulties in the ordinary finite element method; time consuming numerical integration of stiffness matrix along plate thickness and overestimation of stiffness due to shape functions with too strong compatibility conditions for localized plastic deformations.Basic numerical examples are studied to verify the validity of the present method.